{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "name": "Japan virus-model.ipynb", "provenance": [], "collapsed_sections": [], "toc_visible": true }, "kernelspec": { "display_name": "Python 3", "name": "python3" } }, "cells": [ { "cell_type": "markdown", "metadata": { "id": "AJX1jgLnX70s" }, "source": [ "# Epidemiology model\n", "\n", "https://nbviewer.jupyter.org/github/pyro-ppl/pyro/blob/sir-tutorial-ii/tutorial/source/epi_regional.ipynb?fbclid=IwAR3Gv8tLuiEjOmZh7-NQUa_ggm_QUqtSc5TxRZ0_pSxVA7Y3lWWzSFGKjrA \n" ] }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "z6UoAzRe1pMh", "outputId": "8479e532-d591-4b5b-c0cb-29d2285f6256" }, "source": [ "!git clone https://github.com/pyro-ppl/pyro.git" ], "execution_count": null, "outputs": [ { "output_type": "stream", "text": [ "fatal: destination path 'pyro' already exists and is not an empty directory.\n" ], "name": "stdout" } ] }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "ryMxWMvbD8Nc", "outputId": "9bf9c42c-2c07-4fbb-d992-7fda93cced3e" }, "source": [ "%cd /content/pyro\n" ], "execution_count": null, "outputs": [ { "output_type": "stream", "text": [ "/content/pyro\n" ], "name": "stdout" } ] }, { "cell_type": "code", "metadata": { "id": "w8MT-jR48mLX" }, "source": [ "!pip install .[extras]" ], "execution_count": null, "outputs": [] }, { "cell_type": "code", "metadata": { "id": "7AUI1jmXcX4u" }, "source": [ "import os\n", "import logging\n", "import urllib.request\n", "from collections import OrderedDict\n", "\n", "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "import torch\n", "import pyro\n", "import pyro.distributions as dist\n", "from pyro.contrib.epidemiology import CompartmentalModel, binomial_dist, infection_dist\n", "from pyro.ops.tensor_utils import convolve\n", "\n", "%matplotlib inline\n", "pyro.enable_validation(True) \n", "torch.set_default_dtype(torch.double) \n" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "hzpnb36feNgS" }, "source": [ " ## Model without Policies\n", " " ] }, { "cell_type": "code", "metadata": { "id": "bsaJcjx6xVLo" }, "source": [ "class CovidModel(CompartmentalModel):\n", " def __init__(self, population, new_cases, new_recovered, new_deaths):\n", " '''\n", " population (int) – Total population = S + E + I + R.\n", " '''\n", " assert len(new_cases) == len(new_recovered) == len(new_deaths)\n", "\n", " compartments = (\"S\", \"E\", \"I\", \"D\") # R is implicit.\n", " duration = len(new_cases)\n", " super().__init__(compartments, duration, population)\n", "\n", " self.new_cases = new_cases\n", " self.new_deaths = new_deaths\n", " self.new_recovered = new_recovered\n", " \n", "\n", " def global_model(self):\n", " tau_i = pyro.sample(\"rec_time\", dist.Normal(15.0, 3.0))\n", " tau_e = pyro.sample(\"incub_time\", dist.Normal(5.0, 1.0))\n", " # R0 = pyro.sample(\"R0\", dist.LogNormal(0., 1.))\n", " R0 = pyro.sample(\"R0\", dist.Normal(2.5, 0.5))\n", " rho = pyro.sample(\"rho\", dist.Beta(10, 10)) # About 50% response rate.\n", " mort_rate = pyro.sample(\"mort_rate\", dist.Beta(2, 50)) # About 2% mortality rate.\n", " rec_rate = pyro.sample(\"rec_rate\",dist.Beta(10, 10)) # About 50% recovery rate.\n", " return R0, tau_e, tau_i, rho, mort_rate, rec_rate\n", "\n", " def initialize(self, params):\n", " # Start with a single infection.\n", " return {\"S\": self.population - 1, \"E\": 0, \"I\": 1, \"D\": 0}\n", "\n", " def transition(self, params, state, t):\n", " R0, tau_e, tau_i, rho, mort_rate, rec_rate = params\n", "\n", " # Sample flows between compartments.\n", " S2E = pyro.sample(\"S2E_{}\".format(t),\n", " infection_dist(individual_rate=R0 / tau_i,\n", " num_susceptible=state[\"S\"],\n", " num_infectious=state[\"I\"],\n", " population=self.population))\n", " E2I = pyro.sample(\"E2I_{}\".format(t),\n", " binomial_dist(state[\"E\"], 1 / tau_e )) \n", " I2R = pyro.sample(\"I2R_{}\".format(t),\n", " binomial_dist(state[\"I\"], 1 / tau_i))\n", " I2D = pyro.sample(\"I2D_{}\".format(t),\n", " binomial_dist(state[\"I\"], mort_rate / tau_i))\n", "\n", " # Update compartments with flows.\n", " state[\"S\"] = state[\"S\"] - S2E \n", " state[\"E\"] = state[\"E\"] + S2E - E2I\n", " state[\"I\"] = state[\"I\"] + E2I - I2R - I2D\n", " state[\"D\"] = state[\"D\"] + I2D\n", "\n", " # Condition on observations.\n", " t_is_observed = isinstance(t, slice) or t < self.duration\n", " pyro.sample(\"new_cases_{}\".format(t),\n", " binomial_dist(S2E, rho),\n", " obs=self.new_cases[t] if t_is_observed else None)\n", " pyro.sample(\"new_deaths_{}\".format(t),\n", " binomial_dist(I2D, 1),\n", " obs=self.new_deaths[t] if t_is_observed else None)\n", " pyro.sample(\"new_recovered_{}\".format(t),\n", " binomial_dist(I2R, rho),\n", " obs=self.new_recovered[t] if t_is_observed else None)\n", " \n", " def compute_flows(self, prev, curr, t):\n", " S2E = prev[\"S\"] - curr[\"S\"] # S can only go to E.\n", " I2D = curr[\"D\"] - prev[\"D\"] # D can only have come from I.\n", " # We deduce the remaining flows by conservation of mass:\n", " # curr - prev = inflows - outflows\n", " E2I = prev[\"E\"] - curr[\"E\"] + S2E\n", " I2R = prev[\"I\"] - curr[\"I\"] + E2I - I2D\n", " return {\n", " \"S2E_{}\".format(t): S2E,\n", " \"E2I_{}\".format(t): E2I,\n", " \"I2D_{}\".format(t): I2D,\n", " \"I2R_{}\".format(t): I2R,\n", " }" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "kgKCZvRfMi_3" }, "source": [ "## Create Country" ] }, { "cell_type": "code", "metadata": { "id": "koX5yGHrsuib" }, "source": [ "# function to make the time series of confirmed and daily confirmed cases for a specific country\n", "def create_country (country, start_date, end_date, state = False) : \n", "\n", " url = 'https://raw.githubusercontent.com/assemzh/ProbProg-COVID-19/master/full_grouped.csv'\n", " data = pd.read_csv(url)\n", "\n", " data.Date = pd.to_datetime(data.Date)\n", "\n", " if state :\n", " df = data.loc[data[\"Province/State\"] == country, [\"Province/State\", \"Date\", \"Confirmed\", \"Deaths\", \"Recovered\", \"Active\", \"New cases\", \"New deaths\", \"New recovered\"]]\n", " else : \n", " df = data.loc[data[\"Country/Region\"] == country, [\"Country/Region\", \"Date\", \"Confirmed\", \"Deaths\", \"Recovered\", \"Active\", \"New cases\", \"New deaths\", \"New recovered\"]]\n", " df.columns = [\"country\", \"date\", \"confirmed\", \"deaths\", \"recovered\", \"active\", \"new_cases\", \"new_deaths\", \"new_recovered\"]\n", "\n", " # group by country and date\n", " df = df.groupby(['country','date'])['confirmed', 'deaths', 'recovered',\"active\", \"new_cases\", \"new_deaths\", \"new_recovered\"].sum().reset_index()\n", "\n", " # convert date string to datetime\n", " df.date = pd.to_datetime(df.date)\n", " df = df.sort_values(by = \"date\")\n", " df = df[df.date >= start_date]\n", " df = df[df.date <= end_date]\n", "\n", " active = df['active'].tolist()\n", " recovered = df['recovered'].tolist()\n", " deaths = df['deaths'].tolist()\n", " new_cases = df['new_cases'].tolist()\n", " new_recovered = df['new_recovered'].tolist()\n", " new_deaths = df['new_deaths'].tolist()\n", " \n", " active = torch.tensor(list(map(float, active))).view(len(active),1) \n", " recovered = torch.tensor(list(map(float, recovered))).view(len(recovered),1) \n", " deaths = torch.tensor(list(map(float, deaths))).view(len(deaths),1) \n", " new_cases = torch.tensor(list(map(float, new_cases))).view(len(new_cases),1) \n", " new_recovered = torch.tensor(list(map(float, new_recovered))).view(len(new_recovered),1) \n", " new_deaths = torch.tensor(list(map(float, new_deaths))).view(len(new_deaths),1) \n", "\n", "\n", " return_data = {\n", " 'active':active,\n", " 'recovered':recovered,\n", " 'deaths':deaths,\n", " 'new_cases':new_cases,\n", " 'new_recovered': new_recovered,\n", " 'new_deaths':new_deaths }\n", " \n", " return return_data\n" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "nxRxbNr8zt3O" }, "source": [ "## Get data for countries\n" ] }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "V4O6XUbM9Ff3", "outputId": "140a289b-897e-4df2-8088-a011871f3876" }, "source": [ "Japan = create_country(\"Japan\", start_date = \"2020-02-01\", end_date = \"2020-04-01\")\n", "Sweden = create_country(\"Sweden\", start_date = \"2020-02-01\", end_date = \"2020-04-01\")\n" ], "execution_count": null, "outputs": [ { "output_type": "stream", "text": [ "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:16: FutureWarning: Indexing with multiple keys (implicitly converted to a tuple of keys) will be deprecated, use a list instead.\n", " app.launch_new_instance()\n" ], "name": "stderr" } ] }, { "cell_type": "markdown", "metadata": { "id": "XTUPDWD9e_9o" }, "source": [ "##Train the model using MCMC.\n", "\n" ] }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "bX4Jq5qmC6Ke", "outputId": "6063babb-5020-4aec-eeef-a3e49d10b9f7" }, "source": [ "%%time\n", "Japan_model = CovidModel(126500000, Japan[\"new_cases\"], Japan[\"new_recovered\"], Japan[\"new_deaths\"] )\n", "pyro.set_rng_seed(20210521)\n", "Japan_mcmc = Japan_model.fit_mcmc(num_samples=500, warmup_steps = 200)\n", "Japan_mcmc.summary()" ], "execution_count": null, "outputs": [ { "output_type": "stream", "text": [ "INFO \t Running inference...\n", "Warmup: 0%| | 0/700 [00:00, ?it/s]INFO \t Heuristic init: R0=2.64, incub_time=3.56, mort_rate=0.0147, rec_rate=0.675, rec_time=8.59, rho=0.178\n", "Sample: 100%|██████████| 700/700 [00:58, 11.89it/s, step size=2.11e-03, acc. prob=0.731]\n" ], "name": "stderr" }, { "output_type": "stream", "text": [ "\n", " mean std median 5.0% 95.0% n_eff r_hat\n", " R0 2.60 0.01 2.59 2.59 2.62 4.13 1.43\n", " auxiliary[0,0] 126499886.77 1.08 126499886.19 126499886.15 126499889.01 4.25 1.36\n", " auxiliary[0,1] 126499769.19 2.23 126499768.03 126499767.82 126499773.74 4.36 1.37\n", " auxiliary[0,2] 126499647.83 2.74 126499646.40 126499646.10 126499653.37 4.23 1.41\n", " auxiliary[0,3] 126499535.96 6.14 126499533.05 126499531.95 126499548.16 4.36 1.40\n", " auxiliary[0,4] 126499424.13 8.69 126499420.06 126499418.42 126499441.69 4.34 1.40\n", " auxiliary[0,5] 126499314.64 10.66 126499309.65 126499307.31 126499336.33 4.29 1.41\n", " auxiliary[0,6] 126499206.81 14.79 126499199.98 126499196.97 126499236.67 4.35 1.41\n", " auxiliary[0,7] 126499098.07 17.60 126499089.71 126499086.30 126499134.19 4.29 1.41\n", " auxiliary[0,8] 126498987.18 22.51 126498976.38 126498972.55 126499034.20 4.29 1.41\n", " auxiliary[0,9] 126498871.47 25.33 126498859.33 126498854.66 126498924.56 4.20 1.42\n", "auxiliary[0,10] 126498749.30 28.85 126498735.30 126498728.94 126498808.63 4.11 1.45\n", "auxiliary[0,11] 126498618.46 31.63 126498603.08 126498596.64 126498684.44 4.08 1.45\n", "auxiliary[0,12] 126498471.88 32.53 126498456.64 126498449.31 126498539.46 4.02 1.47\n", "auxiliary[0,13] 126498311.64 33.42 126498295.52 126498287.98 126498379.86 4.05 1.46\n", "auxiliary[0,14] 126498139.40 37.20 126498122.06 126498112.69 126498216.14 4.12 1.44\n", "auxiliary[0,15] 126497946.51 35.91 126497930.35 126497920.92 126498020.61 4.08 1.46\n", "auxiliary[0,16] 126497735.99 37.47 126497717.47 126497708.92 126497813.03 4.12 1.44\n", "auxiliary[0,17] 126497506.50 37.94 126497488.23 126497479.37 126497585.38 4.11 1.44\n", "auxiliary[0,18] 126497260.28 40.03 126497242.03 126497232.53 126497343.74 4.02 1.47\n", "auxiliary[0,19] 126496986.40 38.44 126496967.42 126496958.88 126497064.56 4.00 1.47\n", "auxiliary[0,20] 126496687.04 38.77 126496669.34 126496658.88 126496767.82 4.01 1.48\n", "auxiliary[0,21] 126496368.46 42.52 126496348.99 126496336.45 126496456.08 4.12 1.45\n", "auxiliary[0,22] 126496005.72 41.06 126495987.28 126495973.48 126496092.15 4.07 1.47\n", "auxiliary[0,23] 126495611.91 42.68 126495591.93 126495581.75 126495700.14 4.07 1.45\n", "auxiliary[0,24] 126495176.38 45.59 126495155.41 126495144.86 126495267.99 4.07 1.45\n", "auxiliary[0,25] 126494710.66 47.46 126494688.44 126494676.27 126494807.10 4.05 1.46\n", "auxiliary[0,26] 126494201.17 44.54 126494181.74 126494167.03 126494295.51 3.99 1.50\n", "auxiliary[0,27] 126493631.82 44.50 126493611.52 126493599.19 126493725.13 3.98 1.48\n", "auxiliary[0,28] 126493008.58 47.35 126492986.86 126492974.47 126493109.14 4.29 1.42\n", "auxiliary[0,29] 126492350.19 55.27 126492324.25 126492311.14 126492469.95 4.32 1.40\n", "auxiliary[0,30] 126491592.01 50.77 126491568.00 126491558.10 126491699.52 4.13 1.45\n", "auxiliary[0,31] 126490723.06 46.78 126490703.01 126490685.15 126490815.51 3.52 1.64\n", "auxiliary[0,32] 126489763.47 44.44 126489741.40 126489730.62 126489860.53 4.14 1.45\n", "auxiliary[0,33] 126488722.46 46.97 126488697.85 126488690.16 126488823.77 4.14 1.42\n", "auxiliary[0,34] 126487574.40 45.96 126487552.21 126487547.21 126487674.86 4.54 1.36\n", "auxiliary[0,35] 126486281.16 38.90 126486265.26 126486250.21 126486361.78 4.60 1.41\n", "auxiliary[0,36] 126484839.83 44.44 126484820.97 126484804.80 126484931.63 3.86 1.53\n", "auxiliary[0,37] 126483256.75 29.79 126483244.45 126483234.53 126483318.98 5.15 1.21\n", "auxiliary[0,38] 126481534.67 39.71 126481516.44 126481503.98 126481612.73 4.57 1.38\n", "auxiliary[0,39] 126479622.43 61.85 126479592.28 126479583.72 126479761.40 4.57 1.31\n", "auxiliary[0,40] 126477509.72 62.88 126477483.83 126477466.46 126477649.54 4.51 1.44\n", "auxiliary[0,41] 126475189.21 59.17 126475166.30 126475144.38 126475315.04 4.08 1.50\n", "auxiliary[0,42] 126472661.77 57.46 126472629.42 126472612.28 126472774.72 3.95 1.42\n", "auxiliary[0,43] 126469765.98 53.07 126469739.73 126469721.30 126469867.70 4.17 1.43\n", "auxiliary[0,44] 126466614.70 26.34 126466604.23 126466592.95 126466670.33 5.40 1.25\n", "auxiliary[0,45] 126463251.02 24.64 126463262.04 126463210.39 126463276.63 3.68 1.61\n", "auxiliary[0,46] 126459385.02 69.78 126459415.68 126459257.23 126459443.89 3.84 1.44\n", "auxiliary[0,47] 126455362.35 182.65 126455460.84 126455014.27 126455498.08 3.65 1.55\n", "auxiliary[0,48] 126451044.65 382.00 126451233.96 126450296.61 126451346.45 3.53 1.60\n", "auxiliary[0,49] 126446411.45 626.71 126446708.61 126445126.29 126446866.42 3.77 1.53\n", "auxiliary[0,50] 126441718.64 1006.13 126442190.01 126439610.65 126442457.58 3.86 1.51\n", "auxiliary[0,51] 126436668.79 1492.39 126437401.38 126433591.49 126437696.29 4.02 1.46\n", "auxiliary[0,52] 126431346.87 1992.94 126432308.12 126427221.21 126432675.91 4.19 1.42\n", "auxiliary[0,53] 126425611.19 2372.03 126426746.04 126420710.75 126427118.46 4.38 1.39\n", "auxiliary[0,54] 126419370.66 2538.28 126420597.39 126414227.13 126420949.27 4.43 1.38\n", "auxiliary[0,55] 126412814.97 2675.92 126414100.84 126407381.88 126414535.98 4.41 1.39\n", "auxiliary[0,56] 126405703.18 2812.20 126407045.39 126399905.57 126407500.33 4.36 1.40\n", "auxiliary[0,57] 126398391.35 3066.61 126399871.07 126392120.98 126400360.71 4.37 1.39\n", "auxiliary[0,58] 126390904.15 3612.76 126392631.72 126383495.15 126393254.97 4.34 1.40\n", "auxiliary[0,59] 126384489.08 4451.49 126386620.27 126375361.59 126387385.28 4.33 1.40\n", "auxiliary[0,60] 126381831.46 4941.58 126384212.70 126371667.42 126385045.64 4.35 1.40\n", " auxiliary[1,0] 111.60 0.70 111.23 111.19 113.05 4.33 1.35\n", " auxiliary[1,1] 184.64 0.62 184.37 184.05 185.83 3.89 1.54\n", " auxiliary[1,2] 228.03 2.48 226.82 226.44 232.95 4.39 1.38\n", " auxiliary[1,3] 261.27 1.96 260.31 260.04 265.43 4.36 1.39\n", " auxiliary[1,4] 291.05 2.25 290.01 289.67 295.61 4.76 1.34\n", " auxiliary[1,5] 317.26 3.32 315.68 315.12 324.07 4.48 1.38\n", " auxiliary[1,6] 310.66 2.01 309.73 309.35 314.84 4.33 1.40\n", " auxiliary[1,7] 315.81 2.15 314.68 314.44 320.44 4.22 1.42\n", " auxiliary[1,8] 339.74 1.39 338.92 338.78 342.37 3.58 1.52\n", " auxiliary[1,9] 361.68 1.23 361.07 360.81 363.81 4.27 1.39\n", "auxiliary[1,10] 397.82 0.77 397.51 397.19 399.17 4.40 1.42\n", "auxiliary[1,11] 399.95 0.39 400.06 399.34 400.53 6.38 1.03\n", "auxiliary[1,12] 441.64 1.10 441.08 440.89 443.88 4.23 1.40\n", "auxiliary[1,13] 460.20 1.90 459.24 458.88 464.05 4.19 1.32\n", "auxiliary[1,14] 482.22 0.59 482.42 480.87 482.81 5.60 1.31\n", "auxiliary[1,15] 542.72 0.51 542.54 542.13 543.40 4.29 1.75\n", "auxiliary[1,16] 598.87 0.43 598.82 598.31 599.51 3.35 2.09\n", "auxiliary[1,17] 665.36 1.40 664.79 664.24 668.29 4.02 1.53\n", "auxiliary[1,18] 709.82 0.73 710.13 708.32 710.49 5.24 1.18\n", "auxiliary[1,19] 804.26 1.16 803.70 803.40 806.56 3.83 1.51\n", "auxiliary[1,20] 890.25 1.63 889.44 889.22 893.83 4.53 1.36\n", "auxiliary[1,21] 958.38 0.81 958.00 957.55 959.83 4.14 1.31\n", "auxiliary[1,22] 1061.53 3.36 1060.02 1059.05 1069.08 4.52 1.38\n", "auxiliary[1,23] 1161.52 1.18 1161.02 1160.27 1163.77 3.87 1.48\n", "auxiliary[1,24] 1268.42 0.59 1268.62 1267.72 1269.18 5.44 1.32\n", "auxiliary[1,25] 1393.02 1.52 1393.76 1389.96 1394.22 4.09 1.42\n", "auxiliary[1,26] 1503.69 0.96 1503.51 1502.64 1505.46 9.02 1.12\n", "auxiliary[1,27] 1659.30 1.19 1658.79 1658.14 1661.62 5.10 1.35\n", "auxiliary[1,28] 1816.70 3.07 1815.31 1813.64 1822.10 4.81 1.27\n", "auxiliary[1,29] 1897.37 1.15 1897.69 1895.18 1898.79 5.85 1.11\n", "auxiliary[1,30] 2122.70 1.92 2121.70 2120.70 2125.87 3.00 2.07\n", "auxiliary[1,31] 2388.13 2.26 2387.57 2385.70 2393.36 6.11 1.06\n", "auxiliary[1,32] 2667.36 1.99 2667.51 2665.06 2670.44 2.84 2.25\n", "auxiliary[1,33] 2942.96 3.93 2944.68 2934.99 2946.25 4.46 1.36\n", "auxiliary[1,34] 3261.55 3.31 3259.94 3257.98 3267.65 3.78 1.53\n", "auxiliary[1,35] 3645.86 1.90 3645.54 3643.82 3650.00 11.35 1.00\n", "auxiliary[1,36] 4040.25 2.34 4040.90 4035.99 4042.66 9.87 1.23\n", "auxiliary[1,37] 4489.82 5.23 4487.47 4484.60 4498.76 3.27 1.71\n", "auxiliary[1,38] 5001.54 7.09 5004.92 4987.44 5006.97 4.63 1.26\n", "auxiliary[1,39] 5486.85 9.99 5491.64 5468.16 5494.69 4.14 1.31\n", "auxiliary[1,40] 6069.61 2.17 6068.97 6067.01 6073.80 19.08 1.13\n", "auxiliary[1,41] 6708.11 11.44 6702.93 6700.38 6732.05 4.62 1.26\n", "auxiliary[1,42] 7360.00 6.01 7359.79 7350.80 7370.84 7.00 1.01\n", "auxiliary[1,43] 8241.76 5.18 8242.78 8232.97 8250.03 5.69 1.05\n", "auxiliary[1,44] 9075.78 3.78 9075.68 9069.58 9082.08 5.87 1.01\n", "auxiliary[1,45] 9937.44 10.55 9938.15 9916.55 9952.21 3.27 1.90\n", "auxiliary[1,46] 11140.37 20.04 11151.23 11102.24 11154.74 3.84 1.47\n", "auxiliary[1,47] 12273.10 21.17 12283.67 12231.51 12289.07 4.23 1.41\n", "auxiliary[1,48] 13563.29 9.13 13564.26 13549.89 13576.09 3.74 1.81\n", "auxiliary[1,49] 14962.23 39.31 14977.14 14892.07 14999.00 3.53 1.67\n", "auxiliary[1,50] 16377.12 59.34 16401.00 16259.60 16430.94 3.67 1.60\n", "auxiliary[1,51] 18233.56 81.41 18275.10 18059.81 18291.02 3.88 1.51\n", "auxiliary[1,52] 20169.07 101.86 20220.53 19950.78 20235.38 4.33 1.37\n", "auxiliary[1,53] 22440.97 127.78 22502.11 22163.37 22523.87 4.36 1.40\n", "auxiliary[1,54] 25094.80 169.10 25181.94 24735.54 25205.64 4.27 1.40\n", "auxiliary[1,55] 27886.87 146.05 27954.95 27584.43 27979.04 4.72 1.26\n", "auxiliary[1,56] 31109.06 138.51 31174.22 30845.70 31197.79 5.15 1.26\n", "auxiliary[1,57] 34219.17 37.81 34232.91 34143.37 34250.03 5.72 1.18\n", "auxiliary[1,58] 37632.18 122.25 37578.47 37525.44 37868.28 3.52 1.64\n", "auxiliary[1,59] 40454.77 480.27 40224.77 40090.28 41435.04 3.87 1.49\n", "auxiliary[1,60] 38643.17 1510.70 37916.53 37637.57 41753.58 4.25 1.41\n", " auxiliary[2,0] 0.57 0.00 0.57 0.57 0.58 5.09 1.46\n", " auxiliary[2,1] 27.89 0.03 27.87 27.87 27.94 5.44 1.27\n", " auxiliary[2,2] 82.36 0.30 82.22 82.14 82.98 4.23 1.44\n", " auxiliary[2,3] 134.34 0.52 134.08 133.96 135.44 3.95 1.47\n", " auxiliary[2,4] 187.31 1.08 186.78 186.53 189.57 4.18 1.42\n", " auxiliary[2,5] 238.05 1.72 237.20 236.96 241.53 4.68 1.32\n", " auxiliary[2,6] 315.35 2.46 314.15 313.75 320.29 4.16 1.43\n", " auxiliary[2,7] 376.28 3.66 374.47 373.93 383.73 4.34 1.38\n", " auxiliary[2,8] 413.15 1.97 412.16 411.90 417.16 4.09 1.43\n", " auxiliary[2,9] 450.77 2.26 449.64 449.36 455.22 4.53 1.31\n", "auxiliary[2,10] 471.55 0.72 471.29 470.95 472.99 4.13 1.54\n", "auxiliary[2,11] 530.54 0.59 530.30 529.87 531.64 5.31 1.15\n", "auxiliary[2,12] 566.89 0.80 566.63 566.17 568.27 6.61 1.11\n", "auxiliary[2,13] 637.28 2.06 636.28 635.83 641.60 4.27 1.39\n", "auxiliary[2,14] 709.46 0.67 709.49 708.13 710.45 7.69 1.00\n", "auxiliary[2,15] 761.86 2.63 760.83 759.92 767.22 4.05 1.49\n", "auxiliary[2,16] 827.36 2.76 825.93 825.40 833.03 3.83 1.48\n", "auxiliary[2,17] 895.12 2.05 894.07 893.66 899.08 4.18 1.34\n", "auxiliary[2,18] 985.49 0.84 985.52 984.20 986.73 2.76 2.25\n", "auxiliary[2,19] 1050.76 1.95 1049.70 1049.10 1054.39 3.56 1.53\n", "auxiliary[2,20] 1142.83 2.32 1141.82 1140.48 1147.54 4.26 1.46\n", "auxiliary[2,21] 1251.91 0.43 1251.84 1251.35 1252.65 7.45 1.04\n", "auxiliary[2,22] 1370.17 2.39 1369.12 1368.10 1374.18 4.09 1.46\n", "auxiliary[2,23] 1510.13 4.80 1507.77 1506.91 1519.57 4.34 1.38\n", "auxiliary[2,24] 1678.62 1.59 1678.21 1676.89 1681.83 7.93 1.06\n", "auxiliary[2,25] 1835.91 0.59 1835.83 1834.76 1836.66 13.52 1.16\n", "auxiliary[2,26] 2035.57 1.15 2035.48 2033.13 2036.43 11.14 1.00\n", "auxiliary[2,27] 2220.79 5.33 2218.11 2216.78 2232.33 3.99 1.48\n", "auxiliary[2,28] 2441.87 1.80 2441.80 2439.08 2444.54 2.71 2.51\n", "auxiliary[2,29] 2727.65 1.21 2727.40 2725.92 2729.62 6.44 1.01\n", "auxiliary[2,30] 2971.28 2.30 2971.15 2967.14 2973.74 6.23 1.00\n", "auxiliary[2,31] 3266.65 2.35 3267.10 3262.89 3269.52 4.42 1.63\n", "auxiliary[2,32] 3603.99 4.70 3601.71 3599.79 3613.11 3.64 1.63\n", "auxiliary[2,33] 3980.93 4.18 3979.29 3976.79 3988.73 3.91 1.53\n", "auxiliary[2,34] 4372.42 2.91 4372.70 4364.57 4374.80 11.30 1.03\n", "auxiliary[2,35] 4781.69 7.01 4778.20 4775.67 4795.17 3.93 1.37\n", "auxiliary[2,36] 5272.42 6.17 5275.37 5260.29 5277.78 3.79 1.39\n", "auxiliary[2,37] 5797.24 7.81 5795.27 5789.26 5810.23 2.79 2.16\n", "auxiliary[2,38] 6321.72 4.76 6321.14 6315.46 6329.43 7.80 1.01\n", "auxiliary[2,39] 7004.66 4.90 7006.25 6994.11 7009.58 6.23 1.03\n", "auxiliary[2,40] 7718.24 9.64 7713.73 7709.46 7737.99 3.73 1.65\n", "auxiliary[2,41] 8489.53 4.61 8488.96 8482.21 8496.41 5.80 1.39\n", "auxiliary[2,42] 9350.48 11.05 9346.67 9339.16 9370.00 3.54 1.72\n", "auxiliary[2,43] 10315.69 4.10 10315.38 10311.79 10323.65 14.50 1.21\n", "auxiliary[2,44] 11545.43 8.66 11549.49 11528.61 11554.31 4.89 1.19\n", "auxiliary[2,45] 12783.10 8.17 12781.00 12770.90 12797.20 7.23 1.17\n", "auxiliary[2,46] 14095.89 9.77 14096.28 14081.08 14111.18 5.56 1.03\n", "auxiliary[2,47] 15563.34 17.94 15568.89 15524.51 15578.99 5.23 1.17\n", "auxiliary[2,48] 17125.60 10.98 17129.79 17106.17 17137.00 5.36 1.29\n", "auxiliary[2,49] 19013.09 7.80 19013.32 19005.65 19027.13 16.75 1.06\n", "auxiliary[2,50] 21085.49 40.98 21105.26 21002.25 21120.15 3.95 1.33\n", "auxiliary[2,51] 23261.81 83.97 23307.86 23086.12 23318.50 3.84 1.44\n", "auxiliary[2,52] 25878.99 112.77 25934.40 25653.84 25958.89 4.14 1.43\n", "auxiliary[2,53] 28736.32 177.85 28828.42 28380.68 28854.27 3.88 1.47\n", "auxiliary[2,54] 31875.47 235.22 31977.19 31394.11 32028.75 4.63 1.38\n", "auxiliary[2,55] 35303.67 199.92 35395.98 34874.02 35422.88 4.81 1.33\n", "auxiliary[2,56] 38904.18 107.59 38939.32 38710.54 38994.33 6.49 1.12\n", "auxiliary[2,57] 42835.89 67.19 42823.23 42771.97 42947.32 3.66 1.75\n", "auxiliary[2,58] 46647.47 438.83 46449.79 46332.95 47553.15 4.08 1.46\n", "auxiliary[2,59] 49971.50 918.84 49546.05 49357.84 51857.54 4.29 1.41\n", "auxiliary[2,60] 54158.16 374.28 53988.56 53889.52 54944.33 4.11 1.46\n", " auxiliary[3,0] 0.50 0.00 0.50 0.50 0.50 15.92 1.05\n", " auxiliary[3,1] 0.50 0.00 0.50 0.50 0.50 5.75 1.33\n", " auxiliary[3,2] 0.50 0.00 0.50 0.50 0.50 10.37 1.25\n", " auxiliary[3,3] 0.50 0.00 0.50 0.50 0.50 5.10 1.40\n", " auxiliary[3,4] 0.50 0.00 0.50 0.50 0.50 5.15 1.43\n", " auxiliary[3,5] 0.50 0.00 0.50 0.49 0.50 4.40 1.55\n", " auxiliary[3,6] 0.50 0.00 0.50 0.50 0.50 5.12 1.17\n", " auxiliary[3,7] 0.50 0.00 0.50 0.50 0.50 5.71 1.16\n", " auxiliary[3,8] 0.50 0.00 0.50 0.50 0.50 4.11 1.84\n", " auxiliary[3,9] 0.50 0.00 0.50 0.50 0.50 7.83 1.32\n", "auxiliary[3,10] 0.50 0.00 0.50 0.50 0.50 8.91 1.24\n", "auxiliary[3,11] 0.50 0.00 0.51 0.50 0.51 4.12 1.45\n", "auxiliary[3,12] 1.20 0.00 1.20 1.20 1.20 4.63 1.41\n", "auxiliary[3,13] 1.19 0.00 1.19 1.19 1.19 8.56 1.02\n", "auxiliary[3,14] 1.27 0.00 1.27 1.27 1.28 5.72 1.04\n", "auxiliary[3,15] 1.62 0.00 1.62 1.62 1.62 4.62 1.30\n", "auxiliary[3,16] 1.89 0.00 1.89 1.89 1.89 5.65 1.19\n", "auxiliary[3,17] 2.06 0.00 2.06 2.06 2.06 8.20 1.21\n", "auxiliary[3,18] 2.84 0.00 2.84 2.84 2.85 7.56 1.09\n", "auxiliary[3,19] 3.40 0.00 3.40 3.40 3.40 15.68 1.29\n", "auxiliary[3,20] 3.81 0.00 3.81 3.80 3.81 6.13 1.17\n", "auxiliary[3,21] 4.53 0.00 4.53 4.52 4.53 9.16 1.34\n", "auxiliary[3,22] 4.92 0.01 4.92 4.92 4.93 3.70 1.64\n", "auxiliary[3,23] 5.24 0.01 5.24 5.24 5.26 5.44 1.38\n", "auxiliary[3,24] 4.98 0.02 4.99 4.94 5.00 4.26 1.44\n", "auxiliary[3,25] 5.96 0.02 5.97 5.91 5.98 3.88 1.51\n", "auxiliary[3,26] 7.98 0.05 7.95 7.94 8.09 4.08 1.46\n", "auxiliary[3,27] 8.61 0.03 8.62 8.54 8.63 4.49 1.41\n", "auxiliary[3,28] 9.68 0.03 9.67 9.66 9.75 3.83 1.49\n", "auxiliary[3,29] 10.06 0.04 10.04 10.03 10.15 4.52 1.40\n", "auxiliary[3,30] 9.86 0.04 9.88 9.79 9.89 3.93 1.48\n", "auxiliary[3,31] 10.16 0.04 10.13 10.12 10.24 4.00 1.45\n", "auxiliary[3,32] 9.87 0.01 9.87 9.86 9.88 4.48 1.46\n", "auxiliary[3,33] 9.51 0.01 9.52 9.49 9.52 4.80 1.32\n", "auxiliary[3,34] 9.45 0.01 9.46 9.43 9.46 5.47 1.36\n", "auxiliary[3,35] 9.73 0.01 9.73 9.70 9.74 3.44 1.74\n", "auxiliary[3,36] 10.42 0.12 10.47 10.17 10.50 4.22 1.43\n", "auxiliary[3,37] 12.86 0.08 12.82 12.82 13.01 5.27 1.26\n", "auxiliary[3,38] 14.72 0.24 14.83 14.21 14.86 4.59 1.34\n", "auxiliary[3,39] 18.13 0.14 18.07 18.05 18.42 5.10 1.30\n", "auxiliary[3,40] 21.01 0.05 20.99 20.97 21.09 3.74 1.59\n", "auxiliary[3,41] 23.76 0.11 23.72 23.68 23.98 5.74 1.18\n", "auxiliary[3,42] 26.31 0.23 26.40 25.85 26.50 3.66 1.60\n", "auxiliary[3,43] 29.69 0.89 30.14 27.85 30.31 4.10 1.44\n", "auxiliary[3,44] 34.81 1.28 35.43 32.20 35.72 3.99 1.47\n", "auxiliary[3,45] 41.81 1.64 42.62 38.36 42.92 4.16 1.42\n", "auxiliary[3,46] 50.24 1.81 51.14 46.44 51.29 4.63 1.33\n", "auxiliary[3,47] 59.52 1.40 60.14 56.81 60.18 5.83 1.22\n", "auxiliary[3,48] 69.16 0.55 69.06 68.80 70.57 8.80 1.14\n", "auxiliary[3,49] 78.65 2.17 77.58 77.06 83.00 3.86 1.51\n", "auxiliary[3,50] 87.57 4.62 85.34 84.57 97.34 4.22 1.42\n", "auxiliary[3,51] 95.69 7.15 92.25 91.18 110.42 4.43 1.38\n", "auxiliary[3,52] 102.96 9.51 98.42 97.15 122.26 4.56 1.36\n", "auxiliary[3,53] 109.25 11.57 103.75 102.26 132.48 4.63 1.35\n", "auxiliary[3,54] 114.27 13.20 108.03 106.37 140.59 4.68 1.34\n", "auxiliary[3,55] 117.92 14.33 111.21 109.41 146.45 4.71 1.34\n", "auxiliary[3,56] 120.68 15.07 113.60 111.74 150.68 4.72 1.34\n", "auxiliary[3,57] 122.86 15.60 115.51 113.59 153.85 4.73 1.34\n", "auxiliary[3,58] 124.64 15.95 117.12 115.21 156.28 4.74 1.34\n", "auxiliary[3,59] 126.11 16.17 118.47 116.50 158.19 4.74 1.34\n", "auxiliary[3,60] 127.29 16.28 119.62 117.68 159.56 4.74 1.34\n", " incub_time 3.59 0.01 3.60 3.57 3.60 3.97 1.47\n", " mort_rate 0.01 0.00 0.01 0.01 0.01 3.33 1.76\n", " rec_rate 0.68 0.00 0.68 0.68 0.68 4.46 1.37\n", " rec_time 8.62 0.01 8.62 8.61 8.62 3.94 1.48\n", " rho 0.07 0.00 0.07 0.07 0.07 11.88 1.04\n", "\n", "Number of divergences: 363\n", "CPU times: user 58.8 s, sys: 525 ms, total: 59.3 s\n", "Wall time: 59.2 s\n" ], "name": "stdout" } ] }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "lHf-1YdQ7PPw", "outputId": "fac2e840-0061-4a03-a08d-cf894a9fb252" }, "source": [ "%%time\n", "Japan_model = CovidModel(126500000, Japan[\"new_cases\"], Japan[\"new_recovered\"], Japan[\"new_deaths\"] )\n", "Japan_mcmc = Japan_model.fit_mcmc(num_samples=500, warmup_steps = 200)\n", "Japan_mcmc.summary()" ], "execution_count": null, "outputs": [ { "output_type": "stream", "text": [ "INFO \t Running inference...\n", "Warmup: 0%| | 0/700 [00:00, ?it/s]INFO \t Heuristic init: R0=1.74, incub_time=5.76, mort_rate=0.0166, rec_rate=0.343, rec_time=14.8, rho=0.191\n", "Sample: 100%|██████████| 700/700 [03:17, 3.55it/s, step size=1.52e-05, acc. prob=0.999]\n" ], "name": "stderr" }, { "output_type": "stream", "text": [ "\n", " mean std median 5.0% 95.0% n_eff r_hat\n", " R0 1.74 0.00 1.74 1.74 1.74 3.20 1.61\n", " auxiliary[0,0] 126499865.75 0.00 126499865.75 126499865.74 126499865.75 4.63 1.45\n", " auxiliary[0,1] 126499752.70 0.14 126499752.73 126499752.50 126499752.87 3.01 1.99\n", " auxiliary[0,2] 126499637.31 0.30 126499637.23 126499636.92 126499637.75 2.94 2.03\n", " auxiliary[0,3] 126499516.28 0.06 126499516.28 126499516.20 126499516.36 2.51 2.60\n", " auxiliary[0,4] 126499394.94 0.01 126499394.94 126499394.92 126499394.97 3.27 2.07\n", " auxiliary[0,5] 126499290.14 0.01 126499290.14 126499290.12 126499290.15 7.21 1.00\n", " auxiliary[0,6] 126499183.37 0.03 126499183.36 126499183.32 126499183.42 2.37 3.46\n", " auxiliary[0,7] 126499071.08 0.04 126499071.08 126499071.03 126499071.14 2.65 2.38\n", " auxiliary[0,8] 126498947.86 0.01 126498947.86 126498947.84 126498947.87 5.63 1.26\n", " auxiliary[0,9] 126498832.96 0.03 126498832.96 126498832.92 126498833.00 4.10 2.01\n", "auxiliary[0,10] 126498734.89 0.03 126498734.89 126498734.85 126498734.93 4.61 1.00\n", "auxiliary[0,11] 126498620.31 0.03 126498620.31 126498620.24 126498620.35 2.84 2.21\n", "auxiliary[0,12] 126498498.65 0.03 126498498.65 126498498.61 126498498.69 5.61 1.08\n", "auxiliary[0,13] 126498393.04 0.05 126498393.01 126498392.97 126498393.12 2.50 3.05\n", "auxiliary[0,14] 126498287.25 0.04 126498287.25 126498287.17 126498287.29 4.51 1.50\n", "auxiliary[0,15] 126498170.50 0.05 126498170.52 126498170.39 126498170.56 4.62 1.40\n", "auxiliary[0,16] 126498059.60 0.03 126498059.61 126498059.56 126498059.64 5.21 1.35\n", "auxiliary[0,17] 126497944.10 0.02 126497944.10 126497944.07 126497944.14 7.20 1.09\n", "auxiliary[0,18] 126497822.64 0.02 126497822.64 126497822.61 126497822.68 11.19 1.05\n", "auxiliary[0,19] 126497702.27 0.04 126497702.26 126497702.22 126497702.33 5.09 1.18\n", "auxiliary[0,20] 126497580.38 0.05 126497580.40 126497580.30 126497580.46 5.23 1.28\n", "auxiliary[0,21] 126497459.43 0.04 126497459.43 126497459.35 126497459.49 5.89 1.21\n", "auxiliary[0,22] 126497329.11 0.07 126497329.10 126497329.02 126497329.23 3.49 1.44\n", "auxiliary[0,23] 126497202.74 0.05 126497202.75 126497202.66 126497202.82 3.45 1.96\n", "auxiliary[0,24] 126497073.68 0.05 126497073.67 126497073.60 126497073.76 3.31 2.35\n", "auxiliary[0,25] 126496935.95 0.04 126496935.96 126496935.85 126496935.99 7.17 1.44\n", "auxiliary[0,26] 126496800.82 0.04 126496800.82 126496800.76 126496800.87 15.58 1.15\n", "auxiliary[0,27] 126496666.51 0.12 126496666.52 126496666.33 126496666.70 3.19 2.14\n", "auxiliary[0,28] 126496525.22 0.07 126496525.24 126496525.11 126496525.33 3.32 1.81\n", "auxiliary[0,29] 126496380.17 0.16 126496380.22 126496379.93 126496380.36 2.45 2.77\n", "auxiliary[0,30] 126496214.26 0.07 126496214.26 126496214.17 126496214.39 4.08 2.07\n", "auxiliary[0,31] 126496049.06 0.04 126496049.06 126496049.00 126496049.11 12.06 1.12\n", "auxiliary[0,32] 126495872.58 0.11 126495872.57 126495872.40 126495872.73 4.76 1.38\n", "auxiliary[0,33] 126495691.92 0.05 126495691.92 126495691.85 126495691.99 6.98 1.22\n", "auxiliary[0,34] 126495500.35 0.08 126495500.33 126495500.25 126495500.51 7.07 1.06\n", "auxiliary[0,35] 126495315.45 0.08 126495315.46 126495315.31 126495315.55 5.09 1.00\n", "auxiliary[0,36] 126495114.57 0.09 126495114.57 126495114.44 126495114.74 5.86 1.32\n", "auxiliary[0,37] 126494923.07 0.06 126494923.06 126494922.99 126494923.16 4.19 1.69\n", "auxiliary[0,38] 126494704.98 0.17 126494705.05 126494704.64 126494705.14 4.38 1.32\n", "auxiliary[0,39] 126494483.07 0.20 126494483.07 126494482.75 126494483.33 2.71 2.23\n", "auxiliary[0,40] 126494264.88 0.06 126494264.89 126494264.79 126494264.99 16.01 1.00\n", "auxiliary[0,41] 126494022.45 0.13 126494022.44 126494022.26 126494022.62 5.87 1.15\n", "auxiliary[0,42] 126493763.99 0.17 126493763.97 126493763.77 126493764.28 2.61 2.96\n", "auxiliary[0,43] 126493510.12 0.26 126493510.06 126493509.76 126493510.51 2.68 2.20\n", "auxiliary[0,44] 126493268.18 0.09 126493268.18 126493268.06 126493268.34 9.23 1.00\n", "auxiliary[0,45] 126492998.71 0.09 126492998.70 126492998.57 126492998.85 5.64 1.07\n", "auxiliary[0,46] 126492739.26 0.27 126492739.28 126492738.91 126492739.70 2.99 2.00\n", "auxiliary[0,47] 126492443.28 0.13 126492443.27 126492443.07 126492443.48 4.48 1.51\n", "auxiliary[0,48] 126492150.99 0.18 126492151.01 126492150.74 126492151.27 2.52 2.69\n", "auxiliary[0,49] 126491855.11 0.13 126491855.13 126491854.90 126491855.31 4.82 1.25\n", "auxiliary[0,50] 126491518.59 0.10 126491518.60 126491518.40 126491518.73 8.55 1.00\n", "auxiliary[0,51] 126491193.12 0.24 126491193.13 126491192.78 126491193.50 2.88 1.89\n", "auxiliary[0,52] 126490854.50 0.38 126490854.48 126490853.80 126490855.06 3.36 1.80\n", "auxiliary[0,53] 126490470.29 0.10 126490470.27 126490470.12 126490470.45 13.37 1.04\n", "auxiliary[0,54] 126490097.74 0.23 126490097.67 126490097.44 126490098.07 3.54 1.56\n", "auxiliary[0,55] 126489699.10 0.40 126489698.89 126489698.60 126489699.73 2.51 2.94\n", "auxiliary[0,56] 126489257.85 0.21 126489257.81 126489257.56 126489258.19 4.87 1.35\n", "auxiliary[0,57] 126488831.36 0.27 126488831.39 126488830.90 126488831.75 4.51 1.42\n", "auxiliary[0,58] 126488442.33 0.41 126488442.22 126488441.83 126488443.01 3.32 1.50\n", "auxiliary[0,59] 126488044.47 0.59 126488044.61 126488043.29 126488045.14 3.05 1.93\n", "auxiliary[0,60] 126487658.84 0.13 126487658.84 126487658.63 126487659.03 12.99 1.00\n", " auxiliary[1,0] 134.60 0.00 134.60 134.59 134.60 2.98 2.42\n", " auxiliary[1,1] 218.94 0.11 218.96 218.79 219.08 2.96 2.03\n", " auxiliary[1,2] 284.44 0.20 284.39 284.20 284.73 2.89 2.08\n", " auxiliary[1,3] 351.87 0.01 351.88 351.85 351.89 2.84 2.09\n", " auxiliary[1,4] 410.85 0.01 410.85 410.82 410.86 3.82 1.63\n", " auxiliary[1,5] 434.23 0.01 434.23 434.21 434.24 3.08 3.32\n", " auxiliary[1,6] 463.86 0.01 463.86 463.84 463.88 5.19 1.04\n", " auxiliary[1,7] 499.24 0.02 499.24 499.22 499.27 3.88 1.10\n", " auxiliary[1,8] 532.26 0.01 532.26 532.25 532.27 9.45 1.17\n", " auxiliary[1,9] 561.01 0.01 561.01 561.00 561.03 3.14 2.00\n", "auxiliary[1,10] 550.55 0.01 550.56 550.54 550.57 5.71 1.00\n", "auxiliary[1,11] 574.70 0.01 574.70 574.69 574.71 8.49 1.02\n", "auxiliary[1,12] 582.83 0.02 582.83 582.79 582.85 3.34 1.84\n", "auxiliary[1,13] 575.46 0.01 575.46 575.44 575.48 3.06 1.99\n", "auxiliary[1,14] 576.94 0.01 576.94 576.93 576.95 8.10 1.22\n", "auxiliary[1,15] 597.72 0.02 597.72 597.70 597.75 2.58 2.75\n", "auxiliary[1,16] 614.04 0.01 614.04 614.01 614.06 2.97 2.07\n", "auxiliary[1,17] 630.23 0.01 630.23 630.21 630.25 9.44 1.00\n", "auxiliary[1,18] 645.14 0.01 645.14 645.12 645.16 6.34 1.12\n", "auxiliary[1,19] 661.41 0.02 661.42 661.38 661.43 4.85 1.47\n", "auxiliary[1,20] 683.02 0.02 683.02 682.99 683.05 2.86 2.11\n", "auxiliary[1,21] 683.96 0.01 683.96 683.95 683.97 4.31 1.46\n", "auxiliary[1,22] 726.93 0.02 726.93 726.91 726.96 2.69 2.36\n", "auxiliary[1,23] 730.29 0.02 730.29 730.26 730.31 4.16 1.34\n", "auxiliary[1,24] 734.93 0.01 734.93 734.92 734.95 8.92 1.02\n", "auxiliary[1,25] 748.73 0.01 748.74 748.71 748.75 3.88 1.28\n", "auxiliary[1,26] 754.39 0.02 754.40 754.36 754.42 3.91 1.47\n", "auxiliary[1,27] 755.63 0.01 755.63 755.61 755.65 3.17 2.10\n", "auxiliary[1,28] 776.78 0.01 776.78 776.77 776.79 10.95 1.00\n", "auxiliary[1,29] 796.13 0.02 796.13 796.10 796.17 3.27 1.82\n", "auxiliary[1,30] 821.79 0.02 821.78 821.77 821.82 3.59 1.46\n", "auxiliary[1,31] 853.98 0.01 853.98 853.96 853.99 18.42 1.00\n", "auxiliary[1,32] 884.45 0.01 884.45 884.43 884.47 7.77 1.06\n", "auxiliary[1,33] 930.47 0.02 930.47 930.42 930.50 4.89 1.53\n", "auxiliary[1,34] 957.89 0.02 957.89 957.86 957.92 4.28 1.20\n", "auxiliary[1,35] 992.64 0.03 992.63 992.61 992.68 2.75 2.20\n", "auxiliary[1,36] 1028.37 0.05 1028.35 1028.31 1028.44 2.47 3.13\n", "auxiliary[1,37] 1021.99 0.02 1021.99 1021.96 1022.03 2.94 1.87\n", "auxiliary[1,38] 1093.52 0.03 1093.52 1093.47 1093.57 2.98 1.94\n", "auxiliary[1,39] 1134.49 0.02 1134.49 1134.46 1134.52 3.37 2.61\n", "auxiliary[1,40] 1158.88 0.01 1158.88 1158.86 1158.90 7.58 1.02\n", "auxiliary[1,41] 1208.63 0.02 1208.63 1208.59 1208.67 3.98 1.52\n", "auxiliary[1,42] 1275.98 0.04 1275.99 1275.93 1276.03 2.67 2.66\n", "auxiliary[1,43] 1327.18 0.02 1327.18 1327.15 1327.21 7.19 1.02\n", "auxiliary[1,44] 1345.17 0.03 1345.18 1345.13 1345.21 2.82 2.08\n", "auxiliary[1,45] 1396.95 0.02 1396.95 1396.91 1396.98 6.13 1.20\n", "auxiliary[1,46] 1385.14 0.01 1385.14 1385.12 1385.17 5.62 1.42\n", "auxiliary[1,47] 1447.68 0.03 1447.67 1447.64 1447.72 4.95 1.27\n", "auxiliary[1,48] 1499.05 0.02 1499.06 1499.00 1499.08 3.50 1.64\n", "auxiliary[1,49] 1517.63 0.01 1517.63 1517.61 1517.65 13.11 1.04\n", "auxiliary[1,50] 1607.85 0.02 1607.84 1607.82 1607.88 9.18 1.15\n", "auxiliary[1,51] 1645.11 0.04 1645.12 1645.05 1645.17 4.63 1.37\n", "auxiliary[1,52] 1713.50 0.05 1713.51 1713.44 1713.57 5.36 1.00\n", "auxiliary[1,53] 1816.91 0.02 1816.91 1816.87 1816.95 10.76 1.17\n", "auxiliary[1,54] 1859.53 0.05 1859.54 1859.45 1859.58 2.89 2.36\n", "auxiliary[1,55] 1928.38 0.03 1928.38 1928.34 1928.43 4.15 1.51\n", "auxiliary[1,56] 2016.54 0.02 2016.54 2016.50 2016.58 10.45 1.01\n", "auxiliary[1,57] 2114.16 0.05 2114.15 2114.09 2114.24 4.46 1.38\n", "auxiliary[1,58] 2095.68 0.02 2095.68 2095.65 2095.71 17.08 1.01\n", "auxiliary[1,59] 2153.37 0.04 2153.37 2153.31 2153.43 6.38 1.25\n", "auxiliary[1,60] 2281.32 0.04 2281.31 2281.25 2281.37 4.55 1.18\n", " auxiliary[2,0] 1.73 0.00 1.73 1.73 1.73 4.95 1.64\n", " auxiliary[2,1] 24.22 0.00 24.22 24.21 24.22 3.61 1.69\n", " auxiliary[2,2] 71.13 0.01 71.13 71.12 71.15 2.98 1.98\n", " auxiliary[2,3] 117.45 0.00 117.45 117.45 117.45 6.56 1.13\n", " auxiliary[2,4] 169.95 0.00 169.95 169.94 169.96 3.15 2.02\n", " auxiliary[2,5] 240.09 0.01 240.09 240.08 240.10 3.16 2.22\n", " auxiliary[2,6] 304.01 0.01 304.01 303.99 304.02 2.46 3.23\n", " auxiliary[2,7] 365.65 0.01 365.65 365.63 365.66 3.63 1.89\n", " auxiliary[2,8] 438.48 0.01 438.48 438.47 438.50 3.32 1.73\n", " auxiliary[2,9] 502.32 0.01 502.32 502.30 502.33 3.57 1.64\n", "auxiliary[2,10] 580.38 0.01 580.38 580.37 580.40 3.01 2.33\n", "auxiliary[2,11] 637.39 0.01 637.39 637.38 637.41 10.98 1.03\n", "auxiliary[2,12] 713.50 0.01 713.50 713.48 713.52 9.04 1.01\n", "auxiliary[2,13] 774.14 0.01 774.14 774.12 774.17 5.47 1.40\n", "auxiliary[2,14] 823.02 0.01 823.02 823.00 823.04 7.58 1.06\n", "auxiliary[2,15] 871.52 0.02 871.51 871.49 871.55 3.39 1.69\n", "auxiliary[2,16] 907.45 0.01 907.45 907.43 907.47 4.86 1.44\n", "auxiliary[2,17] 946.47 0.01 946.47 946.44 946.49 5.44 1.16\n", "auxiliary[2,18] 992.46 0.04 992.46 992.40 992.51 2.44 3.07\n", "auxiliary[2,19] 1031.32 0.01 1031.32 1031.31 1031.35 12.46 1.00\n", "auxiliary[2,20] 1059.06 0.05 1059.06 1058.99 1059.13 2.36 3.13\n", "auxiliary[2,21] 1099.79 0.04 1099.79 1099.73 1099.84 3.27 1.65\n", "auxiliary[2,22] 1114.85 0.02 1114.84 1114.82 1114.88 3.12 2.76\n", "auxiliary[2,23] 1147.49 0.03 1147.49 1147.45 1147.55 3.22 1.63\n", "auxiliary[2,24] 1186.95 0.02 1186.95 1186.92 1186.99 5.20 1.74\n", "auxiliary[2,25] 1241.05 0.02 1241.05 1241.02 1241.08 3.59 1.76\n", "auxiliary[2,26] 1285.66 0.03 1285.67 1285.61 1285.70 5.42 1.23\n", "auxiliary[2,27] 1328.70 0.03 1328.70 1328.65 1328.75 5.63 1.01\n", "auxiliary[2,28] 1354.60 0.02 1354.60 1354.58 1354.63 4.38 1.74\n", "auxiliary[2,29] 1385.47 0.04 1385.48 1385.40 1385.52 3.90 1.57\n", "auxiliary[2,30] 1449.50 0.03 1449.50 1449.46 1449.55 4.95 1.20\n", "auxiliary[2,31] 1495.18 0.03 1495.18 1495.13 1495.22 3.36 2.23\n", "auxiliary[2,32] 1555.71 0.05 1555.70 1555.64 1555.80 4.75 1.16\n", "auxiliary[2,33] 1602.89 0.04 1602.90 1602.83 1602.94 5.27 1.19\n", "auxiliary[2,34] 1674.79 0.07 1674.77 1674.69 1674.90 2.49 2.96\n", "auxiliary[2,35] 1696.20 0.05 1696.20 1696.15 1696.27 2.48 3.47\n", "auxiliary[2,36] 1751.34 0.02 1751.33 1751.31 1751.38 10.78 1.00\n", "auxiliary[2,37] 1799.14 0.03 1799.14 1799.11 1799.19 10.49 1.37\n", "auxiliary[2,38] 1834.91 0.04 1834.91 1834.86 1835.00 4.14 1.61\n", "auxiliary[2,39] 1895.87 0.03 1895.88 1895.81 1895.92 4.36 1.54\n", "auxiliary[2,40] 1942.83 0.05 1942.83 1942.76 1942.91 4.56 1.05\n", "auxiliary[2,41] 2012.69 0.04 2012.69 2012.61 2012.74 4.48 1.09\n", "auxiliary[2,42] 2076.34 0.04 2076.34 2076.27 2076.39 3.22 1.95\n", "auxiliary[2,43] 2145.92 0.06 2145.95 2145.81 2145.99 4.45 1.28\n", "auxiliary[2,44] 2215.29 0.03 2215.29 2215.22 2215.33 6.15 1.06\n", "auxiliary[2,45] 2306.87 0.03 2306.87 2306.82 2306.90 6.76 1.40\n", "auxiliary[2,46] 2426.26 0.05 2426.27 2426.17 2426.33 3.21 1.81\n", "auxiliary[2,47] 2527.23 0.05 2527.23 2527.15 2527.32 5.65 1.39\n", "auxiliary[2,48] 2603.07 0.04 2603.06 2603.00 2603.12 8.78 1.08\n", "auxiliary[2,49] 2686.05 0.05 2686.05 2685.98 2686.12 4.94 1.34\n", "auxiliary[2,50] 2777.27 0.13 2777.25 2777.11 2777.48 2.54 2.80\n", "auxiliary[2,51] 2887.75 0.06 2887.73 2887.66 2887.83 6.12 1.08\n", "auxiliary[2,52] 2943.13 0.06 2943.12 2943.05 2943.24 3.24 1.92\n", "auxiliary[2,53] 3026.30 0.07 3026.29 3026.19 3026.40 2.86 2.26\n", "auxiliary[2,54] 3133.50 0.05 3133.49 3133.44 3133.59 5.33 1.44\n", "auxiliary[2,55] 3263.54 0.04 3263.54 3263.49 3263.60 7.50 1.39\n", "auxiliary[2,56] 3422.30 0.06 3422.32 3422.20 3422.37 3.78 1.60\n", "auxiliary[2,57] 3542.19 0.06 3542.18 3542.10 3542.28 4.86 1.35\n", "auxiliary[2,58] 3689.72 0.08 3689.71 3689.61 3689.83 3.49 1.52\n", "auxiliary[2,59] 3864.01 0.12 3863.99 3863.81 3864.20 3.56 1.44\n", "auxiliary[2,60] 4016.95 0.14 4016.97 4016.77 4017.18 2.74 2.34\n", " auxiliary[3,0] 0.50 0.00 0.50 0.50 0.50 2.64 3.52\n", " auxiliary[3,1] 0.50 0.00 0.50 0.50 0.50 4.27 1.47\n", " auxiliary[3,2] 0.50 0.00 0.50 0.50 0.50 2.83 2.34\n", " auxiliary[3,3] 0.50 0.00 0.50 0.50 0.50 5.29 1.40\n", " auxiliary[3,4] 0.50 0.00 0.50 0.50 0.50 3.70 1.38\n", " auxiliary[3,5] 0.50 0.00 0.50 0.50 0.50 2.85 2.49\n", " auxiliary[3,6] 0.50 0.00 0.50 0.50 0.50 3.36 1.45\n", " auxiliary[3,7] 0.50 0.00 0.50 0.50 0.50 3.41 1.80\n", " auxiliary[3,8] 0.61 0.00 0.61 0.61 0.61 2.67 2.42\n", " auxiliary[3,9] 1.31 0.00 1.31 1.31 1.31 6.50 1.11\n", "auxiliary[3,10] 1.07 0.00 1.07 1.07 1.07 5.14 1.06\n", "auxiliary[3,11] 1.61 0.00 1.61 1.61 1.61 2.44 3.50\n", "auxiliary[3,12] 2.45 0.00 2.45 2.45 2.45 11.30 1.00\n", "auxiliary[3,13] 2.41 0.00 2.41 2.41 2.41 5.23 1.09\n", "auxiliary[3,14] 2.88 0.00 2.88 2.88 2.88 3.03 1.98\n", "auxiliary[3,15] 3.13 0.00 3.13 3.13 3.13 5.64 1.38\n", "auxiliary[3,16] 2.91 0.00 2.91 2.91 2.91 5.25 1.04\n", "auxiliary[3,17] 3.50 0.00 3.50 3.50 3.50 3.28 1.74\n", "auxiliary[3,18] 3.88 0.00 3.88 3.88 3.88 4.65 1.06\n", "auxiliary[3,19] 4.12 0.00 4.12 4.12 4.12 6.22 1.04\n", "auxiliary[3,20] 4.12 0.00 4.12 4.12 4.12 4.73 1.47\n", "auxiliary[3,21] 3.86 0.00 3.86 3.86 3.86 3.19 1.92\n", "auxiliary[3,22] 4.42 0.00 4.42 4.42 4.42 3.04 1.98\n", "auxiliary[3,23] 4.51 0.00 4.51 4.51 4.51 8.33 1.16\n", "auxiliary[3,24] 4.60 0.00 4.60 4.60 4.60 4.11 1.79\n", "auxiliary[3,25] 5.32 0.00 5.32 5.32 5.32 2.70 2.21\n", "auxiliary[3,26] 7.58 0.00 7.58 7.58 7.58 3.43 1.73\n", "auxiliary[3,27] 8.00 0.00 8.00 8.00 8.00 3.50 1.64\n", "auxiliary[3,28] 9.61 0.00 9.61 9.61 9.61 8.15 1.25\n", "auxiliary[3,29] 10.61 0.00 10.61 10.60 10.61 3.15 1.81\n", "auxiliary[3,30] 10.91 0.00 10.91 10.91 10.91 3.86 1.13\n", "auxiliary[3,31] 10.65 0.00 10.65 10.65 10.65 5.27 1.27\n", "auxiliary[3,32] 11.17 0.00 11.17 11.17 11.17 8.37 1.16\n", "auxiliary[3,33] 11.70 0.00 11.70 11.70 11.70 4.87 1.08\n", "auxiliary[3,34] 11.83 0.00 11.83 11.83 11.83 6.37 1.02\n", "auxiliary[3,35] 11.86 0.00 11.86 11.86 11.86 5.56 1.01\n", "auxiliary[3,36] 12.18 0.00 12.18 12.18 12.18 11.31 1.05\n", "auxiliary[3,37] 16.56 0.00 16.56 16.55 16.56 5.43 1.30\n", "auxiliary[3,38] 17.10 0.00 17.10 17.09 17.10 2.80 2.75\n", "auxiliary[3,39] 21.38 0.00 21.38 21.38 21.38 5.28 1.00\n", "auxiliary[3,40] 23.30 0.00 23.30 23.30 23.30 2.72 2.51\n", "auxiliary[3,41] 26.40 0.00 26.40 26.40 26.40 8.75 1.18\n", "auxiliary[3,42] 28.92 0.00 28.92 28.92 28.92 3.44 1.90\n", "auxiliary[3,43] 29.50 0.00 29.50 29.50 29.50 2.83 2.11\n", "auxiliary[3,44] 33.87 0.00 33.87 33.87 33.87 2.65 2.45\n", "auxiliary[3,45] 35.74 0.00 35.74 35.74 35.74 2.76 2.69\n", "auxiliary[3,46] 35.78 0.00 35.78 35.78 35.78 8.54 1.06\n", "auxiliary[3,47] 36.39 0.00 36.39 36.38 36.39 2.50 2.81\n", "auxiliary[3,48] 39.73 0.00 39.73 39.73 39.74 7.31 1.03\n", "auxiliary[3,49] 42.30 0.00 42.30 42.30 42.30 6.24 1.00\n", "auxiliary[3,50] 46.77 0.00 46.77 46.77 46.78 2.77 2.26\n", "auxiliary[3,51] 48.59 0.00 48.59 48.59 48.59 3.04 1.98\n", "auxiliary[3,52] 49.57 0.00 49.57 49.57 49.57 3.27 2.61\n", "auxiliary[3,53] 51.15 0.00 51.15 51.14 51.15 3.33 1.73\n", "auxiliary[3,54] 52.88 0.00 52.88 52.88 52.89 3.74 1.83\n", "auxiliary[3,55] 55.31 0.00 55.31 55.31 55.31 11.90 1.14\n", "auxiliary[3,56] 57.90 0.00 57.90 57.89 57.90 6.99 1.07\n", "auxiliary[3,57] 59.89 0.00 59.89 59.89 59.89 4.59 1.38\n", "auxiliary[3,58] 60.96 0.00 60.96 60.95 60.96 3.94 1.50\n", "auxiliary[3,59] 62.76 0.00 62.76 62.76 62.76 2.77 2.09\n", "auxiliary[3,60] 64.48 0.00 64.48 64.48 64.48 2.93 2.35\n", " incub_time 5.76 0.00 5.76 5.76 5.76 3.23 1.64\n", " mort_rate 0.02 0.00 0.02 0.02 0.02 3.67 1.75\n", " rec_rate 0.34 0.00 0.34 0.34 0.34 6.91 1.06\n", " rec_time 14.82 0.00 14.82 14.82 14.82 2.94 1.92\n", " rho 0.19 0.00 0.19 0.19 0.19 2.59 2.41\n", "\n", "Number of divergences: 0\n", "CPU times: user 3min 16s, sys: 1.16 s, total: 3min 17s\n", "Wall time: 3min 17s\n" ], "name": "stdout" } ] }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "bjxkg2oIC2oi", "outputId": "a33eab76-043c-4085-be99-92d2b770badc" }, "source": [ "%%time\n", "Japan_model = CovidModel(126500000, Japan[\"new_cases\"], Japan[\"new_recovered\"], Japan[\"new_deaths\"] )\n", "Japan_mcmc = Japan_model.fit_mcmc(num_samples=500, warmup_steps = 200)\n", "Japan_mcmc.summary()" ], "execution_count": null, "outputs": [ { "output_type": "stream", "text": [ "INFO \t Running inference...\n", "Warmup: 0%| | 0/700 [00:00, ?it/s]INFO \t Heuristic init: R0=1.92, incub_time=6.15, mort_rate=0.019, rec_rate=0.571, rec_time=14.9, rho=0.185\n", "Sample: 100%|██████████| 700/700 [03:14, 3.60it/s, step size=8.57e-05, acc. prob=0.897]\n" ], "name": "stderr" }, { "output_type": "stream", "text": [ "\n", " mean std median 5.0% 95.0% n_eff r_hat\n", " R0 1.92 0.00 1.92 1.92 1.92 2.54 2.62\n", " auxiliary[0,0] 126499876.90 0.82 126499876.77 126499875.87 126499877.80 2.34 4.23\n", " auxiliary[0,1] 126499777.08 0.42 126499777.28 126499776.40 126499777.53 2.55 2.58\n", " auxiliary[0,2] 126499662.89 0.20 126499662.94 126499662.55 126499663.17 2.74 2.25\n", " auxiliary[0,3] 126499555.96 0.22 126499556.03 126499555.65 126499556.29 2.48 2.79\n", " auxiliary[0,4] 126499440.88 0.19 126499440.94 126499440.49 126499441.14 2.89 2.15\n", " auxiliary[0,5] 126499322.65 0.26 126499322.74 126499322.23 126499322.99 2.78 2.09\n", " auxiliary[0,6] 126499198.40 0.29 126499198.55 126499197.83 126499198.70 2.70 2.48\n", " auxiliary[0,7] 126499088.87 0.31 126499088.79 126499088.51 126499089.34 2.38 3.08\n", " auxiliary[0,8] 126498989.71 0.61 126498989.85 126498988.75 126498990.41 2.49 2.64\n", " auxiliary[0,9] 126498884.78 0.51 126498884.95 126498884.01 126498885.35 2.58 2.45\n", "auxiliary[0,10] 126498769.17 0.41 126498769.29 126498768.53 126498769.73 2.67 2.30\n", "auxiliary[0,11] 126498657.95 0.32 126498657.91 126498657.43 126498658.40 2.59 2.68\n", "auxiliary[0,12] 126498552.61 0.22 126498552.63 126498552.20 126498552.96 3.39 1.81\n", "auxiliary[0,13] 126498443.47 0.34 126498443.48 126498442.98 126498444.09 4.60 1.48\n", "auxiliary[0,14] 126498331.42 0.29 126498331.59 126498331.00 126498331.76 2.58 2.87\n", "auxiliary[0,15] 126498219.22 0.44 126498219.34 126498218.29 126498219.65 3.37 1.75\n", "auxiliary[0,16] 126498105.58 0.34 126498105.63 126498105.09 126498106.11 2.68 2.25\n", "auxiliary[0,17] 126497991.99 0.43 126497992.18 126497991.31 126497992.56 2.77 2.11\n", "auxiliary[0,18] 126497877.34 0.22 126497877.38 126497876.94 126497877.68 3.20 1.87\n", "auxiliary[0,19] 126497761.70 0.44 126497761.95 126497761.07 126497762.26 2.87 2.05\n", "auxiliary[0,20] 126497644.25 0.60 126497644.57 126497643.08 126497644.80 2.89 1.93\n", "auxiliary[0,21] 126497517.41 0.42 126497517.37 126497516.82 126497518.11 2.75 2.23\n", "auxiliary[0,22] 126497381.98 0.35 126497381.95 126497381.33 126497382.46 4.85 1.13\n", "auxiliary[0,23] 126497249.07 0.31 126497249.12 126497248.57 126497249.53 4.71 1.87\n", "auxiliary[0,24] 126497112.97 0.34 126497112.92 126497112.34 126497113.41 3.39 2.16\n", "auxiliary[0,25] 126496974.51 0.85 126496974.82 126496973.28 126496975.60 2.48 2.96\n", "auxiliary[0,26] 126496828.54 0.28 126496828.59 126496828.07 126496828.91 6.55 1.30\n", "auxiliary[0,27] 126496675.09 0.36 126496675.21 126496674.44 126496675.48 3.25 1.54\n", "auxiliary[0,28] 126496517.02 0.30 126496517.03 126496516.46 126496517.41 5.68 1.23\n", "auxiliary[0,29] 126496359.39 0.47 126496359.65 126496358.73 126496359.97 2.87 2.05\n", "auxiliary[0,30] 126496193.52 0.53 126496193.52 126496192.81 126496194.35 2.67 2.39\n", "auxiliary[0,31] 126496016.58 0.53 126496016.80 126496015.53 126496017.11 3.36 1.64\n", "auxiliary[0,32] 126495826.36 0.61 126495826.53 126495825.37 126495827.18 3.28 1.72\n", "auxiliary[0,33] 126495624.80 0.40 126495624.77 126495624.36 126495625.56 8.52 1.05\n", "auxiliary[0,34] 126495412.78 0.66 126495412.90 126495411.61 126495413.59 2.90 1.97\n", "auxiliary[0,35] 126495204.81 0.77 126495204.92 126495203.68 126495205.86 2.51 3.39\n", "auxiliary[0,36] 126494985.16 0.43 126494985.17 126494984.50 126494985.84 5.99 1.27\n", "auxiliary[0,37] 126494756.74 0.67 126494756.66 126494755.46 126494757.85 5.79 1.35\n", "auxiliary[0,38] 126494505.92 0.62 126494506.01 126494505.04 126494506.89 2.98 2.11\n", "auxiliary[0,39] 126494250.80 0.48 126494250.85 126494250.02 126494251.51 4.50 1.01\n", "auxiliary[0,40] 126493995.17 1.53 126493995.21 126493992.96 126493997.47 2.62 2.52\n", "auxiliary[0,41] 126493716.43 0.30 126493716.42 126493715.99 126493716.97 5.09 1.20\n", "auxiliary[0,42] 126493434.02 1.07 126493433.73 126493432.15 126493435.33 2.70 2.60\n", "auxiliary[0,43] 126493145.30 0.34 126493145.28 126493144.74 126493145.84 8.06 1.01\n", "auxiliary[0,44] 126492851.62 1.03 126492852.06 126492849.91 126492852.96 2.71 2.39\n", "auxiliary[0,45] 126492552.12 0.58 126492552.16 126492551.21 126492553.05 5.76 1.31\n", "auxiliary[0,46] 126492253.04 0.84 126492253.02 126492251.95 126492254.60 3.65 2.02\n", "auxiliary[0,47] 126491920.66 0.64 126491920.62 126491919.67 126491921.59 5.81 1.12\n", "auxiliary[0,48] 126491602.23 0.68 126491602.35 126491601.04 126491603.29 8.10 1.05\n", "auxiliary[0,49] 126491266.34 0.88 126491266.19 126491265.16 126491267.96 5.96 1.29\n", "auxiliary[0,50] 126490897.70 0.37 126490897.75 126490897.11 126490898.27 15.07 1.04\n", "auxiliary[0,51] 126490511.81 0.43 126490511.85 126490511.09 126490512.47 13.28 1.18\n", "auxiliary[0,52] 126490130.25 2.22 126490131.39 126490126.51 126490132.64 2.93 2.00\n", "auxiliary[0,53] 126489694.01 1.03 126489694.35 126489692.32 126489695.32 3.55 1.68\n", "auxiliary[0,54] 126489255.99 0.66 126489256.05 126489255.10 126489257.10 7.52 1.17\n", "auxiliary[0,55] 126488824.54 1.70 126488824.21 126488822.58 126488828.12 3.06 2.07\n", "auxiliary[0,56] 126488360.36 1.84 126488360.59 126488357.35 126488362.80 2.64 2.22\n", "auxiliary[0,57] 126487923.05 3.31 126487922.64 126487918.67 126487928.06 2.49 2.95\n", "auxiliary[0,58] 126487552.34 5.90 126487550.45 126487545.31 126487562.72 2.69 2.25\n", "auxiliary[0,59] 126487187.30 5.19 126487187.42 126487181.38 126487195.74 2.48 3.02\n", "auxiliary[0,60] 126486818.38 6.57 126486816.97 126486810.09 126486828.59 2.50 2.84\n", " auxiliary[1,0] 119.67 0.77 119.52 118.70 120.52 2.35 4.19\n", " auxiliary[1,1] 200.64 0.31 200.75 200.14 200.95 2.53 2.58\n", " auxiliary[1,2] 263.74 0.16 263.78 263.50 263.96 2.47 2.66\n", " auxiliary[1,3] 317.88 0.03 317.88 317.85 317.93 2.76 3.42\n", " auxiliary[1,4] 372.42 0.14 372.44 372.22 372.60 2.48 2.69\n", " auxiliary[1,5] 419.12 0.12 419.14 418.94 419.28 2.46 2.76\n", " auxiliary[1,6] 469.83 0.12 469.81 469.64 470.02 2.65 2.58\n", " auxiliary[1,7] 495.43 0.19 495.49 495.12 495.66 2.89 1.97\n", " auxiliary[1,8] 503.70 0.05 503.71 503.61 503.76 2.86 2.52\n", " auxiliary[1,9] 531.60 0.08 531.60 531.45 531.69 2.83 2.42\n", "auxiliary[1,10] 571.12 0.07 571.10 571.02 571.23 3.05 2.13\n", "auxiliary[1,11] 578.16 0.08 578.15 578.03 578.27 3.47 1.98\n", "auxiliary[1,12] 585.42 0.06 585.42 585.33 585.51 3.97 1.59\n", "auxiliary[1,13] 599.58 0.12 599.55 599.38 599.74 2.64 2.66\n", "auxiliary[1,14] 622.55 0.06 622.53 622.46 622.67 7.99 1.21\n", "auxiliary[1,15] 634.46 0.04 634.46 634.39 634.52 10.33 1.15\n", "auxiliary[1,16] 652.67 0.04 652.67 652.62 652.75 6.75 1.07\n", "auxiliary[1,17] 663.18 0.09 663.18 663.09 663.33 4.56 1.49\n", "auxiliary[1,18] 669.22 0.14 669.27 669.02 669.39 2.47 3.09\n", "auxiliary[1,19] 646.58 0.02 646.58 646.55 646.61 25.80 1.02\n", "auxiliary[1,20] 648.11 0.08 648.12 647.97 648.23 4.32 1.50\n", "auxiliary[1,21] 674.61 0.10 674.61 674.46 674.77 3.09 2.16\n", "auxiliary[1,22] 701.62 0.05 701.61 701.52 701.69 5.55 1.23\n", "auxiliary[1,23] 720.43 0.06 720.42 720.34 720.51 3.81 1.78\n", "auxiliary[1,24] 722.47 0.12 722.52 722.29 722.64 2.67 2.30\n", "auxiliary[1,25] 714.99 0.05 715.00 714.91 715.07 9.96 1.08\n", "auxiliary[1,26] 736.28 0.05 736.28 736.21 736.37 6.19 1.11\n", "auxiliary[1,27] 784.56 0.10 784.58 784.42 784.71 2.68 2.57\n", "auxiliary[1,28] 808.66 0.10 808.65 808.53 808.80 2.85 2.81\n", "auxiliary[1,29] 822.80 0.14 822.81 822.57 822.99 2.84 2.29\n", "auxiliary[1,30] 856.48 0.05 856.50 856.41 856.56 5.20 1.65\n", "auxiliary[1,31] 891.73 0.09 891.73 891.55 891.87 6.05 1.46\n", "auxiliary[1,32] 938.54 0.05 938.53 938.48 938.63 9.86 1.02\n", "auxiliary[1,33] 988.65 0.06 988.65 988.57 988.76 7.03 1.11\n", "auxiliary[1,34] 1047.65 0.11 1047.65 1047.48 1047.85 5.79 1.23\n", "auxiliary[1,35] 1093.95 0.15 1093.92 1093.76 1094.20 2.73 2.55\n", "auxiliary[1,36] 1122.89 0.09 1122.89 1122.76 1123.06 5.30 1.06\n", "auxiliary[1,37] 1141.21 0.14 1141.24 1140.97 1141.40 3.62 1.48\n", "auxiliary[1,38] 1230.38 0.09 1230.37 1230.24 1230.53 10.03 1.00\n", "auxiliary[1,39] 1300.24 0.16 1300.23 1300.04 1300.50 2.84 2.34\n", "auxiliary[1,40] 1340.15 0.19 1340.14 1339.82 1340.44 3.41 1.78\n", "auxiliary[1,41] 1433.37 0.14 1433.34 1433.16 1433.59 3.02 2.30\n", "auxiliary[1,42] 1501.00 0.10 1501.00 1500.84 1501.14 4.83 1.68\n", "auxiliary[1,43] 1548.73 0.28 1548.84 1548.25 1549.03 3.58 1.55\n", "auxiliary[1,44] 1594.92 0.15 1594.88 1594.75 1595.19 6.40 1.24\n", "auxiliary[1,45] 1637.38 0.14 1637.39 1637.15 1637.62 6.96 1.05\n", "auxiliary[1,46] 1654.44 0.41 1654.36 1653.88 1654.96 2.43 4.56\n", "auxiliary[1,47] 1741.09 0.15 1741.07 1740.87 1741.37 8.00 1.75\n", "auxiliary[1,48] 1764.65 0.27 1764.66 1764.21 1765.03 2.69 2.53\n", "auxiliary[1,49] 1799.47 0.28 1799.49 1799.13 1799.85 2.47 4.28\n", "auxiliary[1,50] 1891.17 0.11 1891.18 1891.02 1891.33 11.07 1.06\n", "auxiliary[1,51] 1955.49 0.13 1955.47 1955.24 1955.66 6.95 1.33\n", "auxiliary[1,52] 2013.00 0.19 2013.04 2012.70 2013.25 3.38 2.10\n", "auxiliary[1,53] 2162.55 0.23 2162.52 2162.19 2162.89 2.82 2.15\n", "auxiliary[1,54] 2276.05 0.24 2276.01 2275.69 2276.49 4.48 1.07\n", "auxiliary[1,55] 2347.45 0.18 2347.48 2347.18 2347.75 7.34 1.11\n", "auxiliary[1,56] 2497.91 0.28 2497.82 2497.53 2498.34 2.77 2.08\n", "auxiliary[1,57] 2618.72 0.26 2618.67 2618.23 2619.11 5.26 1.22\n", "auxiliary[1,58] 2650.88 0.16 2650.87 2650.62 2651.11 12.28 1.00\n", "auxiliary[1,59] 2707.51 0.17 2707.51 2707.30 2707.88 7.00 1.22\n", "auxiliary[1,60] 2826.36 0.36 2826.36 2825.90 2826.93 3.45 1.84\n", " auxiliary[2,0] 0.50 0.00 0.50 0.50 0.50 2.79 2.43\n", " auxiliary[2,1] 11.37 0.00 11.37 11.37 11.37 14.76 1.23\n", " auxiliary[2,2] 52.14 0.01 52.14 52.12 52.15 2.64 2.41\n", " auxiliary[2,3] 93.27 0.03 93.27 93.24 93.31 2.45 2.69\n", " auxiliary[2,4] 140.85 0.01 140.86 140.83 140.87 2.99 1.95\n", " auxiliary[2,5] 198.73 0.02 198.73 198.70 198.76 5.45 1.25\n", " auxiliary[2,6] 256.96 0.02 256.95 256.94 257.00 4.48 1.37\n", " auxiliary[2,7] 323.34 0.12 323.38 323.13 323.47 2.53 2.63\n", " auxiliary[2,8] 394.09 0.07 394.12 393.95 394.15 4.01 1.27\n", " auxiliary[2,9] 449.64 0.07 449.64 449.56 449.75 2.60 3.44\n", "auxiliary[2,10] 502.90 0.07 502.93 502.79 502.99 3.80 1.44\n", "auxiliary[2,11] 581.17 0.03 581.17 581.13 581.22 18.64 1.00\n", "auxiliary[2,12] 647.27 0.17 647.37 647.03 647.46 2.49 2.84\n", "auxiliary[2,13] 708.39 0.13 708.36 708.20 708.56 2.71 3.10\n", "auxiliary[2,14] 756.90 0.11 756.94 756.74 757.05 2.96 2.34\n", "auxiliary[2,15] 814.43 0.20 814.39 814.14 814.70 2.52 2.64\n", "auxiliary[2,16] 861.36 0.07 861.35 861.24 861.47 6.14 1.37\n", "auxiliary[2,17] 911.55 0.09 911.58 911.40 911.67 5.68 1.77\n", "auxiliary[2,18] 953.68 0.15 953.76 953.43 953.85 2.80 2.13\n", "auxiliary[2,19] 1020.03 0.07 1020.05 1019.93 1020.12 8.46 1.20\n", "auxiliary[2,20] 1059.50 0.12 1059.48 1059.36 1059.70 7.73 1.27\n", "auxiliary[2,21] 1091.28 0.11 1091.29 1091.10 1091.43 3.54 1.61\n", "auxiliary[2,22] 1137.08 0.15 1137.14 1136.78 1137.25 3.35 1.71\n", "auxiliary[2,23] 1172.31 0.15 1172.29 1172.09 1172.54 5.31 1.29\n", "auxiliary[2,24] 1222.77 0.14 1222.77 1222.56 1222.98 2.89 2.40\n", "auxiliary[2,25] 1278.37 0.23 1278.33 1278.07 1278.74 2.65 2.22\n", "auxiliary[2,26] 1319.92 0.11 1319.90 1319.77 1320.09 5.05 1.09\n", "auxiliary[2,27] 1339.80 0.11 1339.84 1339.56 1339.91 6.00 1.31\n", "auxiliary[2,28] 1386.44 0.11 1386.45 1386.28 1386.62 3.32 2.27\n", "auxiliary[2,29] 1429.09 0.09 1429.09 1428.98 1429.30 9.64 1.02\n", "auxiliary[2,30] 1462.89 0.06 1462.90 1462.80 1462.99 18.80 1.03\n", "auxiliary[2,31] 1501.51 0.19 1501.57 1501.12 1501.74 4.83 1.16\n", "auxiliary[2,32] 1545.80 0.15 1545.71 1545.62 1546.03 3.07 1.81\n", "auxiliary[2,33] 1599.71 0.11 1599.68 1599.58 1599.95 8.47 1.25\n", "auxiliary[2,34] 1656.39 0.16 1656.39 1656.01 1656.58 8.59 1.21\n", "auxiliary[2,35] 1689.61 0.27 1689.54 1689.22 1690.10 3.30 1.62\n", "auxiliary[2,36] 1763.54 0.13 1763.52 1763.37 1763.70 8.41 1.12\n", "auxiliary[2,37] 1850.20 0.35 1850.11 1849.74 1850.74 2.51 2.81\n", "auxiliary[2,38] 1904.11 0.19 1904.09 1903.81 1904.40 3.17 1.84\n", "auxiliary[2,39] 1958.49 0.22 1958.45 1958.21 1958.84 3.47 2.52\n", "auxiliary[2,40] 2042.97 0.21 2043.02 2042.63 2043.27 4.45 1.30\n", "auxiliary[2,41] 2103.79 0.23 2103.71 2103.47 2104.20 3.74 1.83\n", "auxiliary[2,42] 2178.01 0.29 2178.09 2177.55 2178.40 2.59 2.55\n", "auxiliary[2,43] 2292.88 0.23 2292.88 2292.57 2293.30 3.78 1.72\n", "auxiliary[2,44] 2384.37 0.29 2384.41 2383.92 2384.79 2.80 2.24\n", "auxiliary[2,45] 2492.25 0.42 2492.24 2491.58 2492.84 2.87 2.37\n", "auxiliary[2,46] 2604.95 0.23 2604.98 2604.64 2605.30 4.98 1.02\n", "auxiliary[2,47] 2692.83 0.25 2692.92 2692.39 2693.14 3.41 1.70\n", "auxiliary[2,48] 2798.40 0.77 2798.63 2797.16 2799.34 2.68 2.25\n", "auxiliary[2,49] 2889.80 0.48 2889.50 2889.25 2890.57 2.67 2.34\n", "auxiliary[2,50] 2990.39 0.23 2990.41 2989.96 2990.71 6.07 1.39\n", "auxiliary[2,51] 3124.46 0.41 3124.46 3123.98 3125.03 3.06 2.70\n", "auxiliary[2,52] 3216.89 0.18 3216.89 3216.65 3217.19 11.36 1.02\n", "auxiliary[2,53] 3301.12 0.21 3301.12 3300.78 3301.43 14.39 1.12\n", "auxiliary[2,54] 3407.08 0.25 3407.09 3406.62 3407.47 6.91 1.08\n", "auxiliary[2,55] 3562.34 0.31 3562.29 3561.86 3562.81 3.38 1.83\n", "auxiliary[2,56] 3707.09 0.35 3707.03 3706.49 3707.68 7.33 1.02\n", "auxiliary[2,57] 3867.46 0.32 3867.47 3866.99 3867.97 4.94 1.28\n", "auxiliary[2,58] 4065.53 0.89 4065.49 4064.39 4066.71 2.48 3.47\n", "auxiliary[2,59] 4267.64 0.79 4267.50 4266.64 4268.75 2.41 3.45\n", "auxiliary[2,60] 4429.29 0.49 4429.19 4428.59 4430.09 3.85 2.00\n", " auxiliary[3,0] 0.57 0.00 0.57 0.57 0.57 3.11 2.02\n", " auxiliary[3,1] 0.63 0.00 0.63 0.63 0.63 2.59 2.95\n", " auxiliary[3,2] 0.86 0.00 0.86 0.86 0.86 3.96 1.70\n", " auxiliary[3,3] 0.63 0.00 0.63 0.62 0.63 3.33 1.83\n", " auxiliary[3,4] 0.66 0.00 0.66 0.66 0.66 6.21 1.37\n", " auxiliary[3,5] 0.50 0.00 0.50 0.50 0.50 8.56 1.21\n", " auxiliary[3,6] 0.50 0.00 0.50 0.50 0.50 6.54 1.34\n", " auxiliary[3,7] 0.73 0.00 0.73 0.73 0.73 6.14 1.50\n", " auxiliary[3,8] 1.25 0.00 1.25 1.25 1.25 5.38 1.83\n", " auxiliary[3,9] 1.30 0.00 1.30 1.30 1.30 3.33 1.86\n", "auxiliary[3,10] 1.40 0.00 1.40 1.40 1.40 18.60 1.13\n", "auxiliary[3,11] 1.26 0.00 1.26 1.26 1.26 3.06 1.90\n", "auxiliary[3,12] 2.06 0.00 2.06 2.06 2.06 2.81 2.56\n", "auxiliary[3,13] 2.22 0.00 2.22 2.22 2.22 3.18 1.94\n", "auxiliary[3,14] 2.27 0.00 2.27 2.27 2.27 3.23 2.05\n", "auxiliary[3,15] 2.18 0.00 2.18 2.18 2.18 12.88 1.02\n", "auxiliary[3,16] 2.40 0.00 2.40 2.40 2.40 3.44 2.47\n", "auxiliary[3,17] 2.28 0.00 2.28 2.28 2.28 5.31 1.24\n", "auxiliary[3,18] 2.68 0.00 2.68 2.67 2.68 3.25 2.05\n", "auxiliary[3,19] 2.67 0.00 2.67 2.67 2.67 6.52 1.42\n", "auxiliary[3,20] 3.06 0.00 3.06 3.06 3.06 3.34 1.73\n", "auxiliary[3,21] 2.53 0.00 2.53 2.53 2.53 3.56 1.88\n", "auxiliary[3,22] 2.72 0.00 2.72 2.72 2.72 2.59 2.75\n", "auxiliary[3,23] 2.61 0.00 2.61 2.61 2.62 2.85 2.03\n", "auxiliary[3,24] 3.06 0.00 3.06 3.06 3.06 3.40 2.28\n", "auxiliary[3,25] 4.05 0.00 4.05 4.05 4.05 4.54 1.62\n", "auxiliary[3,26] 6.14 0.00 6.14 6.14 6.14 8.62 1.40\n", "auxiliary[3,27] 6.51 0.00 6.51 6.51 6.51 5.10 1.18\n", "auxiliary[3,28] 7.49 0.00 7.49 7.49 7.49 4.53 1.57\n", "auxiliary[3,29] 8.77 0.00 8.77 8.77 8.78 3.52 1.59\n", "auxiliary[3,30] 8.46 0.00 8.46 8.46 8.46 2.43 3.13\n", "auxiliary[3,31] 8.15 0.00 8.15 8.15 8.16 3.19 2.04\n", "auxiliary[3,32] 7.83 0.00 7.83 7.83 7.83 2.63 2.44\n", "auxiliary[3,33] 8.07 0.00 8.07 8.07 8.07 2.88 2.26\n", "auxiliary[3,34] 8.33 0.00 8.33 8.33 8.33 14.35 1.00\n", "auxiliary[3,35] 8.16 0.00 8.16 8.16 8.16 7.33 1.01\n", "auxiliary[3,36] 8.44 0.00 8.44 8.44 8.45 2.44 2.93\n", "auxiliary[3,37] 11.94 0.00 11.94 11.94 11.95 3.24 1.82\n", "auxiliary[3,38] 12.74 0.00 12.74 12.73 12.75 2.78 2.17\n", "auxiliary[3,39] 17.07 0.01 17.07 17.06 17.08 2.55 2.82\n", "auxiliary[3,40] 18.54 0.00 18.54 18.54 18.54 3.77 1.42\n", "auxiliary[3,41] 21.02 0.00 21.02 21.02 21.02 11.63 1.00\n", "auxiliary[3,42] 23.18 0.01 23.18 23.17 23.19 2.57 2.54\n", "auxiliary[3,43] 24.44 0.01 24.45 24.43 24.46 2.47 2.75\n", "auxiliary[3,44] 27.48 0.01 27.48 27.46 27.49 2.63 2.46\n", "auxiliary[3,45] 29.43 0.01 29.44 29.42 29.44 2.42 2.91\n", "auxiliary[3,46] 30.15 0.00 30.15 30.15 30.16 6.68 1.39\n", "auxiliary[3,47] 31.19 0.02 31.19 31.17 31.22 2.49 2.61\n", "auxiliary[3,48] 33.96 0.00 33.96 33.96 33.97 3.66 1.58\n", "auxiliary[3,49] 37.30 0.00 37.30 37.30 37.30 15.05 1.16\n", "auxiliary[3,50] 40.71 0.01 40.71 40.70 40.73 2.59 3.85\n", "auxiliary[3,51] 43.19 0.01 43.19 43.17 43.20 3.21 1.89\n", "auxiliary[3,52] 44.98 0.01 44.98 44.97 44.99 2.53 2.64\n", "auxiliary[3,53] 46.76 0.01 46.76 46.75 46.77 2.85 2.20\n", "auxiliary[3,54] 48.64 0.00 48.64 48.63 48.65 7.05 1.26\n", "auxiliary[3,55] 50.64 0.00 50.65 50.64 50.65 3.98 1.26\n", "auxiliary[3,56] 52.71 0.01 52.71 52.70 52.72 4.00 1.51\n", "auxiliary[3,57] 54.50 0.00 54.50 54.49 54.50 6.49 1.64\n", "auxiliary[3,58] 56.01 0.01 56.01 56.00 56.03 2.67 2.48\n", "auxiliary[3,59] 57.35 0.00 57.35 57.35 57.36 8.62 1.29\n", "auxiliary[3,60] 58.46 0.01 58.46 58.45 58.47 8.26 1.22\n", " incub_time 6.15 0.00 6.15 6.15 6.15 4.40 1.62\n", " mort_rate 0.02 0.00 0.02 0.02 0.02 2.70 2.40\n", " rec_rate 0.57 0.00 0.57 0.57 0.57 8.39 1.03\n", " rec_time 14.86 0.00 14.86 14.86 14.87 10.36 1.22\n", " rho 0.20 0.00 0.20 0.20 0.20 2.41 3.03\n", "\n", "Number of divergences: 0\n", "CPU times: user 3min 13s, sys: 1.18 s, total: 3min 14s\n", "Wall time: 3min 14s\n" ], "name": "stdout" } ] }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "w0K54sVQC2ea", "outputId": "5a312f61-e87e-4501-a263-f72b096e1f6d" }, "source": [ "%%time\n", "Japan_model = CovidModel(126500000, Japan[\"new_cases\"], Japan[\"new_recovered\"], Japan[\"new_deaths\"] )\n", "Japan_mcmc = Japan_model.fit_mcmc(num_samples=500, warmup_steps = 200)\n", "Japan_mcmc.summary()" ], "execution_count": null, "outputs": [ { "output_type": "stream", "text": [ "INFO \t Running inference...\n", "Warmup: 0%| | 0/700 [00:00, ?it/s]INFO \t Heuristic init: R0=1.99, incub_time=3.9, mort_rate=0.106, rec_rate=0.607, rec_time=16, rho=0.166\n", "Sample: 100%|██████████| 700/700 [03:09, 3.70it/s, step size=4.61e-03, acc. prob=0.926]\n" ], "name": "stderr" }, { "output_type": "stream", "text": [ "\n", " mean std median 5.0% 95.0% n_eff r_hat\n", " R0 1.86 0.08 1.85 1.73 1.97 2.50 2.66\n", " auxiliary[0,0] 126499854.58 1.51 126499855.07 126499851.89 126499856.13 3.32 1.69\n", " auxiliary[0,1] 126499717.84 5.86 126499716.51 126499710.19 126499725.92 2.58 2.41\n", " auxiliary[0,2] 126499576.41 10.26 126499576.34 126499560.94 126499591.70 2.51 2.65\n", " auxiliary[0,3] 126499432.41 18.40 126499431.39 126499407.07 126499460.12 2.57 2.48\n", " auxiliary[0,4] 126499285.99 29.02 126499281.96 126499247.42 126499330.47 2.65 2.34\n", " auxiliary[0,5] 126499138.43 40.51 126499130.06 126499087.96 126499202.12 2.68 2.28\n", " auxiliary[0,6] 126498989.77 53.18 126498974.02 126498922.86 126499074.76 2.69 2.26\n", " auxiliary[0,7] 126498841.09 66.55 126498820.29 126498762.06 126498953.46 2.73 2.21\n", " auxiliary[0,8] 126498692.21 80.89 126498665.32 126498594.94 126498825.49 2.77 2.17\n", " auxiliary[0,9] 126498542.69 95.65 126498511.57 126498429.29 126498702.61 2.80 2.14\n", "auxiliary[0,10] 126498391.67 110.93 126498355.10 126498259.08 126498576.75 2.83 2.11\n", "auxiliary[0,11] 126498239.80 126.09 126498199.35 126498089.90 126498453.89 2.84 2.10\n", "auxiliary[0,12] 126498086.66 141.08 126498039.99 126497922.49 126498325.07 2.86 2.07\n", "auxiliary[0,13] 126497931.56 156.64 126497878.04 126497750.77 126498197.40 2.88 2.05\n", "auxiliary[0,14] 126497774.75 172.26 126497717.59 126497577.13 126498070.25 2.90 2.03\n", "auxiliary[0,15] 126497616.55 187.80 126497556.27 126497401.14 126497937.73 2.93 2.01\n", "auxiliary[0,16] 126497457.74 202.41 126497393.34 126497225.96 126497803.61 2.96 1.99\n", "auxiliary[0,17] 126497295.69 216.50 126497227.78 126497048.82 126497664.80 2.98 1.97\n", "auxiliary[0,18] 126497129.74 229.39 126497056.40 126496870.28 126497525.37 2.99 1.96\n", "auxiliary[0,19] 126496961.80 241.19 126496884.78 126496688.26 126497382.57 3.01 1.95\n", "auxiliary[0,20] 126496790.79 251.17 126496711.50 126496504.42 126497226.32 3.02 1.95\n", "auxiliary[0,21] 126496616.54 259.88 126496535.78 126496318.23 126497067.38 3.03 1.94\n", "auxiliary[0,22] 126496438.23 266.69 126496357.44 126496132.85 126496899.12 3.03 1.94\n", "auxiliary[0,23] 126496257.13 272.45 126496177.23 126495942.79 126496730.03 3.03 1.95\n", "auxiliary[0,24] 126496071.02 276.80 126495992.46 126495754.05 126496550.21 3.03 1.95\n", "auxiliary[0,25] 126495881.77 280.06 126495805.85 126495558.24 126496363.05 3.04 1.95\n", "auxiliary[0,26] 126495688.02 280.94 126495616.66 126495353.65 126496166.87 3.04 1.96\n", "auxiliary[0,27] 126495488.42 279.69 126495422.09 126495148.30 126495956.95 3.03 1.97\n", "auxiliary[0,28] 126495285.07 276.04 126495224.02 126494940.69 126495738.22 3.01 1.99\n", "auxiliary[0,29] 126495076.58 271.85 126495023.33 126494729.36 126495519.30 2.98 2.01\n", "auxiliary[0,30] 126494864.82 266.34 126494816.24 126494515.42 126495292.99 2.94 2.05\n", "auxiliary[0,31] 126494646.93 259.32 126494603.60 126494298.03 126495054.04 2.90 2.09\n", "auxiliary[0,32] 126494424.95 250.36 126494388.88 126494078.09 126494808.20 2.85 2.14\n", "auxiliary[0,33] 126494197.16 240.26 126494167.88 126493857.18 126494554.49 2.79 2.22\n", "auxiliary[0,34] 126493963.42 227.82 126493946.74 126493628.47 126494281.85 2.72 2.32\n", "auxiliary[0,35] 126493724.14 215.08 126493718.15 126493396.83 126493999.91 2.64 2.44\n", "auxiliary[0,36] 126493479.30 199.58 126493485.55 126493157.28 126493705.31 2.56 2.61\n", "auxiliary[0,37] 126493229.43 184.96 126493236.82 126492921.29 126493419.30 2.49 2.77\n", "auxiliary[0,38] 126492972.15 168.51 126492987.50 126492694.48 126493163.18 2.45 2.93\n", "auxiliary[0,39] 126492709.93 153.03 126492734.03 126492466.92 126492901.91 2.45 2.97\n", "auxiliary[0,40] 126492445.09 140.85 126492474.80 126492231.54 126492637.23 2.52 2.78\n", "auxiliary[0,41] 126492173.96 130.44 126492175.44 126491980.16 126492368.78 2.74 2.34\n", "auxiliary[0,42] 126491898.03 125.24 126491879.80 126491725.62 126492092.89 3.28 1.81\n", "auxiliary[0,43] 126491616.66 128.08 126491603.55 126491442.50 126491811.30 4.25 1.40\n", "auxiliary[0,44] 126491331.30 136.59 126491326.93 126491175.15 126491522.66 5.51 1.16\n", "auxiliary[0,45] 126491044.39 152.02 126491050.80 126490904.64 126491226.98 6.62 1.05\n", "auxiliary[0,46] 126490754.42 172.78 126490775.28 126490581.22 126490930.18 7.34 1.00\n", "auxiliary[0,47] 126490457.91 198.69 126490497.34 126490247.12 126490627.94 7.67 1.00\n", "auxiliary[0,48] 126490160.39 228.08 126490219.30 126489908.13 126490332.71 7.64 1.03\n", "auxiliary[0,49] 126489859.23 260.82 126489939.01 126489560.39 126490036.25 7.37 1.07\n", "auxiliary[0,50] 126489556.45 295.02 126489660.96 126489201.66 126489741.30 6.88 1.11\n", "auxiliary[0,51] 126489250.27 332.18 126489380.33 126488825.36 126489448.47 6.37 1.15\n", "auxiliary[0,52] 126488943.65 372.62 126489099.61 126488445.64 126489161.73 5.94 1.19\n", "auxiliary[0,53] 126488638.46 413.54 126488820.35 126488057.64 126488872.46 5.58 1.23\n", "auxiliary[0,54] 126488336.24 453.06 126488540.02 126487674.41 126488590.89 5.36 1.25\n", "auxiliary[0,55] 126488035.35 494.35 126488264.51 126487305.06 126488310.50 5.24 1.27\n", "auxiliary[0,56] 126487735.84 535.40 126487983.98 126486941.71 126488030.77 5.20 1.27\n", "auxiliary[0,57] 126487438.38 573.10 126487706.07 126486582.32 126487751.03 5.21 1.28\n", "auxiliary[0,58] 126487146.41 605.19 126487429.72 126486250.22 126487472.60 5.23 1.28\n", "auxiliary[0,59] 126486860.10 629.71 126487154.70 126485934.94 126487197.26 5.25 1.28\n", "auxiliary[0,60] 126486580.74 647.21 126486882.20 126485633.62 126486928.09 5.27 1.27\n", " auxiliary[1,0] 131.51 1.76 130.94 129.76 134.63 3.34 1.70\n", " auxiliary[1,1] 220.81 4.81 221.94 213.82 226.66 2.55 2.43\n", " auxiliary[1,2] 273.82 3.72 272.70 268.77 280.29 2.89 2.08\n", " auxiliary[1,3] 293.31 3.34 292.85 288.26 297.47 4.84 1.00\n", " auxiliary[1,4] 321.69 3.31 321.26 316.29 326.53 4.85 1.05\n", " auxiliary[1,5] 351.57 4.73 349.95 346.97 360.32 4.13 1.38\n", " auxiliary[1,6] 372.48 5.35 370.59 367.22 381.07 3.89 1.53\n", " auxiliary[1,7] 391.80 3.58 390.78 387.86 396.99 4.57 1.45\n", " auxiliary[1,8] 404.10 5.45 401.98 397.77 413.94 4.51 1.32\n", " auxiliary[1,9] 409.98 4.58 408.12 405.81 416.30 5.18 1.25\n", "auxiliary[1,10] 417.59 4.03 417.35 412.13 423.02 4.24 1.62\n", "auxiliary[1,11] 413.42 7.40 409.47 406.35 426.26 3.22 1.69\n", "auxiliary[1,12] 414.33 3.56 413.10 410.09 419.99 3.77 1.65\n", "auxiliary[1,13] 436.82 3.58 436.03 431.24 441.63 3.39 1.81\n", "auxiliary[1,14] 448.62 3.10 448.62 444.52 453.57 4.83 1.00\n", "auxiliary[1,15] 446.39 2.37 446.49 442.82 451.00 5.89 1.37\n", "auxiliary[1,16] 429.81 1.65 429.52 426.84 432.50 5.10 1.36\n", "auxiliary[1,17] 438.88 2.04 438.19 436.34 442.41 4.14 1.45\n", "auxiliary[1,18] 477.90 4.18 476.48 471.84 483.43 2.62 3.33\n", "auxiliary[1,19] 490.35 6.26 488.88 482.35 500.35 2.63 2.38\n", "auxiliary[1,20] 505.19 1.80 504.91 502.65 508.15 6.34 1.07\n", "auxiliary[1,21] 519.78 4.20 518.73 514.76 527.38 4.02 1.55\n", "auxiliary[1,22] 554.18 2.67 554.14 550.24 558.53 5.36 1.35\n", "auxiliary[1,23] 562.54 3.69 561.51 557.83 567.69 3.69 1.71\n", "auxiliary[1,24] 601.79 6.76 601.42 591.77 611.88 2.56 2.70\n", "auxiliary[1,25] 618.34 5.09 618.99 610.92 625.74 2.59 3.11\n", "auxiliary[1,26] 642.81 7.44 642.17 631.65 655.49 2.88 2.10\n", "auxiliary[1,27] 704.51 7.30 703.94 694.67 717.66 2.79 2.23\n", "auxiliary[1,28] 738.56 9.17 738.24 726.32 751.93 2.47 2.74\n", "auxiliary[1,29] 785.73 11.06 781.84 770.04 800.80 2.41 3.13\n", "auxiliary[1,30] 800.40 10.75 799.65 784.96 814.91 2.58 2.60\n", "auxiliary[1,31] 841.49 11.32 840.45 822.70 855.90 2.61 2.49\n", "auxiliary[1,32] 862.47 9.12 859.22 849.76 877.96 2.71 2.45\n", "auxiliary[1,33] 910.24 13.30 912.75 886.22 927.03 2.73 2.28\n", "auxiliary[1,34] 962.04 11.07 967.57 939.70 972.14 3.28 1.72\n", "auxiliary[1,35] 1008.92 19.78 1007.14 979.70 1038.61 2.66 2.29\n", "auxiliary[1,36] 1043.74 10.64 1043.50 1026.47 1058.45 2.92 2.20\n", "auxiliary[1,37] 1077.75 14.69 1084.51 1056.82 1099.67 2.61 2.63\n", "auxiliary[1,38] 1147.11 13.77 1149.16 1129.05 1165.90 2.42 2.94\n", "auxiliary[1,39] 1209.68 7.58 1212.04 1198.05 1220.48 4.77 1.38\n", "auxiliary[1,40] 1241.41 16.13 1244.02 1216.34 1264.89 2.69 2.28\n", "auxiliary[1,41] 1293.38 15.90 1301.34 1261.24 1309.99 3.12 1.84\n", "auxiliary[1,42] 1342.29 10.31 1341.26 1327.85 1359.26 3.34 1.47\n", "auxiliary[1,43] 1396.57 13.25 1402.00 1368.68 1408.51 4.03 1.38\n", "auxiliary[1,44] 1456.05 15.95 1456.45 1431.02 1478.27 4.80 1.04\n", "auxiliary[1,45] 1485.00 16.75 1490.50 1450.56 1503.03 4.82 1.12\n", "auxiliary[1,46] 1510.97 12.71 1507.38 1492.34 1531.56 4.16 1.91\n", "auxiliary[1,47] 1592.11 15.08 1586.18 1575.13 1620.30 4.42 1.43\n", "auxiliary[1,48] 1653.84 19.54 1645.06 1632.27 1687.13 3.78 1.76\n", "auxiliary[1,49] 1738.46 15.24 1744.69 1718.44 1757.44 3.91 1.27\n", "auxiliary[1,50] 1812.81 13.85 1814.12 1788.85 1832.00 3.97 1.48\n", "auxiliary[1,51] 1913.17 10.40 1913.15 1899.11 1931.89 10.46 1.02\n", "auxiliary[1,52] 2010.52 17.33 2010.06 1976.81 2034.33 3.36 2.01\n", "auxiliary[1,53] 2086.25 40.25 2086.51 2027.77 2144.82 2.42 3.17\n", "auxiliary[1,54] 2134.85 34.81 2136.55 2083.08 2188.77 2.98 2.00\n", "auxiliary[1,55] 2179.17 42.93 2180.94 2115.62 2241.31 2.58 2.44\n", "auxiliary[1,56] 2251.56 50.62 2248.86 2180.31 2328.21 2.50 2.66\n", "auxiliary[1,57] 2370.78 60.53 2371.00 2292.83 2471.61 2.48 2.65\n", "auxiliary[1,58] 2448.53 90.48 2451.27 2326.05 2600.23 2.58 2.44\n", "auxiliary[1,59] 2478.43 119.54 2459.28 2302.03 2666.25 2.61 2.43\n", "auxiliary[1,60] 2412.11 169.85 2381.46 2190.29 2687.84 2.65 2.37\n", " auxiliary[2,0] 0.76 0.02 0.76 0.73 0.79 2.48 2.66\n", " auxiliary[2,1] 32.29 0.40 32.28 31.75 32.99 2.95 2.19\n", " auxiliary[2,2] 82.90 1.06 82.76 81.38 84.77 3.00 1.89\n", " auxiliary[2,3] 159.85 2.94 159.05 156.07 164.77 2.55 2.42\n", " auxiliary[2,4] 223.82 1.63 223.32 221.88 226.23 5.28 1.01\n", " auxiliary[2,5] 283.21 2.26 283.68 279.48 286.11 4.68 1.35\n", " auxiliary[2,6] 349.30 3.51 349.29 343.76 353.98 5.81 1.02\n", " auxiliary[2,7] 412.70 6.85 410.52 405.50 424.45 4.30 1.21\n", " auxiliary[2,8] 480.03 6.78 478.64 470.75 490.13 3.87 1.50\n", " auxiliary[2,9] 550.54 9.00 545.98 541.53 566.01 3.27 1.65\n", "auxiliary[2,10] 618.62 11.33 613.82 608.01 637.80 3.53 1.46\n", "auxiliary[2,11] 695.60 8.94 692.32 687.07 707.41 4.66 1.32\n", "auxiliary[2,12] 764.58 14.05 758.47 751.35 789.84 4.02 1.43\n", "auxiliary[2,13] 811.72 14.13 805.32 799.27 836.14 4.28 1.39\n", "auxiliary[2,14] 869.48 14.02 865.11 854.27 890.30 3.68 1.60\n", "auxiliary[2,15] 940.38 10.81 936.33 927.95 957.86 4.42 1.31\n", "auxiliary[2,16] 1022.77 7.45 1019.91 1014.22 1035.75 4.61 1.28\n", "auxiliary[2,17] 1081.35 6.26 1080.25 1072.66 1095.11 4.87 1.10\n", "auxiliary[2,18] 1112.46 9.48 1112.43 1100.36 1127.57 2.91 2.14\n", "auxiliary[2,19] 1171.59 5.40 1169.70 1165.05 1182.00 4.42 1.31\n", "auxiliary[2,20] 1231.31 13.49 1228.35 1212.30 1251.70 2.77 2.19\n", "auxiliary[2,21] 1294.27 15.22 1292.05 1272.71 1318.29 2.75 2.15\n", "auxiliary[2,22] 1341.16 23.32 1334.94 1309.44 1377.33 2.62 2.36\n", "auxiliary[2,23] 1417.76 21.78 1412.99 1389.67 1452.36 2.55 2.73\n", "auxiliary[2,24] 1469.01 20.91 1463.76 1441.04 1500.42 2.49 2.84\n", "auxiliary[2,25] 1546.55 27.37 1539.75 1514.07 1595.74 2.52 2.58\n", "auxiliary[2,26] 1621.20 28.46 1611.49 1584.04 1663.70 2.43 2.94\n", "auxiliary[2,27] 1664.97 31.65 1655.93 1621.20 1711.80 2.47 2.81\n", "auxiliary[2,28] 1741.70 31.57 1733.09 1699.96 1791.79 2.56 2.54\n", "auxiliary[2,29] 1810.94 33.27 1804.19 1765.71 1862.05 2.55 2.48\n", "auxiliary[2,30] 1916.54 37.81 1909.12 1866.51 1977.04 2.49 2.60\n", "auxiliary[2,31] 2001.86 42.39 1999.87 1943.52 2068.61 2.52 2.64\n", "auxiliary[2,32] 2112.20 49.16 2115.53 2038.00 2181.41 2.54 2.54\n", "auxiliary[2,33] 2201.66 49.52 2201.44 2137.16 2282.04 2.46 2.72\n", "auxiliary[2,34] 2294.06 55.86 2289.24 2221.05 2377.26 2.41 2.87\n", "auxiliary[2,35] 2397.76 50.34 2400.55 2326.66 2465.14 2.43 2.85\n", "auxiliary[2,36] 2520.85 60.33 2526.25 2433.96 2602.18 2.43 2.75\n", "auxiliary[2,37] 2650.17 57.67 2654.12 2564.51 2728.26 2.49 2.62\n", "auxiliary[2,38] 2752.65 57.04 2765.97 2657.62 2817.20 2.57 2.49\n", "auxiliary[2,39] 2866.72 63.69 2882.00 2762.74 2942.79 2.50 2.58\n", "auxiliary[2,40] 3014.60 55.79 3041.00 2906.92 3069.06 2.75 2.16\n", "auxiliary[2,41] 3149.22 55.51 3173.10 3043.07 3207.30 2.83 2.03\n", "auxiliary[2,42] 3292.12 61.57 3316.26 3169.17 3359.13 3.25 1.77\n", "auxiliary[2,43] 3436.95 51.61 3465.13 3334.30 3484.82 3.26 1.68\n", "auxiliary[2,44] 3580.70 48.61 3601.57 3468.33 3620.01 3.59 1.55\n", "auxiliary[2,45] 3757.18 46.57 3774.89 3666.60 3801.92 4.85 1.19\n", "auxiliary[2,46] 3940.64 57.91 3958.80 3829.71 3999.43 4.88 1.15\n", "auxiliary[2,47] 4076.89 51.32 4088.90 4004.71 4131.14 6.23 1.01\n", "auxiliary[2,48] 4235.15 51.04 4250.66 4175.15 4302.24 5.77 1.03\n", "auxiliary[2,49] 4375.83 61.08 4368.37 4297.24 4477.85 4.25 1.48\n", "auxiliary[2,50] 4529.82 79.02 4520.87 4426.00 4654.01 3.09 2.00\n", "auxiliary[2,51] 4662.73 109.85 4659.80 4516.51 4829.51 2.56 2.64\n", "auxiliary[2,52] 4800.01 128.54 4798.60 4628.50 4994.88 2.51 2.74\n", "auxiliary[2,53] 4958.29 137.40 4931.54 4779.08 5176.93 2.51 2.66\n", "auxiliary[2,54] 5141.15 176.99 5087.48 4913.23 5412.03 2.47 2.80\n", "auxiliary[2,55] 5327.42 201.71 5267.30 5068.32 5643.08 2.53 2.54\n", "auxiliary[2,56] 5484.29 226.80 5411.40 5212.86 5861.56 2.62 2.35\n", "auxiliary[2,57] 5592.17 248.62 5503.67 5310.55 6030.36 2.74 2.18\n", "auxiliary[2,58] 5735.82 245.14 5632.09 5469.43 6166.84 2.83 2.07\n", "auxiliary[2,59] 5921.28 235.71 5825.73 5681.28 6341.15 2.93 1.97\n", "auxiliary[2,60] 6195.87 198.62 6108.21 5998.94 6546.83 3.03 1.86\n", " auxiliary[3,0] 0.47 0.01 0.46 0.45 0.49 3.60 1.68\n", " auxiliary[3,1] 0.49 0.00 0.49 0.49 0.50 9.15 1.08\n", " auxiliary[3,2] 0.51 0.01 0.51 0.50 0.53 2.67 2.92\n", " auxiliary[3,3] 0.93 0.02 0.93 0.89 0.96 2.57 2.66\n", " auxiliary[3,4] 1.13 0.01 1.13 1.12 1.15 5.31 1.02\n", " auxiliary[3,5] 1.15 0.02 1.15 1.13 1.18 2.44 2.86\n", " auxiliary[3,6] 1.17 0.01 1.17 1.15 1.19 3.21 2.49\n", " auxiliary[3,7] 1.39 0.01 1.39 1.38 1.41 4.12 1.81\n", " auxiliary[3,8] 1.51 0.01 1.51 1.50 1.53 3.00 2.81\n", " auxiliary[3,9] 1.71 0.07 1.72 1.60 1.81 2.54 2.46\n", "auxiliary[3,10] 1.37 0.08 1.37 1.23 1.48 2.52 2.65\n", "auxiliary[3,11] 1.90 0.07 1.91 1.78 2.00 2.65 2.38\n", "auxiliary[3,12] 2.99 0.18 2.93 2.76 3.27 2.71 2.28\n", "auxiliary[3,13] 3.50 0.12 3.49 3.34 3.66 2.36 3.29\n", "auxiliary[3,14] 3.80 0.10 3.78 3.67 3.96 2.61 2.46\n", "auxiliary[3,15] 3.88 0.04 3.88 3.82 3.93 2.80 2.17\n", "auxiliary[3,16] 3.88 0.02 3.88 3.84 3.91 4.39 1.39\n", "auxiliary[3,17] 3.88 0.11 3.93 3.70 3.99 2.74 2.07\n", "auxiliary[3,18] 4.05 0.11 4.05 3.89 4.21 2.63 2.44\n", "auxiliary[3,19] 4.39 0.04 4.39 4.33 4.46 3.85 1.14\n", "auxiliary[3,20] 4.81 0.03 4.81 4.77 4.86 6.01 1.00\n", "auxiliary[3,21] 5.21 0.06 5.18 5.11 5.31 2.91 2.23\n", "auxiliary[3,22] 5.70 0.11 5.68 5.57 5.87 2.75 2.05\n", "auxiliary[3,23] 6.20 0.25 6.20 5.81 6.57 2.54 2.51\n", "auxiliary[3,24] 6.91 0.47 6.95 6.19 7.65 2.76 2.23\n", "auxiliary[3,25] 8.04 0.43 7.96 7.37 8.71 2.58 2.54\n", "auxiliary[3,26] 9.44 0.40 9.34 8.97 10.07 2.62 2.38\n", "auxiliary[3,27] 10.87 0.50 10.72 10.23 11.64 2.53 2.61\n", "auxiliary[3,28] 12.40 0.69 12.32 11.53 13.42 2.38 3.16\n", "auxiliary[3,29] 14.05 0.98 14.21 12.58 15.26 2.43 2.89\n", "auxiliary[3,30] 15.84 1.28 16.31 13.70 17.30 2.61 2.39\n", "auxiliary[3,31] 17.78 1.55 18.46 15.08 19.24 2.89 2.00\n", "auxiliary[3,32] 19.93 1.64 20.76 16.87 21.23 3.24 1.74\n", "auxiliary[3,33] 22.27 1.56 23.09 19.23 23.35 3.77 1.49\n", "auxiliary[3,34] 24.71 1.35 25.27 22.15 25.65 4.88 1.22\n", "auxiliary[3,35] 27.27 1.11 27.48 25.70 28.29 6.43 1.01\n", "auxiliary[3,36] 29.88 1.05 29.92 28.66 31.35 5.28 1.22\n", "auxiliary[3,37] 32.54 1.42 32.41 30.66 34.79 2.88 2.18\n", "auxiliary[3,38] 35.20 2.15 34.98 32.32 38.62 2.47 2.79\n", "auxiliary[3,39] 37.84 3.09 37.20 33.63 42.49 2.50 2.63\n", "auxiliary[3,40] 40.43 4.15 39.30 35.20 47.46 2.62 2.37\n", "auxiliary[3,41] 42.94 5.27 41.36 36.72 52.19 2.76 2.18\n", "auxiliary[3,42] 45.37 6.41 43.33 38.23 56.53 2.89 2.04\n", "auxiliary[3,43] 47.70 7.53 45.18 39.71 60.59 3.01 1.95\n", "auxiliary[3,44] 49.92 8.60 46.95 41.07 64.32 3.11 1.88\n", "auxiliary[3,45] 52.01 9.62 48.61 42.35 67.84 3.21 1.82\n", "auxiliary[3,46] 54.00 10.57 50.22 43.67 71.19 3.29 1.78\n", "auxiliary[3,47] 55.89 11.45 51.78 44.98 74.34 3.36 1.75\n", "auxiliary[3,48] 57.67 12.24 53.16 46.15 77.10 3.42 1.72\n", "auxiliary[3,49] 59.33 12.93 54.57 47.34 79.69 3.47 1.70\n", "auxiliary[3,50] 60.89 13.54 55.88 48.45 81.99 3.51 1.69\n", "auxiliary[3,51] 62.34 14.05 57.10 49.52 84.11 3.55 1.68\n", "auxiliary[3,52] 63.67 14.45 58.22 50.60 85.99 3.57 1.67\n", "auxiliary[3,53] 64.86 14.71 59.32 51.62 87.55 3.59 1.66\n", "auxiliary[3,54] 65.95 14.86 60.34 52.61 88.83 3.60 1.66\n", "auxiliary[3,55] 66.98 14.95 61.34 53.59 90.05 3.61 1.66\n", "auxiliary[3,56] 67.98 15.02 62.33 54.57 91.15 3.61 1.65\n", "auxiliary[3,57] 68.96 15.06 63.23 55.53 92.11 3.61 1.65\n", "auxiliary[3,58] 69.92 15.09 64.24 56.48 93.11 3.62 1.65\n", "auxiliary[3,59] 70.88 15.11 65.20 57.41 94.08 3.62 1.65\n", "auxiliary[3,60] 71.82 15.12 66.13 58.38 95.05 3.62 1.65\n", " incub_time 3.96 0.04 3.96 3.89 4.02 2.53 2.61\n", " mort_rate 0.10 0.00 0.10 0.10 0.10 2.48 2.81\n", " rec_rate 0.61 0.00 0.61 0.61 0.61 4.96 1.05\n", " rec_time 16.05 0.01 16.05 16.03 16.07 2.67 2.47\n", " rho 0.23 0.01 0.23 0.23 0.24 7.02 1.04\n", "\n", "Number of divergences: 0\n", "CPU times: user 3min 8s, sys: 1.17 s, total: 3min 9s\n", "Wall time: 3min 9s\n" ], "name": "stdout" } ] }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "uHtV0RTS9LxB", "outputId": "88dc34e4-51dc-41e4-b48b-1a31209a6b0e" }, "source": [ "%%time\n", "Japan_model = CovidModel(126500000, Japan[\"new_cases\"], Japan[\"new_recovered\"], Japan[\"new_deaths\"] )\n", "Japan_mcmc = Japan_model.fit_mcmc(num_samples=500, warmup_steps = 200)\n", "Japan_mcmc.summary()" ], "execution_count": null, "outputs": [ { "output_type": "stream", "text": [ "INFO \t Running inference...\n", "Warmup: 0%| | 0/700 [00:00, ?it/s]INFO \t Heuristic init: R0=1.75, incub_time=5.27, mort_rate=0.0177, rec_rate=0.486, rec_time=9.02, rho=0.189\n", "Sample: 100%|██████████| 700/700 [03:23, 3.43it/s, step size=3.40e-03, acc. prob=0.900]\n" ], "name": "stderr" }, { "output_type": "stream", "text": [ "\n", " mean std median 5.0% 95.0% n_eff r_hat\n", " R0 1.58 0.05 1.57 1.51 1.65 2.50 2.67\n", " auxiliary[0,0] 126499861.04 0.32 126499861.05 126499860.57 126499861.55 4.43 1.23\n", " auxiliary[0,1] 126499725.56 3.72 126499725.38 126499720.45 126499731.75 2.60 2.41\n", " auxiliary[0,2] 126499582.23 7.36 126499582.32 126499570.46 126499593.10 2.65 2.35\n", " auxiliary[0,3] 126499430.67 14.02 126499428.50 126499408.16 126499451.40 2.63 2.39\n", " auxiliary[0,4] 126499274.14 20.12 126499269.55 126499244.83 126499306.75 2.86 2.08\n", " auxiliary[0,5] 126499111.52 25.77 126499104.47 126499072.74 126499154.02 2.88 2.11\n", " auxiliary[0,6] 126498946.10 32.21 126498937.63 126498896.77 126498995.47 2.86 2.11\n", " auxiliary[0,7] 126498777.60 39.33 126498767.76 126498719.14 126498838.36 2.83 2.14\n", " auxiliary[0,8] 126498608.27 45.02 126498597.00 126498540.61 126498677.24 2.81 2.16\n", " auxiliary[0,9] 126498437.75 51.00 126498424.66 126498360.03 126498515.88 2.78 2.21\n", "auxiliary[0,10] 126498266.56 56.62 126498251.56 126498179.86 126498356.23 2.77 2.21\n", "auxiliary[0,11] 126498095.73 62.22 126498079.77 126497998.08 126498192.64 2.74 2.25\n", "auxiliary[0,12] 126497924.59 68.32 126497907.90 126497819.84 126498032.84 2.70 2.32\n", "auxiliary[0,13] 126497753.85 73.84 126497736.03 126497637.68 126497869.25 2.70 2.32\n", "auxiliary[0,14] 126497582.62 78.82 126497564.33 126497468.00 126497714.89 2.68 2.35\n", "auxiliary[0,15] 126497411.93 84.66 126497393.18 126497277.06 126497540.83 2.67 2.37\n", "auxiliary[0,16] 126497240.73 90.34 126497220.61 126497111.51 126497394.75 2.66 2.37\n", "auxiliary[0,17] 126497068.74 96.33 126497049.37 126496931.58 126497231.08 2.65 2.39\n", "auxiliary[0,18] 126496894.98 102.00 126496875.07 126496750.23 126497066.32 2.64 2.42\n", "auxiliary[0,19] 126496721.68 107.60 126496700.42 126496566.90 126496900.88 2.63 2.43\n", "auxiliary[0,20] 126496546.98 113.44 126496525.31 126496365.09 126496715.59 2.62 2.44\n", "auxiliary[0,21] 126496371.12 119.41 126496350.70 126496182.52 126496551.12 2.62 2.44\n", "auxiliary[0,22] 126496193.25 125.45 126496171.55 126495991.79 126496377.47 2.61 2.45\n", "auxiliary[0,23] 126496014.41 130.95 126495989.42 126495804.62 126496206.16 2.60 2.47\n", "auxiliary[0,24] 126495833.37 136.78 126495811.90 126495614.78 126496031.07 2.60 2.48\n", "auxiliary[0,25] 126495651.69 143.12 126495626.89 126495423.89 126495860.36 2.59 2.50\n", "auxiliary[0,26] 126495468.40 149.58 126495441.93 126495229.80 126495686.40 2.59 2.49\n", "auxiliary[0,27] 126495283.85 156.00 126495254.25 126495033.79 126495510.05 2.58 2.50\n", "auxiliary[0,28] 126495098.02 162.49 126495070.03 126494838.12 126495335.92 2.58 2.51\n", "auxiliary[0,29] 126494910.63 168.81 126494881.42 126494642.60 126495159.46 2.58 2.51\n", "auxiliary[0,30] 126494721.28 174.97 126494689.76 126494443.25 126494978.77 2.57 2.52\n", "auxiliary[0,31] 126494529.17 181.09 126494496.63 126494243.88 126494797.54 2.57 2.52\n", "auxiliary[0,32] 126494334.95 187.12 126494302.30 126494038.02 126494610.99 2.57 2.52\n", "auxiliary[0,33] 126494138.96 192.73 126494104.84 126493832.96 126494424.29 2.56 2.52\n", "auxiliary[0,34] 126493939.80 199.04 126493903.79 126493625.70 126494236.24 2.56 2.54\n", "auxiliary[0,35] 126493736.95 204.71 126493701.00 126493415.49 126494042.26 2.55 2.55\n", "auxiliary[0,36] 126493529.85 209.65 126493493.30 126493205.49 126493846.38 2.54 2.57\n", "auxiliary[0,37] 126493317.99 215.12 126493279.85 126492979.05 126493635.29 2.54 2.58\n", "auxiliary[0,38] 126493101.12 220.51 126493064.83 126492760.95 126493433.87 2.54 2.57\n", "auxiliary[0,39] 126492880.79 224.86 126492846.22 126492536.65 126493223.63 2.54 2.56\n", "auxiliary[0,40] 126492656.53 228.79 126492619.53 126492303.89 126492997.86 2.54 2.55\n", "auxiliary[0,41] 126492427.35 232.35 126492391.14 126492070.92 126492772.59 2.54 2.54\n", "auxiliary[0,42] 126492195.07 235.22 126492154.73 126491829.83 126492541.79 2.54 2.55\n", "auxiliary[0,43] 126491958.25 237.53 126491917.14 126491593.43 126492311.43 2.54 2.54\n", "auxiliary[0,44] 126491714.67 239.46 126491670.15 126491349.18 126492072.21 2.54 2.54\n", "auxiliary[0,45] 126491466.71 239.40 126491424.72 126491095.31 126491823.11 2.55 2.52\n", "auxiliary[0,46] 126491214.03 238.17 126491169.96 126490841.57 126491567.56 2.55 2.52\n", "auxiliary[0,47] 126490959.13 237.24 126490918.46 126490592.25 126491306.98 2.55 2.52\n", "auxiliary[0,48] 126490701.36 234.29 126490663.01 126490342.88 126491047.44 2.55 2.53\n", "auxiliary[0,49] 126490440.82 230.16 126490406.74 126490087.93 126490777.13 2.54 2.53\n", "auxiliary[0,50] 126490175.98 225.44 126490140.51 126489827.27 126490506.33 2.54 2.52\n", "auxiliary[0,51] 126489909.89 221.19 126489877.25 126489560.55 126490223.59 2.54 2.53\n", "auxiliary[0,52] 126489641.76 217.14 126489606.59 126489303.61 126489957.76 2.53 2.56\n", "auxiliary[0,53] 126489371.77 213.40 126489337.78 126489038.97 126489683.29 2.52 2.59\n", "auxiliary[0,54] 126489101.93 209.65 126489072.96 126488769.43 126489409.35 2.50 2.62\n", "auxiliary[0,55] 126488831.46 207.22 126488806.91 126488505.53 126489136.66 2.49 2.66\n", "auxiliary[0,56] 126488559.89 206.98 126488540.04 126488228.25 126488853.01 2.48 2.68\n", "auxiliary[0,57] 126488288.67 208.06 126488275.22 126487956.44 126488579.53 2.46 2.71\n", "auxiliary[0,58] 126488018.08 210.84 126488010.18 126487672.65 126488306.48 2.45 2.76\n", "auxiliary[0,59] 126487748.74 214.59 126487744.91 126487445.86 126488086.18 2.44 2.79\n", "auxiliary[0,60] 126487483.09 219.64 126487475.53 126487172.89 126487826.16 2.44 2.79\n", " auxiliary[1,0] 124.28 0.46 124.13 123.66 125.01 3.21 1.66\n", " auxiliary[1,1] 213.89 3.00 213.93 209.19 218.30 2.59 2.41\n", " auxiliary[1,2] 264.63 2.78 263.74 261.22 269.33 2.74 2.17\n", " auxiliary[1,3] 307.50 3.91 306.93 302.26 313.32 2.58 2.51\n", " auxiliary[1,4] 353.87 2.84 353.37 349.64 358.37 3.50 1.73\n", " auxiliary[1,5] 392.70 1.78 392.68 389.86 395.48 4.47 1.95\n", " auxiliary[1,6] 413.77 1.62 413.38 411.11 416.68 7.86 1.07\n", " auxiliary[1,7] 438.22 2.64 437.55 434.45 442.42 2.88 2.27\n", " auxiliary[1,8] 455.81 2.38 456.11 451.88 459.13 4.43 1.42\n", " auxiliary[1,9] 470.08 3.85 470.09 464.34 475.09 2.59 3.02\n", "auxiliary[1,10] 488.45 2.11 488.88 484.44 491.51 4.84 1.39\n", "auxiliary[1,11] 499.74 3.25 500.87 494.72 504.28 2.99 1.77\n", "auxiliary[1,12] 513.40 1.75 513.25 510.55 515.60 6.85 1.02\n", "auxiliary[1,13] 535.59 1.05 535.72 533.84 537.08 10.95 1.09\n", "auxiliary[1,14] 557.43 2.90 556.47 553.77 562.19 3.34 1.46\n", "auxiliary[1,15] 562.83 2.98 563.85 558.00 566.36 2.76 2.15\n", "auxiliary[1,16] 575.72 3.18 576.64 570.00 579.31 3.20 2.14\n", "auxiliary[1,17] 579.18 1.95 579.46 575.84 581.97 3.63 2.13\n", "auxiliary[1,18] 607.94 1.68 607.77 605.27 610.49 6.49 1.14\n", "auxiliary[1,19] 609.48 4.69 608.60 603.10 616.65 2.68 2.33\n", "auxiliary[1,20] 618.04 1.53 618.25 614.76 619.89 10.75 1.07\n", "auxiliary[1,21] 630.27 2.54 630.33 626.24 633.77 3.77 2.10\n", "auxiliary[1,22] 661.82 1.88 661.90 657.88 664.49 5.61 1.52\n", "auxiliary[1,23] 705.39 2.39 705.85 701.82 709.16 7.06 1.14\n", "auxiliary[1,24] 753.49 2.39 753.04 750.37 757.67 5.07 1.09\n", "auxiliary[1,25] 777.40 2.24 777.43 774.05 781.01 6.24 1.46\n", "auxiliary[1,26] 827.65 2.18 827.81 822.96 830.34 10.78 1.30\n", "auxiliary[1,27] 860.06 6.38 857.52 853.14 871.19 2.97 2.01\n", "auxiliary[1,28] 890.41 3.41 890.17 885.49 895.63 2.86 2.10\n", "auxiliary[1,29] 908.02 2.97 907.78 903.20 911.47 10.99 1.00\n", "auxiliary[1,30] 922.47 12.89 923.59 899.28 938.23 2.84 2.13\n", "auxiliary[1,31] 980.45 8.76 982.64 967.16 991.46 2.46 2.94\n", "auxiliary[1,32] 1039.93 4.41 1041.43 1032.63 1045.91 5.77 1.29\n", "auxiliary[1,33] 1061.92 7.21 1062.35 1044.40 1069.36 4.75 1.42\n", "auxiliary[1,34] 1108.85 12.17 1107.43 1091.58 1130.61 2.80 2.09\n", "auxiliary[1,35] 1166.08 13.81 1171.40 1143.97 1186.83 2.92 2.08\n", "auxiliary[1,36] 1233.04 10.88 1231.48 1220.35 1250.24 2.49 3.08\n", "auxiliary[1,37] 1297.85 15.76 1297.20 1276.07 1321.45 2.44 2.76\n", "auxiliary[1,38] 1388.90 4.81 1388.26 1382.62 1396.72 3.42 2.21\n", "auxiliary[1,39] 1441.30 9.33 1437.11 1430.73 1457.55 2.91 2.00\n", "auxiliary[1,40] 1478.60 15.15 1478.44 1455.62 1499.74 2.62 2.43\n", "auxiliary[1,41] 1531.92 16.48 1529.70 1510.41 1555.18 2.40 2.90\n", "auxiliary[1,42] 1591.64 12.86 1595.76 1573.99 1610.95 2.63 2.41\n", "auxiliary[1,43] 1650.13 9.73 1648.21 1635.53 1664.92 3.08 1.90\n", "auxiliary[1,44] 1745.46 15.44 1748.26 1724.47 1772.89 2.72 2.48\n", "auxiliary[1,45] 1816.34 17.64 1813.12 1790.17 1842.30 2.68 2.27\n", "auxiliary[1,46] 1905.98 9.32 1907.23 1888.10 1918.58 7.03 1.00\n", "auxiliary[1,47] 1969.17 17.45 1974.64 1944.10 1993.88 3.01 2.27\n", "auxiliary[1,48] 2026.01 7.20 2026.55 2012.37 2036.86 4.85 1.86\n", "auxiliary[1,49] 2093.07 7.57 2091.59 2083.64 2107.56 5.36 1.05\n", "auxiliary[1,50] 2210.35 12.95 2208.15 2192.47 2234.46 2.84 2.20\n", "auxiliary[1,51] 2300.31 10.90 2298.67 2284.08 2316.48 2.75 2.33\n", "auxiliary[1,52] 2401.44 16.16 2405.28 2375.64 2422.14 2.51 2.89\n", "auxiliary[1,53] 2511.15 12.42 2512.58 2489.04 2529.02 3.92 1.76\n", "auxiliary[1,54] 2586.58 14.61 2583.88 2565.98 2604.02 3.45 1.72\n", "auxiliary[1,55] 2693.86 18.21 2687.94 2667.99 2727.91 3.86 1.59\n", "auxiliary[1,56] 2791.99 31.98 2778.64 2755.61 2846.86 2.88 2.12\n", "auxiliary[1,57] 2882.04 36.40 2869.84 2829.56 2939.12 3.02 2.01\n", "auxiliary[1,58] 2949.94 43.82 2948.09 2879.82 3020.82 2.72 2.29\n", "auxiliary[1,59] 2945.21 70.33 2938.55 2828.68 3048.51 2.62 2.43\n", "auxiliary[1,60] 2751.37 80.96 2720.47 2650.61 2884.44 3.14 1.90\n", " auxiliary[2,0] 1.39 0.07 1.38 1.31 1.50 2.55 2.59\n", " auxiliary[2,1] 29.10 0.10 29.10 28.93 29.25 4.49 1.05\n", " auxiliary[2,2] 72.20 0.78 71.91 71.30 73.30 2.41 3.06\n", " auxiliary[2,3] 115.73 0.95 115.57 114.44 117.03 2.42 3.67\n", " auxiliary[2,4] 150.00 0.70 150.07 148.72 150.99 4.04 1.13\n", " auxiliary[2,5] 193.88 0.84 193.80 192.53 195.06 6.47 1.09\n", " auxiliary[2,6] 252.85 2.23 252.56 249.84 256.50 2.59 2.43\n", " auxiliary[2,7] 305.97 2.12 305.74 301.93 308.62 4.63 1.50\n", " auxiliary[2,8] 361.25 2.25 360.57 357.98 364.48 3.55 1.49\n", " auxiliary[2,9] 417.52 0.89 417.39 416.05 419.00 11.96 1.04\n", "auxiliary[2,10] 465.86 2.25 465.92 462.42 469.48 3.24 1.79\n", "auxiliary[2,11] 515.94 1.58 515.87 513.32 518.28 6.61 1.03\n", "auxiliary[2,12] 559.79 5.85 561.14 551.08 567.06 2.39 3.27\n", "auxiliary[2,13] 586.88 4.69 585.70 580.03 595.47 2.97 1.90\n", "auxiliary[2,14] 612.94 2.98 613.54 608.50 617.77 3.23 2.17\n", "auxiliary[2,15] 653.40 4.96 654.34 646.44 660.51 2.50 2.64\n", "auxiliary[2,16] 683.66 2.98 684.28 679.19 688.34 3.05 2.65\n", "auxiliary[2,17] 726.06 4.94 726.72 718.69 733.17 2.57 2.33\n", "auxiliary[2,18] 745.62 4.48 746.33 737.40 750.95 2.82 2.07\n", "auxiliary[2,19] 791.07 7.33 794.75 779.53 799.48 2.62 2.55\n", "auxiliary[2,20] 833.29 4.48 834.84 824.93 838.24 2.97 2.00\n", "auxiliary[2,21] 872.34 6.80 873.45 861.28 882.32 2.66 2.36\n", "auxiliary[2,22] 896.62 7.91 896.35 882.38 907.68 3.17 1.98\n", "auxiliary[2,23] 908.29 2.87 908.27 904.49 913.45 4.91 1.67\n", "auxiliary[2,24] 922.84 4.32 922.58 915.95 928.17 3.04 2.15\n", "auxiliary[2,25] 964.57 4.80 964.59 957.94 971.90 2.90 2.29\n", "auxiliary[2,26] 979.85 7.45 980.07 968.70 992.01 3.35 1.84\n", "auxiliary[2,27] 1019.16 5.75 1020.99 1008.67 1026.00 3.80 1.45\n", "auxiliary[2,28] 1063.91 11.07 1063.88 1044.28 1078.53 3.09 1.94\n", "auxiliary[2,29] 1125.85 15.16 1128.07 1102.67 1144.81 2.58 2.36\n", "auxiliary[2,30] 1195.24 4.53 1197.17 1187.85 1200.77 3.20 1.74\n", "auxiliary[2,31] 1225.07 9.83 1225.33 1207.96 1240.15 3.88 1.55\n", "auxiliary[2,32] 1258.06 16.25 1257.43 1236.40 1284.53 2.79 2.08\n", "auxiliary[2,33] 1333.27 12.91 1333.90 1315.27 1352.02 2.50 2.34\n", "auxiliary[2,34] 1389.07 9.44 1391.99 1374.19 1404.18 2.91 2.19\n", "auxiliary[2,35] 1440.46 10.04 1438.04 1429.50 1461.53 2.98 1.99\n", "auxiliary[2,36] 1489.32 12.29 1491.82 1470.93 1506.65 3.27 2.04\n", "auxiliary[2,37] 1548.39 8.44 1549.28 1536.23 1562.29 2.83 2.57\n", "auxiliary[2,38] 1587.73 21.85 1590.21 1558.61 1621.90 2.51 2.64\n", "auxiliary[2,39] 1671.37 18.07 1673.34 1642.24 1692.21 2.56 2.60\n", "auxiliary[2,40] 1775.57 12.15 1775.83 1756.62 1795.45 2.85 2.21\n", "auxiliary[2,41] 1870.04 11.27 1873.28 1852.86 1885.57 3.64 1.62\n", "auxiliary[2,42] 1961.94 13.51 1961.25 1942.93 1982.56 2.71 2.20\n", "auxiliary[2,43] 2061.47 15.66 2066.75 2034.95 2080.24 2.59 2.47\n", "auxiliary[2,44] 2132.21 8.95 2133.91 2113.49 2143.31 4.05 1.49\n", "auxiliary[2,45] 2233.51 7.37 2233.27 2220.74 2245.30 6.90 1.00\n", "auxiliary[2,46] 2321.95 10.11 2322.16 2307.91 2337.59 2.82 3.11\n", "auxiliary[2,47] 2439.56 10.48 2438.99 2424.74 2454.38 2.88 3.12\n", "auxiliary[2,48] 2566.90 8.64 2567.94 2552.35 2578.25 3.20 2.08\n", "auxiliary[2,49] 2687.36 12.96 2690.63 2667.91 2705.08 3.71 1.41\n", "auxiliary[2,50] 2761.99 8.92 2761.88 2748.00 2775.25 3.44 2.22\n", "auxiliary[2,51] 2865.64 17.58 2863.99 2841.94 2892.14 2.46 3.12\n", "auxiliary[2,52] 2960.46 21.69 2952.45 2927.05 2997.90 2.97 2.03\n", "auxiliary[2,53] 3048.65 34.08 3036.38 3003.68 3100.20 2.66 2.39\n", "auxiliary[2,54] 3170.96 41.35 3169.66 3104.82 3233.12 2.78 2.19\n", "auxiliary[2,55] 3261.90 43.98 3257.30 3198.00 3317.61 2.63 2.30\n", "auxiliary[2,56] 3363.14 33.66 3357.38 3315.25 3406.94 3.15 1.89\n", "auxiliary[2,57] 3471.85 32.50 3459.62 3435.12 3524.50 3.31 1.78\n", "auxiliary[2,58] 3602.29 31.28 3595.68 3564.70 3643.10 4.38 1.24\n", "auxiliary[2,59] 3804.18 25.20 3803.29 3769.79 3842.45 3.97 1.20\n", "auxiliary[2,60] 4192.08 18.60 4189.03 4167.44 4227.16 2.84 2.25\n", " auxiliary[3,0] 0.47 0.01 0.47 0.45 0.48 2.90 2.27\n", " auxiliary[3,1] 0.50 0.00 0.50 0.49 0.51 6.26 1.12\n", " auxiliary[3,2] 0.49 0.00 0.49 0.48 0.50 6.42 1.02\n", " auxiliary[3,3] 0.50 0.01 0.50 0.49 0.51 3.41 1.77\n", " auxiliary[3,4] 0.52 0.01 0.52 0.50 0.52 3.57 1.51\n", " auxiliary[3,5] 0.50 0.00 0.50 0.49 0.51 4.97 1.14\n", " auxiliary[3,6] 0.49 0.00 0.49 0.49 0.50 3.58 1.95\n", " auxiliary[3,7] 0.50 0.00 0.50 0.49 0.50 5.33 1.08\n", " auxiliary[3,8] 0.50 0.01 0.50 0.48 0.51 3.31 1.56\n", " auxiliary[3,9] 0.51 0.00 0.51 0.50 0.51 13.92 1.12\n", "auxiliary[3,10] 0.49 0.01 0.49 0.48 0.50 2.99 2.00\n", "auxiliary[3,11] 0.53 0.01 0.53 0.52 0.55 2.81 2.34\n", "auxiliary[3,12] 0.99 0.01 0.99 0.99 1.01 4.12 1.50\n", "auxiliary[3,13] 1.34 0.01 1.34 1.32 1.35 3.39 1.92\n", "auxiliary[3,14] 1.68 0.01 1.68 1.67 1.70 5.46 1.41\n", "auxiliary[3,15] 1.76 0.01 1.76 1.74 1.77 6.12 1.28\n", "auxiliary[3,16] 1.98 0.02 1.98 1.95 2.00 3.29 2.14\n", "auxiliary[3,17] 2.03 0.02 2.02 2.01 2.06 3.31 1.75\n", "auxiliary[3,18] 1.95 0.01 1.95 1.94 1.96 10.81 1.01\n", "auxiliary[3,19] 1.84 0.02 1.84 1.82 1.87 3.21 2.16\n", "auxiliary[3,20] 2.05 0.02 2.05 2.03 2.08 2.56 2.70\n", "auxiliary[3,21] 2.25 0.05 2.24 2.18 2.33 2.53 2.69\n", "auxiliary[3,22] 2.11 0.02 2.12 2.07 2.14 3.43 1.63\n", "auxiliary[3,23] 1.90 0.03 1.91 1.87 1.94 2.50 2.70\n", "auxiliary[3,24] 2.17 0.11 2.21 1.99 2.32 2.58 2.50\n", "auxiliary[3,25] 3.20 0.03 3.19 3.16 3.24 3.27 1.75\n", "auxiliary[3,26] 4.37 0.06 4.35 4.30 4.50 2.97 1.99\n", "auxiliary[3,27] 5.39 0.10 5.39 5.26 5.55 2.62 2.38\n", "auxiliary[3,28] 6.21 0.15 6.17 6.02 6.42 2.42 2.85\n", "auxiliary[3,29] 6.83 0.14 6.80 6.63 7.06 2.86 2.11\n", "auxiliary[3,30] 7.31 0.09 7.26 7.23 7.47 3.40 1.59\n", "auxiliary[3,31] 7.76 0.08 7.72 7.65 7.88 2.71 2.11\n", "auxiliary[3,32] 8.28 0.27 8.28 7.91 8.61 2.35 3.11\n", "auxiliary[3,33] 9.05 0.49 9.10 8.33 9.79 2.49 2.68\n", "auxiliary[3,34] 10.13 0.59 10.24 9.23 11.01 2.61 2.41\n", "auxiliary[3,35] 11.39 0.64 11.53 10.38 12.33 2.64 2.38\n", "auxiliary[3,36] 12.79 0.63 12.91 11.83 13.72 2.65 2.37\n", "auxiliary[3,37] 14.28 0.56 14.33 13.43 15.11 2.66 2.37\n", "auxiliary[3,38] 15.89 0.45 15.93 15.20 16.58 2.56 2.54\n", "auxiliary[3,39] 17.65 0.30 17.69 17.13 18.04 2.48 2.78\n", "auxiliary[3,40] 19.46 0.14 19.43 19.21 19.65 2.63 2.60\n", "auxiliary[3,41] 21.27 0.06 21.25 21.18 21.38 3.40 1.85\n", "auxiliary[3,42] 23.06 0.26 23.03 22.72 23.45 2.53 2.61\n", "auxiliary[3,43] 24.83 0.47 24.78 24.21 25.59 2.55 2.49\n", "auxiliary[3,44] 26.56 0.67 26.51 25.64 27.54 2.55 2.52\n", "auxiliary[3,45] 28.24 0.86 28.17 26.95 29.52 2.55 2.51\n", "auxiliary[3,46] 29.84 1.03 29.69 28.37 31.44 2.54 2.55\n", "auxiliary[3,47] 31.34 1.19 31.13 29.48 33.05 2.55 2.54\n", "auxiliary[3,48] 32.78 1.33 32.56 30.72 34.72 2.55 2.56\n", "auxiliary[3,49] 34.14 1.45 33.90 31.96 36.33 2.56 2.53\n", "auxiliary[3,50] 35.43 1.56 35.16 33.10 37.78 2.57 2.51\n", "auxiliary[3,51] 36.64 1.65 36.40 34.24 39.19 2.58 2.49\n", "auxiliary[3,52] 37.81 1.73 37.59 35.28 40.43 2.59 2.46\n", "auxiliary[3,53] 38.93 1.79 38.68 36.38 41.60 2.60 2.44\n", "auxiliary[3,54] 40.02 1.84 39.76 37.39 42.78 2.61 2.41\n", "auxiliary[3,55] 41.08 1.88 40.78 38.41 43.88 2.62 2.40\n", "auxiliary[3,56] 42.11 1.92 41.81 39.45 45.00 2.63 2.39\n", "auxiliary[3,57] 43.13 1.94 42.81 40.50 46.10 2.63 2.40\n", "auxiliary[3,58] 44.12 1.97 43.74 41.47 47.09 2.62 2.42\n", "auxiliary[3,59] 45.09 1.98 44.73 42.45 48.10 2.62 2.42\n", "auxiliary[3,60] 46.05 1.98 45.67 43.38 49.03 2.63 2.42\n", " incub_time 5.33 0.02 5.33 5.30 5.35 2.58 2.56\n", " mort_rate 0.02 0.00 0.02 0.02 0.02 2.93 2.02\n", " rec_rate 0.48 0.00 0.48 0.48 0.49 2.84 2.19\n", " rec_time 9.06 0.01 9.06 9.04 9.07 2.54 2.64\n", " rho 0.23 0.01 0.23 0.23 0.24 2.51 2.62\n", "\n", "Number of divergences: 0\n", "CPU times: user 3min 23s, sys: 1.28 s, total: 3min 24s\n", "Wall time: 3min 24s\n" ], "name": "stdout" } ] }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "HurrBsBUGQ32", "outputId": "1cd1dacd-3970-4929-c4af-df9ea2273a9d" }, "source": [ "%%time\n", "Japan_model = CovidModel(126500000, Japan[\"new_cases\"], Japan[\"new_recovered\"], Japan[\"new_deaths\"] )\n", "Japan_mcmc = Japan_model.fit_mcmc(num_samples=500, warmup_steps = 200)\n", "Japan_mcmc.summary()" ], "execution_count": null, "outputs": [ { "output_type": "stream", "text": [ "INFO \t Running inference...\n", "Warmup: 0%| | 0/700 [00:00, ?it/s]INFO \t Heuristic init: R0=2.23, incub_time=5.71, mort_rate=0.0162, rec_rate=0.545, rec_time=16.2, rho=0.167\n", "Sample: 100%|██████████| 700/700 [01:07, 10.34it/s, step size=4.11e-04, acc. prob=0.746]\n" ], "name": "stderr" }, { "output_type": "stream", "text": [ "\n", " mean std median 5.0% 95.0% n_eff r_hat\n", " R0 2.23 0.00 2.23 2.23 2.23 4.53 2.19\n", " auxiliary[0,0] 126499886.81 0.05 126499886.80 126499886.75 126499886.89 2.39 3.31\n", " auxiliary[0,1] 126499789.68 0.04 126499789.66 126499789.63 126499789.74 2.56 2.60\n", " auxiliary[0,2] 126499692.94 0.18 126499692.92 126499692.70 126499693.21 2.48 3.05\n", " auxiliary[0,3] 126499590.75 0.26 126499590.65 126499590.45 126499591.11 2.45 3.53\n", " auxiliary[0,4] 126499488.94 0.31 126499488.75 126499488.54 126499489.41 2.52 2.90\n", " auxiliary[0,5] 126499382.64 0.31 126499382.64 126499382.18 126499383.09 2.45 2.80\n", " auxiliary[0,6] 126499281.13 0.52 126499281.00 126499280.43 126499281.96 2.52 2.69\n", " auxiliary[0,7] 126499158.90 0.30 126499158.85 126499158.36 126499159.32 2.67 2.46\n", " auxiliary[0,8] 126499050.99 0.52 126499050.83 126499050.43 126499051.77 2.43 3.73\n", " auxiliary[0,9] 126498936.43 0.52 126498936.27 126498935.81 126498937.31 2.50 3.02\n", "auxiliary[0,10] 126498839.71 0.72 126498839.34 126498838.97 126498841.01 2.67 2.41\n", "auxiliary[0,11] 126498742.33 0.66 126498742.12 126498741.54 126498743.50 2.52 2.68\n", "auxiliary[0,12] 126498633.27 0.64 126498633.02 126498632.38 126498634.28 2.57 2.47\n", "auxiliary[0,13] 126498525.40 0.50 126498525.22 126498524.76 126498526.18 2.51 2.63\n", "auxiliary[0,14] 126498413.44 0.59 126498413.16 126498412.86 126498414.54 3.17 1.74\n", "auxiliary[0,15] 126498298.56 0.36 126498298.42 126498298.13 126498299.19 2.75 2.49\n", "auxiliary[0,16] 126498183.12 0.36 126498183.02 126498182.54 126498183.58 3.21 2.65\n", "auxiliary[0,17] 126498062.10 0.72 126498062.09 126498061.20 126498063.24 2.46 2.97\n", "auxiliary[0,18] 126497938.94 0.54 126497938.83 126497938.14 126497939.64 2.56 2.78\n", "auxiliary[0,19] 126497820.95 0.38 126497820.79 126497820.53 126497821.47 2.96 3.16\n", "auxiliary[0,20] 126497693.17 0.46 126497693.09 126497692.65 126497694.08 2.81 2.19\n", "auxiliary[0,21] 126497551.61 0.65 126497551.34 126497550.98 126497552.83 3.64 1.48\n", "auxiliary[0,22] 126497403.44 0.34 126497403.33 126497403.00 126497404.09 4.89 1.05\n", "auxiliary[0,23] 126497258.83 0.47 126497258.79 126497258.13 126497259.63 3.23 2.06\n", "auxiliary[0,24] 126497104.90 0.34 126497104.89 126497104.31 126497105.46 3.69 1.61\n", "auxiliary[0,25] 126496943.90 0.52 126496943.91 126496943.19 126496944.63 2.55 3.00\n", "auxiliary[0,26] 126496780.44 0.61 126496780.84 126496779.58 126496781.14 2.67 2.31\n", "auxiliary[0,27] 126496607.69 0.43 126496607.64 126496607.11 126496608.38 2.69 2.26\n", "auxiliary[0,28] 126496427.79 0.84 126496427.33 126496426.80 126496429.13 2.61 2.32\n", "auxiliary[0,29] 126496248.34 0.98 126496247.87 126496247.38 126496250.27 3.24 1.82\n", "auxiliary[0,30] 126496061.26 0.40 126496061.17 126496060.55 126496061.73 9.01 1.01\n", "auxiliary[0,31] 126495868.52 0.80 126495868.06 126495867.62 126495869.66 3.13 2.79\n", "auxiliary[0,32] 126495650.66 0.64 126495650.39 126495649.80 126495651.58 2.59 3.11\n", "auxiliary[0,33] 126495433.79 0.85 126495433.69 126495432.75 126495435.11 2.55 2.90\n", "auxiliary[0,34] 126495191.61 0.98 126495191.21 126495190.47 126495193.27 3.18 1.78\n", "auxiliary[0,35] 126494950.45 0.68 126494950.22 126494949.52 126494951.73 4.36 1.22\n", "auxiliary[0,36] 126494679.37 1.04 126494679.14 126494677.85 126494681.15 3.02 2.08\n", "auxiliary[0,37] 126494400.16 0.56 126494400.28 126494399.36 126494400.94 6.86 1.06\n", "auxiliary[0,38] 126494098.54 1.51 126494098.31 126494096.31 126494100.85 2.63 2.42\n", "auxiliary[0,39] 126493774.48 0.23 126493774.49 126493774.17 126493774.87 18.81 1.06\n", "auxiliary[0,40] 126493460.58 0.99 126493460.29 126493459.60 126493462.65 3.55 1.49\n", "auxiliary[0,41] 126493117.10 0.58 126493117.06 126493116.02 126493118.06 8.90 1.17\n", "auxiliary[0,42] 126492774.39 2.10 126492773.48 126492772.19 126492777.93 2.70 2.32\n", "auxiliary[0,43] 126492407.19 0.67 126492407.25 126492406.01 126492408.18 6.62 1.12\n", "auxiliary[0,44] 126492066.51 0.59 126492066.60 126492065.54 126492067.49 14.56 1.13\n", "auxiliary[0,45] 126491687.46 1.98 126491686.76 126491685.29 126491690.98 3.03 2.02\n", "auxiliary[0,46] 126491302.71 1.65 126491302.34 126491300.62 126491305.02 2.70 3.27\n", "auxiliary[0,47] 126490897.56 1.20 126490897.35 126490895.84 126490899.41 3.73 2.24\n", "auxiliary[0,48] 126490457.65 0.77 126490457.63 126490456.34 126490458.88 3.54 1.91\n", "auxiliary[0,49] 126490007.68 1.74 126490007.35 126490005.63 126490011.21 3.11 1.90\n", "auxiliary[0,50] 126489528.89 1.26 126489528.79 126489527.38 126489531.34 6.76 1.19\n", "auxiliary[0,51] 126489025.29 1.05 126489025.41 126489023.26 126489026.65 4.82 1.35\n", "auxiliary[0,52] 126488494.94 2.11 126488494.25 126488491.87 126488498.27 3.44 2.52\n", "auxiliary[0,53] 126487898.17 0.97 126487898.12 126487896.69 126487899.68 5.59 1.69\n", "auxiliary[0,54] 126487308.91 1.50 126487309.27 126487306.22 126487311.15 3.16 1.81\n", "auxiliary[0,55] 126486675.70 1.78 126486676.03 126486672.68 126486678.06 5.36 1.32\n", "auxiliary[0,56] 126486001.38 1.59 126486001.90 126485998.65 126486003.23 4.40 1.90\n", "auxiliary[0,57] 126485349.96 9.15 126485352.74 126485334.42 126485360.99 2.52 2.71\n", "auxiliary[0,58] 126484787.59 9.60 126484790.72 126484773.92 126484803.25 2.60 2.61\n", "auxiliary[0,59] 126484248.99 9.89 126484252.02 126484231.88 126484260.14 2.55 2.68\n", "auxiliary[0,60] 126483694.14 12.51 126483696.90 126483675.75 126483710.74 2.40 3.39\n", " auxiliary[1,0] 113.00 0.05 113.00 112.94 113.08 2.61 2.51\n", " auxiliary[1,1] 189.75 0.06 189.75 189.67 189.85 2.50 2.88\n", " auxiliary[1,2] 244.69 0.07 244.68 244.60 244.79 2.38 3.42\n", " auxiliary[1,3] 294.60 0.12 294.52 294.48 294.79 2.46 3.15\n", " auxiliary[1,4] 336.87 0.16 336.82 336.65 337.11 2.46 3.06\n", " auxiliary[1,5] 375.12 0.13 375.10 374.94 375.34 2.51 2.88\n", " auxiliary[1,6] 401.48 0.03 401.48 401.44 401.53 7.76 1.02\n", " auxiliary[1,7] 437.02 0.22 436.90 436.79 437.37 2.48 2.76\n", " auxiliary[1,8] 473.09 0.12 473.03 472.93 473.28 2.79 2.48\n", " auxiliary[1,9] 513.09 0.25 512.93 512.85 513.53 2.63 2.46\n", "auxiliary[1,10] 524.37 0.06 524.37 524.28 524.45 3.09 2.18\n", "auxiliary[1,11] 533.27 0.03 533.27 533.23 533.32 10.06 1.00\n", "auxiliary[1,12] 549.75 0.07 549.75 549.62 549.85 3.07 2.10\n", "auxiliary[1,13] 559.31 0.11 559.30 559.15 559.47 2.73 2.25\n", "auxiliary[1,14] 577.48 0.07 577.47 577.38 577.59 7.25 1.05\n", "auxiliary[1,15] 605.21 0.04 605.21 605.15 605.27 6.57 1.15\n", "auxiliary[1,16] 593.95 0.10 593.89 593.83 594.12 2.83 2.08\n", "auxiliary[1,17] 612.22 0.09 612.22 612.05 612.33 2.63 2.36\n", "auxiliary[1,18] 649.67 0.06 649.66 649.58 649.78 6.20 1.40\n", "auxiliary[1,19] 643.71 0.04 643.70 643.65 643.76 15.91 1.03\n", "auxiliary[1,20] 655.04 0.06 655.02 654.95 655.13 5.88 1.24\n", "auxiliary[1,21] 693.86 0.06 693.86 693.76 693.94 8.52 1.00\n", "auxiliary[1,22] 725.68 0.12 725.67 725.50 725.89 3.13 2.19\n", "auxiliary[1,23] 746.03 0.05 746.04 745.95 746.10 6.21 1.21\n", "auxiliary[1,24] 775.36 0.07 775.36 775.26 775.47 7.45 1.74\n", "auxiliary[1,25] 807.90 0.15 807.92 807.71 808.10 2.48 2.47\n", "auxiliary[1,26] 854.78 0.17 854.70 854.55 855.01 2.69 2.36\n", "auxiliary[1,27] 873.09 0.08 873.06 872.97 873.20 5.79 1.64\n", "auxiliary[1,28] 919.17 0.07 919.17 919.06 919.28 7.99 1.00\n", "auxiliary[1,29] 934.36 0.13 934.37 934.16 934.54 2.79 2.90\n", "auxiliary[1,30] 980.98 0.18 981.01 980.67 981.24 2.73 2.43\n", "auxiliary[1,31] 1020.06 0.11 1020.07 1019.90 1020.20 3.37 2.70\n", "auxiliary[1,32] 1069.71 0.24 1069.60 1069.41 1070.09 2.89 2.13\n", "auxiliary[1,33] 1102.95 0.08 1102.93 1102.84 1103.07 3.98 2.28\n", "auxiliary[1,34] 1162.77 0.30 1162.65 1162.43 1163.29 2.79 2.28\n", "auxiliary[1,35] 1197.51 0.07 1197.52 1197.38 1197.63 5.44 1.28\n", "auxiliary[1,36] 1262.75 0.26 1262.74 1262.31 1263.12 3.25 1.77\n", "auxiliary[1,37] 1288.68 0.08 1288.68 1288.57 1288.79 9.47 1.02\n", "auxiliary[1,38] 1361.36 0.17 1361.28 1361.13 1361.61 3.75 1.54\n", "auxiliary[1,39] 1437.15 0.24 1437.04 1436.79 1437.58 3.49 1.60\n", "auxiliary[1,40] 1489.17 0.16 1489.18 1488.94 1489.39 3.73 1.65\n", "auxiliary[1,41] 1593.03 0.11 1593.01 1592.88 1593.20 9.97 1.00\n", "auxiliary[1,42] 1673.85 0.15 1673.82 1673.66 1674.11 4.32 1.50\n", "auxiliary[1,43] 1762.96 0.24 1762.91 1762.62 1763.30 3.62 1.84\n", "auxiliary[1,44] 1778.49 0.26 1778.55 1777.97 1778.79 4.02 1.41\n", "auxiliary[1,45] 1858.52 0.34 1858.68 1857.97 1858.99 4.10 1.82\n", "auxiliary[1,46] 1929.34 0.16 1929.31 1929.07 1929.62 7.56 1.00\n", "auxiliary[1,47] 1981.66 0.15 1981.63 1981.47 1981.92 4.87 1.70\n", "auxiliary[1,48] 2116.77 0.21 2116.74 2116.47 2117.19 5.33 1.02\n", "auxiliary[1,49] 2195.35 0.51 2195.45 2194.68 2196.05 2.39 3.34\n", "auxiliary[1,50] 2303.71 0.28 2303.80 2303.13 2304.04 3.78 1.70\n", "auxiliary[1,51] 2374.06 0.14 2374.03 2373.87 2374.33 8.20 1.19\n", "auxiliary[1,52] 2461.97 0.31 2462.00 2461.50 2462.42 2.99 2.25\n", "auxiliary[1,53] 2653.76 0.38 2653.75 2653.29 2654.42 4.19 1.52\n", "auxiliary[1,54] 2769.96 0.58 2769.93 2769.17 2770.96 2.57 2.88\n", "auxiliary[1,55] 2919.77 0.32 2919.80 2919.29 2920.23 4.78 2.13\n", "auxiliary[1,56] 3109.40 0.81 3109.06 3108.65 3110.86 3.41 1.62\n", "auxiliary[1,57] 3259.81 0.25 3259.78 3259.47 3260.22 10.61 1.04\n", "auxiliary[1,58] 3418.93 0.68 3419.05 3417.84 3419.90 2.79 2.64\n", "auxiliary[1,59] 3574.00 0.56 3574.00 3573.09 3574.88 2.82 2.26\n", "auxiliary[1,60] 3747.35 0.71 3747.15 3746.63 3748.79 3.72 1.53\n", " auxiliary[2,0] 0.66 0.00 0.66 0.66 0.66 3.09 2.33\n", " auxiliary[2,1] 20.35 0.00 20.35 20.35 20.36 2.73 3.31\n", " auxiliary[2,2] 52.12 0.01 52.12 52.10 52.13 3.42 1.51\n", " auxiliary[2,3] 93.05 0.03 93.05 93.00 93.10 2.57 2.66\n", " auxiliary[2,4] 140.07 0.02 140.07 140.04 140.09 3.69 1.80\n", " auxiliary[2,5] 194.43 0.06 194.41 194.33 194.51 2.49 3.09\n", " auxiliary[2,6] 254.53 0.02 254.53 254.51 254.56 4.25 1.38\n", " auxiliary[2,7] 325.05 0.10 324.99 324.93 325.24 2.97 1.89\n", " auxiliary[2,8] 378.96 0.08 378.93 378.88 379.09 3.31 1.57\n", " auxiliary[2,9] 433.76 0.15 433.72 433.57 434.02 2.84 2.21\n", "auxiliary[2,10] 496.00 0.13 495.97 495.86 496.19 2.51 3.38\n", "auxiliary[2,11] 558.36 0.08 558.36 558.24 558.50 3.43 1.84\n", "auxiliary[2,12] 622.68 0.17 622.64 622.46 622.95 2.51 3.00\n", "auxiliary[2,13] 688.36 0.24 688.23 688.10 688.80 3.09 1.73\n", "auxiliary[2,14] 743.98 0.07 743.97 743.88 744.10 4.62 1.92\n", "auxiliary[2,15] 790.26 0.11 790.27 790.04 790.39 3.74 1.66\n", "auxiliary[2,16] 870.87 0.14 870.81 870.71 871.10 2.77 2.11\n", "auxiliary[2,17] 926.75 0.05 926.74 926.67 926.84 10.79 1.01\n", "auxiliary[2,18] 959.61 0.30 959.55 959.18 960.05 2.59 2.77\n", "auxiliary[2,19] 1011.85 0.12 1011.84 1011.68 1012.05 4.52 1.12\n", "auxiliary[2,20] 1061.29 0.08 1061.31 1061.16 1061.40 10.12 1.01\n", "auxiliary[2,21] 1106.37 0.07 1106.39 1106.22 1106.46 4.57 1.73\n", "auxiliary[2,22] 1161.58 0.13 1161.55 1161.38 1161.76 3.97 1.48\n", "auxiliary[2,23] 1211.54 0.12 1211.52 1211.37 1211.75 5.65 1.32\n", "auxiliary[2,24] 1260.43 0.09 1260.46 1260.28 1260.60 6.40 1.10\n", "auxiliary[2,25] 1313.29 0.28 1313.25 1312.85 1313.71 2.59 2.82\n", "auxiliary[2,26] 1344.39 0.22 1344.45 1344.09 1344.68 2.53 3.07\n", "auxiliary[2,27] 1416.11 0.13 1416.08 1415.94 1416.30 4.28 1.19\n", "auxiliary[2,28] 1470.46 0.12 1470.47 1470.29 1470.64 4.06 1.76\n", "auxiliary[2,29] 1547.16 0.17 1547.14 1546.92 1547.41 8.53 1.09\n", "auxiliary[2,30] 1590.03 0.53 1589.72 1589.39 1590.83 2.81 3.26\n", "auxiliary[2,31] 1641.47 0.33 1641.56 1640.96 1641.89 2.76 2.88\n", "auxiliary[2,32] 1721.85 0.19 1721.83 1721.60 1722.16 3.22 2.06\n", "auxiliary[2,33] 1800.01 0.15 1800.05 1799.78 1800.24 5.86 1.00\n", "auxiliary[2,34] 1880.51 0.20 1880.50 1880.20 1880.80 3.61 1.96\n", "auxiliary[2,35] 1968.83 0.24 1968.84 1968.44 1969.18 3.81 1.74\n", "auxiliary[2,36] 2060.30 0.29 2060.28 2059.85 2060.73 2.76 2.15\n", "auxiliary[2,37] 2180.33 0.16 2180.28 2180.10 2180.62 7.75 1.00\n", "auxiliary[2,38] 2285.42 0.38 2285.29 2284.97 2286.03 2.84 2.98\n", "auxiliary[2,39] 2405.67 0.32 2405.67 2405.12 2406.11 3.52 1.70\n", "auxiliary[2,40] 2521.51 0.20 2521.47 2521.24 2521.90 3.43 2.00\n", "auxiliary[2,41] 2617.97 0.33 2617.92 2617.55 2618.48 3.12 2.42\n", "auxiliary[2,42] 2726.84 0.24 2726.82 2726.48 2727.23 4.11 1.99\n", "auxiliary[2,43] 2856.25 0.22 2856.26 2855.87 2856.59 5.14 1.11\n", "auxiliary[2,44] 3002.73 0.33 3002.77 3002.16 3003.08 3.78 1.88\n", "auxiliary[2,45] 3123.51 0.24 3123.55 3123.11 3123.90 8.43 1.06\n", "auxiliary[2,46] 3269.58 0.47 3269.56 3268.81 3270.26 3.16 2.28\n", "auxiliary[2,47] 3434.61 0.26 3434.64 3434.12 3434.93 7.20 1.19\n", "auxiliary[2,48] 3523.67 0.28 3523.76 3523.16 3524.01 3.74 1.58\n", "auxiliary[2,49] 3668.78 0.37 3668.80 3668.17 3669.35 6.28 1.09\n", "auxiliary[2,50] 3818.59 0.43 3818.62 3817.78 3819.18 3.22 2.27\n", "auxiliary[2,51] 4007.06 0.78 4006.84 4005.96 4008.30 3.76 1.63\n", "auxiliary[2,52] 4193.09 0.56 4192.90 4192.41 4193.97 2.67 2.96\n", "auxiliary[2,53] 4351.72 0.34 4351.69 4351.27 4352.33 8.06 1.00\n", "auxiliary[2,54] 4546.88 0.53 4546.79 4546.05 4547.78 4.11 1.57\n", "auxiliary[2,55] 4749.05 0.50 4749.07 4748.35 4749.94 8.08 1.25\n", "auxiliary[2,56] 4965.42 0.40 4965.39 4964.74 4965.98 11.29 1.02\n", "auxiliary[2,57] 5263.68 0.23 5263.67 5263.34 5264.06 23.89 1.00\n", "auxiliary[2,58] 5511.36 1.02 5511.29 5509.70 5512.48 2.53 3.53\n", "auxiliary[2,59] 5778.54 1.08 5778.98 5777.00 5779.87 2.76 2.60\n", "auxiliary[2,60] 6065.71 1.10 6065.34 6064.36 6067.67 2.58 2.98\n", " auxiliary[3,0] 0.50 0.00 0.50 0.50 0.50 6.50 1.12\n", " auxiliary[3,1] 0.50 0.00 0.50 0.50 0.50 8.21 1.20\n", " auxiliary[3,2] 0.50 0.00 0.50 0.50 0.50 6.61 1.01\n", " auxiliary[3,3] 0.50 0.00 0.50 0.50 0.50 2.85 2.54\n", " auxiliary[3,4] 0.50 0.00 0.50 0.50 0.50 6.10 1.07\n", " auxiliary[3,5] 0.50 0.00 0.50 0.50 0.50 4.18 1.59\n", " auxiliary[3,6] 0.50 0.00 0.50 0.50 0.50 6.10 1.20\n", " auxiliary[3,7] 0.50 0.00 0.50 0.50 0.50 3.61 1.96\n", " auxiliary[3,8] 0.50 0.00 0.50 0.50 0.50 2.54 3.71\n", " auxiliary[3,9] 0.50 0.00 0.50 0.50 0.50 5.03 1.00\n", "auxiliary[3,10] 0.50 0.00 0.50 0.50 0.50 5.33 1.50\n", "auxiliary[3,11] 0.50 0.00 0.50 0.50 0.50 3.39 1.52\n", "auxiliary[3,12] 1.12 0.00 1.12 1.12 1.12 3.59 1.30\n", "auxiliary[3,13] 1.39 0.00 1.39 1.39 1.39 6.00 1.12\n", "auxiliary[3,14] 1.40 0.00 1.40 1.40 1.40 3.51 1.80\n", "auxiliary[3,15] 1.54 0.00 1.54 1.54 1.54 5.63 1.37\n", "auxiliary[3,16] 1.39 0.00 1.39 1.39 1.39 5.67 1.33\n", "auxiliary[3,17] 1.20 0.00 1.19 1.19 1.20 2.89 1.95\n", "auxiliary[3,18] 1.48 0.00 1.48 1.48 1.48 4.58 1.50\n", "auxiliary[3,19] 1.63 0.00 1.63 1.63 1.63 5.53 1.03\n", "auxiliary[3,20] 1.56 0.00 1.55 1.55 1.56 4.67 1.15\n", "auxiliary[3,21] 2.07 0.00 2.07 2.07 2.07 8.95 1.02\n", "auxiliary[3,22] 2.53 0.00 2.53 2.53 2.53 9.51 1.06\n", "auxiliary[3,23] 2.59 0.00 2.59 2.59 2.59 3.98 1.63\n", "auxiliary[3,24] 2.60 0.00 2.60 2.60 2.60 2.57 3.16\n", "auxiliary[3,25] 3.49 0.00 3.49 3.49 3.49 4.72 1.02\n", "auxiliary[3,26] 5.66 0.00 5.66 5.66 5.66 6.02 1.33\n", "auxiliary[3,27] 5.46 0.00 5.46 5.46 5.46 4.87 1.78\n", "auxiliary[3,28] 6.96 0.00 6.96 6.96 6.96 2.67 2.30\n", "auxiliary[3,29] 7.74 0.00 7.74 7.74 7.74 3.91 1.83\n", "auxiliary[3,30] 7.82 0.00 7.82 7.82 7.82 4.53 1.67\n", "auxiliary[3,31] 7.53 0.00 7.53 7.52 7.53 2.99 1.91\n", "auxiliary[3,32] 7.52 0.00 7.52 7.52 7.52 8.33 1.01\n", "auxiliary[3,33] 7.72 0.00 7.72 7.71 7.72 3.68 1.42\n", "auxiliary[3,34] 7.57 0.00 7.57 7.56 7.57 4.42 1.02\n", "auxiliary[3,35] 7.32 0.00 7.32 7.32 7.33 9.64 1.03\n", "auxiliary[3,36] 7.72 0.00 7.72 7.72 7.73 2.42 3.27\n", "auxiliary[3,37] 11.27 0.00 11.27 11.27 11.28 2.55 2.59\n", "auxiliary[3,38] 11.41 0.01 11.41 11.40 11.42 2.57 2.59\n", "auxiliary[3,39] 15.71 0.01 15.71 15.70 15.73 2.85 2.15\n", "auxiliary[3,40] 17.36 0.01 17.36 17.34 17.37 2.53 2.70\n", "auxiliary[3,41] 20.47 0.00 20.47 20.47 20.47 3.03 2.23\n", "auxiliary[3,42] 23.73 0.01 23.72 23.71 23.74 2.44 4.03\n", "auxiliary[3,43] 25.43 0.02 25.44 25.41 25.45 2.37 3.36\n", "auxiliary[3,44] 28.81 0.02 28.81 28.78 28.84 2.55 2.80\n", "auxiliary[3,45] 30.59 0.01 30.59 30.58 30.60 2.85 2.48\n", "auxiliary[3,46] 30.92 0.01 30.93 30.91 30.93 2.93 2.12\n", "auxiliary[3,47] 31.80 0.02 31.80 31.77 31.83 2.60 2.51\n", "auxiliary[3,48] 34.43 0.01 34.43 34.42 34.44 3.04 2.00\n", "auxiliary[3,49] 37.27 0.00 37.27 37.27 37.28 6.11 1.09\n", "auxiliary[3,50] 40.68 0.01 40.67 40.66 40.70 2.64 2.33\n", "auxiliary[3,51] 43.09 0.02 43.08 43.07 43.13 2.66 2.31\n", "auxiliary[3,52] 44.90 0.00 44.90 44.89 44.91 6.92 1.02\n", "auxiliary[3,53] 46.60 0.01 46.60 46.59 46.62 2.77 2.21\n", "auxiliary[3,54] 48.53 0.01 48.53 48.51 48.55 2.45 3.40\n", "auxiliary[3,55] 50.81 0.01 50.81 50.80 50.82 3.91 1.63\n", "auxiliary[3,56] 53.02 0.01 53.02 53.02 53.04 3.75 1.76\n", "auxiliary[3,57] 54.83 0.02 54.82 54.81 54.86 2.40 3.51\n", "auxiliary[3,58] 56.19 0.01 56.19 56.17 56.21 2.62 2.36\n", "auxiliary[3,59] 57.17 0.01 57.17 57.15 57.18 3.12 2.14\n", "auxiliary[3,60] 58.08 0.01 58.07 58.07 58.08 4.62 2.44\n", " incub_time 5.71 0.00 5.71 5.71 5.71 7.97 1.01\n", " mort_rate 0.02 0.00 0.02 0.02 0.02 5.30 1.10\n", " rec_rate 0.55 0.00 0.55 0.55 0.55 5.06 1.37\n", " rec_time 16.18 0.00 16.18 16.18 16.18 3.73 2.62\n", " rho 0.17 0.00 0.17 0.17 0.17 2.55 2.62\n", "\n", "Number of divergences: 499\n", "CPU times: user 1min 7s, sys: 507 ms, total: 1min 7s\n", "Wall time: 1min 7s\n" ], "name": "stdout" } ] }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "uVHoVCQxK7uC", "outputId": "09ae3073-eb6b-46d1-849b-1e85db6b9520" }, "source": [ "%%time\n", "Japan_model = CovidModel(126500000, Japan[\"new_cases\"], Japan[\"new_recovered\"], Japan[\"new_deaths\"] )\n", "Japan_mcmc = Japan_model.fit_mcmc(num_samples=500, warmup_steps = 200)\n", "Japan_mcmc.summary()" ], "execution_count": null, "outputs": [ { "output_type": "stream", "text": [ "INFO \t Running inference...\n", "Warmup: 0%| | 0/700 [00:00, ?it/s]INFO \t Heuristic init: R0=1.82, incub_time=6.18, mort_rate=0.0269, rec_rate=0.522, rec_time=21.3, rho=0.179\n", "Sample: 100%|██████████| 700/700 [03:14, 3.59it/s, step size=2.83e-03, acc. prob=0.902]\n" ], "name": "stderr" }, { "output_type": "stream", "text": [ "\n", " mean std median 5.0% 95.0% n_eff r_hat\n", " R0 1.79 0.01 1.80 1.77 1.81 2.61 2.43\n", " auxiliary[0,0] 126499875.14 1.63 126499875.67 126499872.40 126499877.39 3.23 1.59\n", " auxiliary[0,1] 126499754.75 6.21 126499753.75 126499746.75 126499764.75 2.55 2.54\n", " auxiliary[0,2] 126499625.88 10.52 126499624.23 126499611.53 126499643.13 2.50 2.74\n", " auxiliary[0,3] 126499489.51 14.12 126499487.21 126499470.48 126499513.28 2.54 2.59\n", " auxiliary[0,4] 126499348.50 17.42 126499345.65 126499322.72 126499376.29 2.57 2.53\n", " auxiliary[0,5] 126499203.81 21.27 126499199.38 126499173.62 126499236.91 2.52 2.61\n", " auxiliary[0,6] 126499056.45 25.10 126499050.11 126499018.49 126499094.75 2.56 2.54\n", " auxiliary[0,7] 126498907.65 29.93 126498902.53 126498862.83 126498954.15 2.58 2.47\n", " auxiliary[0,8] 126498757.91 34.95 126498751.36 126498704.63 126498810.43 2.60 2.46\n", " auxiliary[0,9] 126498607.76 40.82 126498600.37 126498549.00 126498670.83 2.58 2.51\n", "auxiliary[0,10] 126498458.77 46.22 126498451.22 126498393.21 126498528.66 2.57 2.55\n", "auxiliary[0,11] 126498308.67 52.53 126498300.50 126498233.69 126498386.42 2.56 2.55\n", "auxiliary[0,12] 126498158.67 59.89 126498149.87 126498072.50 126498247.10 2.57 2.52\n", "auxiliary[0,13] 126498008.49 66.55 126497998.35 126497914.21 126498106.58 2.58 2.50\n", "auxiliary[0,14] 126497858.89 73.18 126497846.26 126497757.49 126497967.71 2.57 2.51\n", "auxiliary[0,15] 126497708.45 79.51 126497696.07 126497597.52 126497827.85 2.56 2.52\n", "auxiliary[0,16] 126497558.14 86.50 126497542.96 126497438.03 126497687.85 2.56 2.53\n", "auxiliary[0,17] 126497407.69 92.82 126497392.30 126497278.05 126497545.60 2.57 2.51\n", "auxiliary[0,18] 126497257.26 99.44 126497241.25 126497116.75 126497406.90 2.58 2.49\n", "auxiliary[0,19] 126497106.76 106.54 126497088.96 126496958.82 126497268.31 2.58 2.49\n", "auxiliary[0,20] 126496956.50 114.03 126496937.21 126496799.09 126497128.80 2.57 2.50\n", "auxiliary[0,21] 126496805.82 121.89 126496785.56 126496635.96 126496988.19 2.56 2.51\n", "auxiliary[0,22] 126496655.76 129.55 126496633.80 126496475.78 126496849.77 2.55 2.53\n", "auxiliary[0,23] 126496505.51 137.62 126496482.48 126496313.62 126496713.14 2.55 2.53\n", "auxiliary[0,24] 126496355.02 145.34 126496328.35 126496151.89 126496573.23 2.55 2.54\n", "auxiliary[0,25] 126496204.02 152.69 126496175.65 126495991.65 126496435.47 2.55 2.55\n", "auxiliary[0,26] 126496052.19 160.59 126496022.88 126495828.54 126496295.58 2.55 2.53\n", "auxiliary[0,27] 126495900.39 168.78 126495870.34 126495664.80 126496157.35 2.55 2.52\n", "auxiliary[0,28] 126495747.56 176.76 126495714.66 126495499.23 126496015.63 2.55 2.52\n", "auxiliary[0,29] 126495593.54 184.09 126495560.44 126495332.98 126495871.40 2.55 2.52\n", "auxiliary[0,30] 126495437.79 191.63 126495403.44 126495168.69 126495729.14 2.55 2.53\n", "auxiliary[0,31] 126495280.46 199.66 126495245.72 126495003.65 126495585.24 2.54 2.54\n", "auxiliary[0,32] 126495121.08 207.70 126495083.11 126494834.15 126495443.08 2.54 2.54\n", "auxiliary[0,33] 126494959.99 215.23 126494923.38 126494659.94 126495293.12 2.54 2.55\n", "auxiliary[0,34] 126494796.78 222.12 126494758.79 126494488.62 126495138.45 2.53 2.55\n", "auxiliary[0,35] 126494630.96 228.14 126494594.60 126494315.06 126494982.76 2.54 2.54\n", "auxiliary[0,36] 126494464.26 234.36 126494426.90 126494138.39 126494825.82 2.54 2.54\n", "auxiliary[0,37] 126494295.79 239.41 126494260.34 126493960.43 126494664.60 2.53 2.55\n", "auxiliary[0,38] 126494124.70 244.74 126494089.92 126493783.47 126494502.22 2.53 2.55\n", "auxiliary[0,39] 126493950.91 250.04 126493912.57 126493602.70 126494337.22 2.53 2.55\n", "auxiliary[0,40] 126493776.32 255.20 126493738.06 126493416.46 126494170.28 2.53 2.56\n", "auxiliary[0,41] 126493599.94 260.63 126493561.49 126493233.78 126494001.33 2.53 2.56\n", "auxiliary[0,42] 126493420.34 265.94 126493382.32 126493043.22 126493826.76 2.52 2.57\n", "auxiliary[0,43] 126493239.68 271.25 126493198.38 126492855.24 126493653.58 2.52 2.57\n", "auxiliary[0,44] 126493057.85 276.32 126493016.83 126492666.44 126493480.67 2.52 2.57\n", "auxiliary[0,45] 126492873.34 281.47 126492832.41 126492474.07 126493304.11 2.52 2.57\n", "auxiliary[0,46] 126492686.02 286.45 126492640.83 126492279.96 126493125.16 2.52 2.57\n", "auxiliary[0,47] 126492496.40 291.43 126492450.89 126492084.46 126492940.95 2.52 2.57\n", "auxiliary[0,48] 126492303.66 296.18 126492254.31 126491887.95 126492759.50 2.52 2.58\n", "auxiliary[0,49] 126492108.82 301.13 126492060.30 126491682.68 126492568.60 2.51 2.59\n", "auxiliary[0,50] 126491910.31 306.06 126491863.01 126491477.78 126492375.68 2.51 2.61\n", "auxiliary[0,51] 126491709.45 310.23 126491663.15 126491266.99 126492184.30 2.50 2.62\n", "auxiliary[0,52] 126491505.23 314.45 126491459.02 126491057.46 126491983.99 2.50 2.62\n", "auxiliary[0,53] 126491298.27 318.89 126491253.96 126490840.61 126491777.35 2.50 2.63\n", "auxiliary[0,54] 126491088.95 323.72 126491044.58 126490620.33 126491570.89 2.50 2.63\n", "auxiliary[0,55] 126490876.92 328.89 126490831.78 126490405.20 126491368.54 2.50 2.63\n", "auxiliary[0,56] 126490662.41 334.50 126490614.62 126490179.54 126491161.10 2.50 2.62\n", "auxiliary[0,57] 126490447.00 340.69 126490399.77 126489958.36 126490959.82 2.50 2.62\n", "auxiliary[0,58] 126490231.00 347.47 126490181.97 126489735.55 126490749.86 2.50 2.61\n", "auxiliary[0,59] 126490013.01 354.13 126489958.90 126489506.59 126490540.32 2.50 2.60\n", "auxiliary[0,60] 126489794.15 361.55 126489737.52 126489278.71 126490332.36 2.50 2.59\n", " auxiliary[1,0] 110.93 1.55 110.43 108.95 113.73 3.39 1.48\n", " auxiliary[1,1] 198.02 5.55 198.88 189.26 205.23 2.54 2.56\n", " auxiliary[1,2] 266.13 8.16 266.78 253.23 277.12 2.44 2.93\n", " auxiliary[1,3] 337.79 9.18 338.24 323.38 350.23 2.50 2.72\n", " auxiliary[1,4] 377.44 7.64 377.61 366.47 390.58 2.82 2.21\n", " auxiliary[1,5] 420.52 7.48 420.69 411.49 432.35 2.41 3.09\n", " auxiliary[1,6] 450.30 5.16 449.76 443.43 458.67 2.98 2.13\n", " auxiliary[1,7] 475.83 3.33 474.79 470.66 480.19 3.62 1.65\n", " auxiliary[1,8] 513.72 3.30 513.23 507.53 517.62 5.94 1.29\n", " auxiliary[1,9] 536.06 3.81 535.80 529.57 543.00 4.17 1.69\n", "auxiliary[1,10] 546.57 1.69 546.79 543.56 548.80 5.44 1.45\n", "auxiliary[1,11] 576.91 2.26 576.37 573.81 581.02 3.65 1.79\n", "auxiliary[1,12] 587.22 2.10 587.59 583.16 590.11 7.95 1.25\n", "auxiliary[1,13] 610.38 1.69 610.32 607.77 613.14 8.39 1.00\n", "auxiliary[1,14] 620.17 2.52 619.89 615.48 623.89 6.16 1.54\n", "auxiliary[1,15] 637.83 3.17 638.91 632.28 641.92 4.12 1.53\n", "auxiliary[1,16] 648.20 5.29 648.82 640.80 655.27 2.63 3.06\n", "auxiliary[1,17] 654.27 2.56 653.64 651.04 659.46 4.14 1.36\n", "auxiliary[1,18] 657.58 2.58 656.90 654.22 662.54 6.19 1.25\n", "auxiliary[1,19] 662.18 1.65 662.15 659.33 664.43 6.13 1.22\n", "auxiliary[1,20] 657.29 2.79 656.99 653.55 662.19 4.38 1.26\n", "auxiliary[1,21] 689.57 3.44 688.09 684.29 695.08 3.26 2.31\n", "auxiliary[1,22] 706.82 1.90 707.02 703.88 710.17 6.07 1.18\n", "auxiliary[1,23] 715.63 1.52 715.44 713.13 717.81 11.01 1.15\n", "auxiliary[1,24] 719.26 1.17 719.21 717.24 721.01 11.88 1.01\n", "auxiliary[1,25] 712.93 2.57 712.36 709.34 716.59 4.39 1.12\n", "auxiliary[1,26] 736.99 2.90 736.88 733.02 742.33 3.10 1.99\n", "auxiliary[1,27] 735.44 2.75 735.57 730.16 738.53 3.34 1.86\n", "auxiliary[1,28] 743.42 5.30 744.00 735.59 749.79 2.36 3.87\n", "auxiliary[1,29] 748.25 5.50 746.36 741.25 758.09 2.92 1.95\n", "auxiliary[1,30] 764.05 4.71 764.28 754.86 770.65 3.55 1.78\n", "auxiliary[1,31] 787.54 5.72 786.22 780.60 796.93 2.85 2.08\n", "auxiliary[1,32] 822.95 3.15 823.54 817.19 827.49 5.23 1.40\n", "auxiliary[1,33] 850.90 8.18 852.11 837.01 860.85 2.55 2.55\n", "auxiliary[1,34] 888.27 7.55 893.01 878.34 897.75 2.48 3.37\n", "auxiliary[1,35] 946.45 4.35 947.14 939.50 953.26 3.41 2.03\n", "auxiliary[1,36] 955.39 5.45 952.78 948.54 963.91 2.82 2.02\n", "auxiliary[1,37] 961.99 3.84 961.43 957.03 968.40 3.40 1.62\n", "auxiliary[1,38] 1004.19 4.09 1004.85 998.29 1009.81 2.72 3.02\n", "auxiliary[1,39] 1064.85 4.06 1065.34 1058.75 1071.22 5.63 1.14\n", "auxiliary[1,40] 1097.19 5.28 1096.64 1089.49 1104.70 2.55 2.70\n", "auxiliary[1,41] 1102.75 4.03 1101.95 1096.25 1108.28 6.01 1.19\n", "auxiliary[1,42] 1159.85 7.98 1160.64 1147.41 1170.78 2.60 2.73\n", "auxiliary[1,43] 1181.85 6.91 1181.07 1172.00 1192.83 3.21 1.67\n", "auxiliary[1,44] 1187.55 3.08 1187.91 1182.43 1192.15 7.82 1.11\n", "auxiliary[1,45] 1209.66 9.70 1205.46 1198.25 1225.41 2.57 2.53\n", "auxiliary[1,46] 1240.76 8.76 1235.65 1230.66 1253.67 2.70 2.31\n", "auxiliary[1,47] 1263.41 5.14 1263.25 1253.37 1271.56 5.26 1.36\n", "auxiliary[1,48] 1307.03 4.41 1307.81 1299.56 1313.35 5.03 1.23\n", "auxiliary[1,49] 1330.91 8.88 1329.04 1320.02 1344.15 2.42 3.03\n", "auxiliary[1,50] 1385.62 5.52 1384.14 1379.17 1395.17 3.58 1.62\n", "auxiliary[1,51] 1447.66 7.35 1445.26 1438.00 1459.19 3.33 1.70\n", "auxiliary[1,52] 1509.83 4.66 1509.97 1502.06 1516.84 7.75 1.10\n", "auxiliary[1,53] 1569.84 5.47 1571.02 1560.06 1578.14 3.50 1.66\n", "auxiliary[1,54] 1620.06 8.56 1616.30 1609.99 1633.17 2.46 3.14\n", "auxiliary[1,55] 1685.80 9.93 1683.86 1669.82 1700.01 2.86 2.19\n", "auxiliary[1,56] 1759.09 5.27 1760.78 1748.46 1765.54 4.31 1.51\n", "auxiliary[1,57] 1810.41 5.53 1811.95 1799.66 1816.12 3.41 1.80\n", "auxiliary[1,58] 1839.52 7.09 1839.06 1828.65 1849.76 6.32 1.01\n", "auxiliary[1,59] 1888.84 8.10 1886.09 1876.00 1901.31 3.62 1.61\n", "auxiliary[1,60] 1900.01 10.12 1903.70 1885.81 1915.24 2.78 2.68\n", " auxiliary[2,0] 1.07 0.01 1.07 1.05 1.09 2.88 2.07\n", " auxiliary[2,1] 18.46 0.27 18.44 18.10 18.93 2.65 2.33\n", " auxiliary[2,2] 47.29 0.66 47.33 46.33 48.44 2.70 2.39\n", " auxiliary[2,3] 70.10 0.55 69.96 69.37 71.00 2.74 2.07\n", " auxiliary[2,4] 125.92 2.19 125.77 123.07 128.63 2.31 3.60\n", " auxiliary[2,5] 175.49 1.19 175.54 173.48 177.24 4.40 1.47\n", " auxiliary[2,6] 238.03 1.66 237.59 235.10 240.36 3.03 1.98\n", " auxiliary[2,7] 302.84 2.51 302.35 299.78 308.12 4.07 1.54\n", " auxiliary[2,8] 352.94 1.98 352.89 349.02 356.08 5.27 1.08\n", " auxiliary[2,9] 417.62 1.58 417.49 415.94 421.53 8.03 1.10\n", "auxiliary[2,10] 489.63 1.74 489.68 486.72 492.13 5.22 1.00\n", "auxiliary[2,11] 540.75 3.31 541.49 534.56 544.68 3.80 1.78\n", "auxiliary[2,12] 610.42 2.04 610.01 607.43 614.23 5.98 1.13\n", "auxiliary[2,13] 665.93 2.89 665.33 661.83 671.29 6.06 1.13\n", "auxiliary[2,14] 732.40 2.10 732.09 729.03 735.77 7.31 1.06\n", "auxiliary[2,15] 790.45 4.02 790.39 783.69 796.93 5.71 1.38\n", "auxiliary[2,16] 854.63 5.92 852.62 847.55 864.97 2.70 2.23\n", "auxiliary[2,17] 922.34 3.63 922.33 917.09 928.65 7.15 1.02\n", "auxiliary[2,18] 991.54 6.43 988.98 983.40 1000.67 3.20 1.74\n", "auxiliary[2,19] 1058.74 4.80 1059.56 1050.35 1066.44 3.86 1.53\n", "auxiliary[2,20] 1133.63 5.29 1133.36 1125.54 1141.82 3.17 1.97\n", "auxiliary[2,21] 1169.23 5.23 1168.59 1162.57 1179.50 3.26 1.77\n", "auxiliary[2,22] 1217.67 3.86 1218.55 1210.05 1222.47 5.15 1.00\n", "auxiliary[2,23] 1273.84 4.77 1274.05 1267.20 1281.64 3.97 1.31\n", "auxiliary[2,24] 1335.00 5.72 1335.21 1326.16 1342.87 3.39 1.73\n", "auxiliary[2,25] 1407.03 6.70 1407.25 1397.95 1418.26 2.81 2.93\n", "auxiliary[2,26] 1447.77 4.85 1447.72 1438.39 1453.67 4.22 1.88\n", "auxiliary[2,27] 1515.00 8.11 1515.79 1502.42 1527.69 2.89 2.11\n", "auxiliary[2,28] 1574.38 8.51 1574.17 1557.92 1586.73 3.64 1.68\n", "auxiliary[2,29] 1639.70 9.57 1640.31 1624.07 1654.61 2.99 2.05\n", "auxiliary[2,30] 1697.41 12.43 1694.10 1681.90 1717.55 2.57 2.47\n", "auxiliary[2,31] 1750.74 14.68 1750.67 1728.70 1771.69 2.45 2.85\n", "auxiliary[2,32] 1795.75 21.64 1795.75 1765.55 1828.53 2.53 2.58\n", "auxiliary[2,33] 1851.32 17.11 1852.36 1827.07 1873.83 2.45 2.79\n", "auxiliary[2,34] 1901.00 18.87 1901.41 1873.46 1929.08 2.61 2.35\n", "auxiliary[2,35] 1934.01 22.43 1932.05 1898.92 1965.56 2.61 2.35\n", "auxiliary[2,36] 2018.79 20.83 2022.37 1984.38 2044.93 2.55 2.51\n", "auxiliary[2,37] 2108.23 20.86 2106.03 2078.50 2137.58 2.53 2.69\n", "auxiliary[2,38] 2165.09 20.07 2162.32 2135.28 2200.36 2.81 2.18\n", "auxiliary[2,39] 2207.75 20.98 2202.25 2179.07 2240.70 2.61 2.36\n", "auxiliary[2,40] 2280.08 17.21 2278.86 2250.88 2307.99 2.85 2.15\n", "auxiliary[2,41] 2382.23 19.64 2384.94 2352.68 2409.20 2.55 2.55\n", "auxiliary[2,42] 2436.44 15.80 2431.22 2411.98 2462.37 3.26 1.81\n", "auxiliary[2,43] 2527.71 17.69 2530.78 2497.35 2551.82 2.98 2.05\n", "auxiliary[2,44] 2637.05 21.24 2637.19 2605.29 2669.62 2.64 2.35\n", "auxiliary[2,45] 2733.18 13.22 2734.64 2709.84 2751.81 3.04 2.02\n", "auxiliary[2,46] 2823.92 14.83 2826.46 2797.18 2845.10 3.04 2.05\n", "auxiliary[2,47] 2926.20 20.31 2930.42 2894.01 2956.18 2.72 2.24\n", "auxiliary[2,48] 3011.02 21.91 3006.45 2982.06 3051.88 2.70 2.29\n", "auxiliary[2,49] 3118.12 16.29 3118.80 3088.49 3139.13 2.79 2.25\n", "auxiliary[2,50] 3198.52 21.24 3193.81 3170.86 3233.15 2.44 3.30\n", "auxiliary[2,51] 3274.18 20.78 3274.03 3240.32 3299.50 2.48 2.95\n", "auxiliary[2,52] 3353.46 25.22 3347.47 3318.69 3386.27 2.42 3.04\n", "auxiliary[2,53] 3438.38 26.02 3426.44 3410.15 3479.59 2.69 2.35\n", "auxiliary[2,54] 3536.04 23.33 3527.30 3505.35 3573.95 2.68 2.22\n", "auxiliary[2,55] 3621.35 25.03 3613.13 3590.67 3664.14 2.67 2.28\n", "auxiliary[2,56] 3701.99 34.08 3687.69 3661.76 3756.21 2.64 2.19\n", "auxiliary[2,57] 3805.90 36.47 3791.04 3761.82 3863.37 2.64 2.23\n", "auxiliary[2,58] 3932.71 44.80 3918.28 3884.41 4008.25 2.68 2.18\n", "auxiliary[2,59] 4041.61 54.92 4036.61 3968.44 4126.61 2.57 2.37\n", "auxiliary[2,60] 4189.84 62.21 4178.35 4108.65 4284.76 2.48 2.56\n", " auxiliary[3,0] 0.47 0.01 0.47 0.46 0.49 2.52 2.68\n", " auxiliary[3,1] 0.63 0.01 0.63 0.62 0.64 2.46 2.70\n", " auxiliary[3,2] 1.00 0.01 1.00 0.99 1.01 5.29 1.02\n", " auxiliary[3,3] 1.25 0.01 1.25 1.23 1.25 3.75 1.67\n", " auxiliary[3,4] 1.48 0.02 1.48 1.44 1.49 2.83 2.11\n", " auxiliary[3,5] 1.59 0.01 1.59 1.57 1.61 2.61 2.81\n", " auxiliary[3,6] 1.38 0.00 1.38 1.38 1.39 6.13 1.13\n", " auxiliary[3,7] 1.29 0.01 1.29 1.28 1.30 2.74 2.33\n", " auxiliary[3,8] 1.27 0.00 1.27 1.26 1.27 9.21 1.00\n", " auxiliary[3,9] 1.20 0.01 1.20 1.18 1.21 2.50 2.56\n", "auxiliary[3,10] 1.24 0.00 1.24 1.23 1.25 3.79 1.84\n", "auxiliary[3,11] 1.56 0.02 1.56 1.53 1.59 2.51 2.97\n", "auxiliary[3,12] 2.29 0.09 2.27 2.17 2.44 2.65 2.32\n", "auxiliary[3,13] 2.32 0.01 2.32 2.31 2.33 5.59 1.49\n", "auxiliary[3,14] 2.37 0.02 2.36 2.34 2.41 2.99 2.23\n", "auxiliary[3,15] 2.75 0.03 2.74 2.71 2.79 4.61 1.47\n", "auxiliary[3,16] 3.03 0.03 3.03 2.98 3.08 3.14 1.86\n", "auxiliary[3,17] 3.13 0.01 3.13 3.12 3.15 5.05 1.40\n", "auxiliary[3,18] 3.27 0.01 3.27 3.25 3.28 7.83 1.12\n", "auxiliary[3,19] 3.39 0.01 3.39 3.38 3.41 3.33 1.78\n", "auxiliary[3,20] 3.59 0.01 3.59 3.57 3.60 6.84 1.18\n", "auxiliary[3,21] 3.72 0.02 3.72 3.70 3.75 2.80 2.65\n", "auxiliary[3,22] 3.87 0.03 3.87 3.82 3.91 2.50 2.90\n", "auxiliary[3,23] 4.08 0.07 4.11 3.96 4.17 2.62 2.46\n", "auxiliary[3,24] 4.67 0.08 4.71 4.53 4.75 2.74 2.19\n", "auxiliary[3,25] 5.49 0.03 5.49 5.45 5.55 3.71 1.61\n", "auxiliary[3,26] 6.26 0.09 6.23 6.15 6.42 3.23 1.85\n", "auxiliary[3,27] 7.00 0.10 6.96 6.88 7.18 2.85 2.23\n", "auxiliary[3,28] 7.61 0.07 7.61 7.50 7.72 2.47 2.79\n", "auxiliary[3,29] 8.16 0.06 8.17 8.08 8.26 2.64 2.80\n", "auxiliary[3,30] 8.70 0.04 8.70 8.64 8.75 7.86 1.09\n", "auxiliary[3,31] 9.22 0.12 9.21 9.08 9.44 2.63 2.41\n", "auxiliary[3,32] 9.81 0.22 9.78 9.53 10.15 2.49 2.59\n", "auxiliary[3,33] 10.56 0.41 10.62 9.94 11.12 2.49 2.65\n", "auxiliary[3,34] 11.58 0.57 11.63 10.63 12.39 2.53 2.58\n", "auxiliary[3,35] 12.93 0.65 13.00 11.99 13.93 2.54 2.56\n", "auxiliary[3,36] 14.60 0.61 14.64 13.69 15.49 2.59 2.47\n", "auxiliary[3,37] 16.30 0.56 16.35 15.49 17.05 2.68 2.33\n", "auxiliary[3,38] 18.10 0.44 18.18 17.42 18.68 2.81 2.13\n", "auxiliary[3,39] 19.91 0.32 20.03 19.40 20.27 3.09 1.87\n", "auxiliary[3,40] 21.74 0.18 21.83 21.41 21.89 3.78 1.45\n", "auxiliary[3,41] 23.60 0.09 23.62 23.47 23.75 4.22 1.21\n", "auxiliary[3,42] 25.47 0.23 25.51 25.13 25.77 2.56 2.42\n", "auxiliary[3,43] 27.30 0.42 27.30 26.74 27.93 2.53 2.59\n", "auxiliary[3,44] 29.09 0.62 29.01 28.28 30.13 2.54 2.58\n", "auxiliary[3,45] 30.83 0.82 30.66 29.78 32.27 2.53 2.60\n", "auxiliary[3,46] 32.51 1.03 32.29 30.96 34.05 2.53 2.58\n", "auxiliary[3,47] 34.12 1.23 33.90 32.30 36.00 2.53 2.56\n", "auxiliary[3,48] 35.71 1.43 35.50 33.57 37.87 2.54 2.54\n", "auxiliary[3,49] 37.27 1.62 36.98 34.90 39.74 2.54 2.54\n", "auxiliary[3,50] 38.74 1.79 38.39 36.17 41.47 2.54 2.53\n", "auxiliary[3,51] 40.10 1.93 39.72 37.34 43.06 2.55 2.51\n", "auxiliary[3,52] 41.38 2.03 41.01 38.50 44.50 2.56 2.51\n", "auxiliary[3,53] 42.57 2.12 42.13 39.68 45.85 2.57 2.49\n", "auxiliary[3,54] 43.70 2.19 43.26 40.72 47.09 2.57 2.50\n", "auxiliary[3,55] 44.77 2.25 44.34 41.70 48.20 2.57 2.50\n", "auxiliary[3,56] 45.81 2.28 45.39 42.74 49.31 2.57 2.51\n", "auxiliary[3,57] 46.81 2.31 46.40 43.76 50.35 2.57 2.51\n", "auxiliary[3,58] 47.79 2.32 47.38 44.76 51.41 2.57 2.51\n", "auxiliary[3,59] 48.76 2.34 48.32 45.69 52.38 2.57 2.52\n", "auxiliary[3,60] 49.70 2.34 49.27 46.64 53.42 2.57 2.52\n", " incub_time 6.18 0.00 6.18 6.18 6.19 7.10 1.28\n", " mort_rate 0.03 0.00 0.03 0.03 0.03 2.90 3.00\n", " rec_rate 0.52 0.00 0.52 0.52 0.52 2.95 2.20\n", " rec_time 21.34 0.00 21.34 21.33 21.35 2.97 2.38\n", " rho 0.28 0.01 0.28 0.27 0.30 2.55 2.51\n", "\n", "Number of divergences: 0\n", "CPU times: user 3min 13s, sys: 1.23 s, total: 3min 15s\n", "Wall time: 3min 15s\n" ], "name": "stdout" } ] } ] }