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      "name": "Non_markov_SIR_covid.ipynb",
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/mazzalab/playgrounds/blob/master/Non_markov_SIR_covid.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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        },
        "outputId": "bea41203-eba4-4401-f764-425a2bd2cf02",
        "cellView": "form"
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      "source": [
        "#@title Import libraries (including Epidemics on Networks - EoN)\n",
        "!pip install EoN\n",
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "import EoN\n",
        "import random\n",
        "from random import sample\n",
        "import ipywidgets as widgets\n",
        "\n",
        "\n",
        "from operator import itemgetter\n",
        "import networkx.linalg\n",
        "from datetime import datetime"
      ],
      "id": "b6f390ac",
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting EoN\n",
            "  Downloading EoN-1.1.tar.gz (113 kB)\n",
            "\u001b[K     |████████████████████████████████| 113 kB 13.0 MB/s \n",
            "\u001b[?25hRequirement already satisfied: networkx in /usr/local/lib/python3.7/dist-packages (from EoN) (2.6.3)\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from EoN) (1.21.6)\n",
            "Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from EoN) (1.4.1)\n",
            "Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from EoN) (3.2.2)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.7/dist-packages (from matplotlib->EoN) (0.11.0)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->EoN) (1.4.2)\n",
            "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->EoN) (2.8.2)\n",
            "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->EoN) (3.0.9)\n",
            "Requirement already satisfied: typing-extensions in /usr/local/lib/python3.7/dist-packages (from kiwisolver>=1.0.1->matplotlib->EoN) (4.2.0)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.7/dist-packages (from python-dateutil>=2.1->matplotlib->EoN) (1.15.0)\n",
            "Building wheels for collected packages: EoN\n",
            "  Building wheel for EoN (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for EoN: filename=EoN-1.1-py3-none-any.whl size=120819 sha256=069f30cc5ae6a9e71a16673c9ed92a5c33dcfc0c115c1956c5575256e8d60095\n",
            "  Stored in directory: /root/.cache/pip/wheels/0b/c0/a4/d6001fd809cb84c027ada5c2ab3b6d1cb2e97fec3f9978eae7\n",
            "Successfully built EoN\n",
            "Installing collected packages: EoN\n",
            "Successfully installed EoN-1.1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "code_folding": [],
        "id": "d398b7b3",
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      "source": [
        "#@title Simulation code\n",
        "def trans_time_fxn(source, target, rate):\n",
        "    return random.expovariate(rate)\n",
        "\n",
        "def rec_time_fxn(node,D):\n",
        "    return D\n",
        "\n",
        "def fast_nonMarkov_SIR_full_data(graph, transmission_rate, recovery_rate, tsim_max, infected_num=None, recovered_num=None, tstart = 0):\n",
        "    G = graph\n",
        "  #  rho = ratio_infected             # initial fraction infected\n",
        "    infected_nodes = infected_num    # index of infected nodes\n",
        "    recovered_nodes = recovered_num  # index of recovedred nodes\n",
        "    tau = transmission_rate          # transmission rate\n",
        "    gamma = recovery_rate            # recovery rate\n",
        "    max_sim_time = tsim_max          # maximum simulation time\n",
        "    D=14\n",
        "\n",
        "    print(\"doing Event-driven simulation\")\n",
        "    full_data = EoN.fast_nonMarkov_SIR(G, trans_time_fxn=trans_time_fxn, rec_time_fxn=rec_time_fxn, trans_time_args=(tau,), rec_time_args=(D,), tmin=tstart, tmax = max_sim_time, initial_infecteds=infected_nodes, initial_recovereds=recovered_nodes, return_full_data = True)\n",
        "\n",
        "    return full_data\n",
        "def simulation_loop(G, toberemoved_nodes, transmission_rate, recovery_rate, tsim_max, init_infected):\n",
        "\n",
        "    #@markdown Choose a vaccination strategy\n",
        "    metrics = \"betweenness\" #@param [\"betweenness\", \"degree\",\"eigenvector\"]\n",
        "\n",
        "    degree_dict=dict(G.degree(G.nodes()))\n",
        "# arricchimento del grafo con le informazioni su centralita' dei vari nodi\n",
        "    if metrics==\"betweenness\":\n",
        "        betweenness_dict=nx.betweenness_centrality(G) # eigenvector centrality, closeness centrality\n",
        "        nx.set_node_attributes(G, betweenness_dict, 'betweenness')\n",
        "        sorted_betweenness=sorted(betweenness_dict.items(), key=itemgetter(1),reverse=True)\n",
        "    elif metrics==\"degree\":\n",
        "        sorted_degree= sorted(degree_dict.items(), key=itemgetter(1),reverse=True)\n",
        "        sorted_degree_rev= sorted(degree_dict.items(), key=itemgetter(1),reverse=False)\n",
        "        nx.set_node_attributes(G, sorted_degree, 'degree')\n",
        "    elif metrics==\"eigenvector\":\n",
        "        eigenvector_dict=nx.eigenvector_centrality(G)\n",
        "        nx.set_node_attributes(G, eigenvector_dict, 'eigenvector')\n",
        "        sorted_eigenvector=sorted(eigenvector_dict.items(),key=itemgetter(1),reverse=True)\n",
        "\n",
        "    vaccination_time  = 2 #@param {type:\"number\"}\n",
        "    trigger_time = int(tsim_max - vaccination_time)\n",
        "\n",
        "    # define random initial infected nodes\n",
        "    ratio = (G.number_of_nodes())*init_infected\n",
        "    init_infected_nodes = sample(list(G.nodes()), int(ratio))\n",
        "    print('Number of initial infected nodes: {}'.format(len(init_infected_nodes)))\n",
        "\n",
        "    # Original graph ---------------------------------------------\n",
        "    print('Original graph')\n",
        "    maxautovaloreoriginale=max(nx.linalg.adjacency_spectrum(G))\n",
        "    # start simulation - full data \n",
        "    # t, S, I\n",
        "    # res_orig = fast_SIS(G, init_infected, transmission_rate, recovery_rate, tsim_max)\n",
        "    res_orig_before = fast_nonMarkov_SIR_full_data(G, transmission_rate, recovery_rate, tsim_max - trigger_time, infected_num=init_infected_nodes)\n",
        "    ## get the node statuses at trigger time\n",
        "    res_orig_before_status = res_orig_before.get_statuses(time=tsim_max - trigger_time)\n",
        "    Snodes = [k for k,v in res_orig_before_status.items() if v == 'S']\n",
        "    Inodes = [k for k,v in res_orig_before_status.items() if v == 'I']\n",
        "    Rnodes = [k for k,v in res_orig_before_status.items() if v == 'R']\n",
        "\n",
        "    print('Number of S nodes before vaccination at time {}: {}'.format(tsim_max-trigger_time, len(Snodes)))\n",
        "    print('Number of I nodes before vaccination at time {}: {}'.format(tsim_max-trigger_time, len(Inodes)))\n",
        "    print('Number of R nodes before vaccination at time {}: {}'.format(tsim_max-trigger_time, len(Rnodes)))\n",
        "    \n",
        "    # restart with infected nodes without any vaccination strategy\n",
        "    res_orig_after = fast_nonMarkov_SIR_full_data(G, transmission_rate, recovery_rate, tsim_max, infected_num=Inodes, recovered_num=Rnodes,  tstart=tsim_max - trigger_time)  \n",
        "    res_orig = (list(res_orig_before.t())+list(res_orig_after.t()[1:]), \n",
        "               list(res_orig_before.S())+list(res_orig_after.S()[1:]),\n",
        "               list(res_orig_before.I())+list(res_orig_after.I()[1:]),\n",
        "               list(res_orig_before.R())+list(res_orig_after.R()[1:]))\n",
        "    \n",
        "    res_orig_after_status = res_orig_after.get_statuses(time=tsim_max)\n",
        "    Snodes_res_orig_after = [k for k,v in res_orig_after_status.items() if v == 'S']\n",
        "    Inodes_res_orig_after = [k for k,v in res_orig_after_status.items() if v == 'I']\n",
        "    Rnodes_res_orig_after = [k for k,v in res_orig_after_status.items() if v == 'R']\n",
        "\n",
        "    print('Final number of S nodes without vaccination: {}'.format(len(Snodes_res_orig_after)))\n",
        "    print('Final number of I nodes without vaccination: {}'.format(len(Inodes_res_orig_after)))\n",
        "    print('Final number of R nodes without vaccination: {}'.format(len(Rnodes_res_orig_after)))   \n",
        "   \n",
        "    print(nx.info(G)+\"\\n\")\n",
        "    print('\\n')   \n",
        "  \n",
        "\n",
        "    # Controlled vaccination -----------------------------------------------\n",
        "    tobevaccinated= list()\n",
        "    Gcopia=nx.Graph()\n",
        "    Gcopia.add_edges_from(G.edges())\n",
        "    \n",
        "    if metrics==\"betweenness\":\n",
        "      sorted_betweenness = [x for x in sorted_betweenness if x[0] not in Inodes]\n",
        "      for d in sorted_betweenness[:tobevaccinated_nodes]:\n",
        "          tobevaccinated.append(d[0])\n",
        "    if metrics==\"degree\":\n",
        "      sorted_degree = [x for x in sorted_degree if x[0] not in Inodes]\n",
        "      for d in sorted_degree[:tobevaccinated_nodes]:\n",
        "          tobevaccinated.append(d[0])\n",
        "    if metrics==\"eigenvector\":\n",
        "      sorted_eigenvector = [x for x in sorted_eigenvector if x[0] not in Inodes]\n",
        "      for d in sorted_eigenvector[:tobevaccinated_nodes]:\n",
        "          tobevaccinated.append(d[0])\n",
        " \n",
        "    print (\"Controlled vaccination\")\n",
        "    Gcopia.remove_nodes_from(tobevaccinated)\n",
        "    maxAutovalorepruned=max(nx.linalg.adjacency_spectrum(Gcopia))\n",
        "\n",
        "    #Nodes to be vaccinated \n",
        "    #print(\"vaccinated nodes: {}\".format(tobevaccinated))\n",
        "\n",
        "  #  Rnodes_union  = list(set(Rnodes).union(tobevaccinated))\n",
        "    print('Number of S nodes vaccinated at time {}: {}'.format(tsim_max-trigger_time, len(set(Snodes).intersection(tobevaccinated))))\n",
        "    print('Number of I nodes vaccinated at time {}: {}'.format(tsim_max-trigger_time, len(set(Inodes).intersection(tobevaccinated))))\n",
        "    print('Number of R nodes after vaccination at time {}: {}'.format(tsim_max-trigger_time, len(Rnodes)))\n",
        "    print('\\n')   \n",
        "    Inodes  = list(set(Inodes).difference(tobevaccinated))\n",
        "    # t, S, I\n",
        "    # restart with infected nodes with controlled vaccination strategy\n",
        "    res_pruned_after = fast_nonMarkov_SIR_full_data(Gcopia, transmission_rate, recovery_rate, tsim_max, infected_num=Inodes, recovered_num=Rnodes, tstart=tsim_max - trigger_time)\n",
        "    print(nx.info(Gcopia)+\"\\n\")\n",
        "\n",
        "    res_fly = (list(res_orig_before.t())+list(res_pruned_after.t()[1:]), \n",
        "               list(res_orig_before.S())+list(res_pruned_after.S()[1:]),\n",
        "               list(res_orig_before.I())+list(res_pruned_after.I()[1:]),\n",
        "               list(res_orig_before.R())+list(res_pruned_after.R()[1:]))\n",
        "\n",
        "    res_pruned_after_status = res_pruned_after.get_statuses(time=tsim_max)\n",
        "    Snodes_res_pruned_after = [k for k,v in res_pruned_after_status.items() if v == 'S']\n",
        "    Inodes_res_pruned_after = [k for k,v in res_pruned_after_status.items() if v == 'I']\n",
        "    Rnodes_res_pruned_after = [k for k,v in res_pruned_after_status.items() if v == 'R']\n",
        "\n",
        "    print('Final number of S nodes after controlled vaccination: {}'.format(len(Snodes_res_pruned_after)))\n",
        "    print('Final number of I nodes after controlled vaccination: {}'.format(len(Inodes_res_pruned_after)))\n",
        "    print('Final number of R nodes after controlled vaccination: {}'.format(len(Rnodes_res_pruned_after)))   \n",
        "    print('\\n')   \n",
        "\n",
        "\n",
        "    # Random vaccination ------------------------------------------------\n",
        "    tobevaccinatedrnd = list()\n",
        "    Grnd=nx.Graph()\n",
        "    Grnd.add_edges_from(G.edges())\n",
        "\n",
        "    print (\"Randomly pruned graph\")\n",
        "    \n",
        "    tobevaccinatedrnd = random.sample(Snodes,tobevaccinated_nodes)\n",
        "\n",
        "    Grnd.remove_nodes_from(tobevaccinatedrnd)\n",
        "\n",
        "    maxAutovalorernd=max(nx.linalg.adjacency_spectrum(Grnd))\n",
        "\n",
        "    #Rnodes_union_rnd  = list(set(Rnodes).union(tobevaccinatedrnd))\n",
        "    print('Number of S nodes vaccinated at time {}: {}'.format(tsim_max-trigger_time, len(set(Snodes).intersection(tobevaccinatedrnd))))\n",
        "    print('Number of I nodes vaccinated at time {}: {}'.format(tsim_max-trigger_time, len(set(Inodes).intersection(tobevaccinatedrnd))))\n",
        "    print('Number of R nodes after vaccination at time {}: {}'.format(tsim_max-trigger_time, len(Rnodes)))\n",
        "    # t, S, I\n",
        "    # restart with infected nodes with random vaccination strategy\n",
        "    res_rnd_after = fast_nonMarkov_SIR_full_data(Grnd, transmission_rate, recovery_rate, tsim_max, infected_num=Inodes, recovered_num=Rnodes, tstart=tsim_max - trigger_time)\n",
        "\n",
        "    res_rnd_after_status = res_rnd_after.get_statuses(time=tsim_max)\n",
        "    Snodes_res_rnd_after = [k for k,v in res_rnd_after_status.items() if v == 'S']\n",
        "    Inodes_res_rnd_after = [k for k,v in res_rnd_after_status.items() if v == 'I']\n",
        "    Rnodes_res_rnd_after = [k for k,v in res_rnd_after_status.items() if v == 'R']\n",
        "\n",
        "    print('Final number of S nodes after random vaccination: {}'.format(len(Snodes_res_rnd_after)))\n",
        "    print('Final number of I nodes after random vaccination: {}'.format(len(Inodes_res_rnd_after)))\n",
        "    print('Final number of R nodes after random vaccination: {}'.format(len(Rnodes_res_rnd_after)))   \n",
        "    print('\\n') \n",
        "\n",
        "    print(nx.info(Grnd)+\"\\n\")\n",
        "\n",
        "\n",
        "\n",
        "    res_rnd = (list(res_orig_before.t())+list(res_rnd_after.t()[1:]), \n",
        "               list(res_orig_before.S())+list(res_rnd_after.S()[1:]),\n",
        "               list(res_orig_before.I())+list(res_rnd_after.I()[1:]),\n",
        "               list(res_orig_before.R())+list(res_rnd_after.R()[1:]))     \n",
        "    #print(res_rnd[0])\n",
        "\n",
        "    #return (maxautovaloreoriginale, maxAutovalorepruned, maxAutovalorernd, res_orig, res_fly, res_rnd, tobevaccinatedrnd, tobevaccinated, tobevaccinated_betweenness, tobevaccinated_eigenvector )\n",
        "    return (maxautovaloreoriginale, maxAutovalorepruned, maxAutovalorernd, res_orig, res_fly, res_rnd, tobevaccinatedrnd, tobevaccinated )"
      ],
      "id": "d398b7b3",
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eb7b7bec",
        "outputId": "8a2c25e5-fdeb-48a8-9331-2eac5a3f03e1",
        "cellView": "form"
      },
      "source": [
        "#@title \n",
        "#@markdown Define the  network properties\n",
        "#@markdown ---\n",
        "network = \"duplication_divergence_graph\" #@param [\"duplication_divergence_graph\", \"fast_gnp_random_graph\",\"barabasi_albert_graph\",\"gnp_random_graph\"]\n",
        "#initial population\n",
        "init_population = 10000 #@param {type:\"number\"}\n",
        "#number of expected partners\n",
        "exp_partners = 5 #@param {type:\"number\"}\n",
        "#percentage of initial population infected\n",
        "init_infected = 0.005 #@param {type:\"number\"}\n",
        "\n",
        "#@markdown Simulation parameters\n",
        "#@markdown ---\n",
        "transmission_rate = 0.4 #@param {type:\"number\"}\n",
        "recovery_rate = 1.0 #@param {type:\"number\"}\n",
        "tsim_max =30 #@param {type:\"number\"}\n",
        "sim_iterations =  1#@param {type:\"number\"}\n",
        "tobevaccinated_nodes = 100 #@param {type:\"number\"}\n",
        "\n",
        "now = datetime.now()\n",
        "current_time = now.strftime(\"%H:%M:%S\")\n",
        "\n",
        "results=list()\n",
        "if network==\"duplication_divergence_graph\":\n",
        "  for i in range(sim_iterations):\n",
        "      print('Start iteration '+ ' ' +str(i))\n",
        "      print(\"Generating graph G with {} nodes\".format(init_population))\n",
        "      G = nx.duplication_divergence_graph(init_population, 0.4, seed=None)\n",
        "      res = simulation_loop(G, tobevaccinated_nodes, transmission_rate, recovery_rate, tsim_max, init_infected)\n",
        "      results.append(res)\n",
        "elif network==\"fast_gnp_random_graph\":\n",
        "  for i in range(sim_iterations):\n",
        "      print('Start iteration '+ ' ' +str(i))\n",
        "      print(\"Generating graph G with {} nodes\".format(init_population))\n",
        "      G = nx.fast_gnp_random_graph(init_population, exp_partners/(init_population-1)) #Erdos-Renyi graph\n",
        "      res = simulation_loop(G, tobevaccinated_nodes, transmission_rate, recovery_rate, tsim_max, init_infected)\n",
        "      results.append(res)\n",
        "elif network==\"barabasi_albert_graph\":\n",
        "  for i in range(sim_iterations):\n",
        "      print('Start iteration '+ ' ' +str(i))\n",
        "      print(\"Generating graph G with {} nodes\".format(init_population))\n",
        "      G = nx.barabasi_albert_graph(init_population, exp_partners)\n",
        "      res = simulation_loop(G, tobevaccinated_nodes, transmission_rate, recovery_rate, tsim_max, init_infected)\n",
        "      results.append(res)\n",
        "elif network==\"gnp_random_graph\":\n",
        "  for i in range(sim_iterations):\n",
        "      print('Start iteration '+ ' ' +str(i))\n",
        "      print(\"Generating graph G with {} nodes\".format(init_population))\n",
        "      G = nx.generators.random_graphs.gnp_random_graph(init_population,0.4) \n",
        "      res = simulation_loop(G, tobevaccinated_nodes, transmission_rate, recovery_rate, tsim_max, init_infected)\n",
        "      results.append(res)\n",
        "\n",
        "print(\"Max autovalore originale: {}\".format(results[0][0]))\n",
        "print(\"Max autovalore pruned: {}\".format(results[0][1]))\n",
        "print(\"Max autovalore random: {}\".format(results[0][2])) \n",
        "\n",
        "final = datetime.now()\n",
        "final_time = final.strftime(\"%H:%M:%S\")\n",
        "print(\"End Time = {}\".format(final - now))\n",
        "print(\"done with simulations\")\n"
      ],
      "id": "eb7b7bec",
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Start iteration  0\n",
            "Generating graph G with 10000 nodes\n",
            "Number of initial infected nodes: 50\n",
            "Original graph\n",
            "doing Event-driven simulation\n",
            "Number of S nodes before vaccination at time 2: 2837\n",
            "Number of I nodes before vaccination at time 2: 7163\n",
            "Number of R nodes before vaccination at time 2: 0\n",
            "doing Event-driven simulation\n",
            "Final number of S nodes without vaccination: 6\n",
            "Final number of I nodes without vaccination: 0\n",
            "Final number of R nodes without vaccination: 9994\n",
            "Graph with 10000 nodes and 35046 edges\n",
            "\n",
            "\n",
            "\n",
            "Controlled vaccination\n",
            "vaccinated nodes: [525, 1074, 1422, 3284, 4054, 957, 1288, 955, 5067, 1497, 1744, 7555, 2650, 1547, 1984, 791, 1662, 1584, 3291, 3376, 4710, 1684, 2442, 1462, 484, 6333, 2129, 1179, 2055, 3447, 6763, 477, 5145, 9780, 1954, 858, 2507, 4058, 1473, 4022, 2548, 7720, 3349, 318, 2962, 4072, 1851, 4874, 6127, 9087, 7159, 6009, 2645, 1224, 5929, 5922, 3975, 1597, 3661, 5384, 6970, 1892, 8011, 3550, 1003, 2054, 2415, 8814, 2194, 2402, 9249, 1031, 2446, 5605, 5823, 7786, 7849, 6984, 1266, 2888, 5426, 1431, 7954, 4067, 5469, 6585, 3759, 816, 8262, 7955, 6926, 2295, 8091, 2421, 5701, 993, 4183, 4488, 1143, 5709]\n",
            "Number of S nodes vaccinated at time 2: 100\n",
            "Number of I nodes vaccinated at time 2: 0\n",
            "Number of R nodes after vaccination at time 2: 0\n",
            "\n",
            "\n",
            "doing Event-driven simulation\n",
            "Graph with 9900 nodes and 34354 edges\n",
            "\n",
            "Final number of S nodes after controlled vaccination: 116\n",
            "Final number of I nodes after controlled vaccination: 0\n",
            "Final number of R nodes after controlled vaccination: 9784\n",
            "\n",
            "\n",
            "Randomly pruned graph\n",
            "Number of S nodes vaccinated at time 2: 100\n",
            "Number of I nodes vaccinated at time 2: 0\n",
            "Number of R nodes after vaccination at time 2: 0\n",
            "doing Event-driven simulation\n",
            "Final number of S nodes after random vaccination: 8\n",
            "Final number of I nodes after random vaccination: 1\n",
            "Final number of R nodes after random vaccination: 9891\n",
            "\n",
            "\n",
            "Graph with 9900 nodes and 34871 edges\n",
            "\n",
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28.33252291220648, 28.37071096154464, 28.608575015753377, 28.989538938086206]\n",
            "Max autovalore originale: (34.572640526427556+0j)\n",
            "Max autovalore pruned: (34.566679964102455+0j)\n",
            "Max autovalore random: (34.51677524555514+0j)\n",
            "End Time = 0:39:45.106996\n",
            "done with simulations\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "okzYqT2vGeBI",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        },
        "outputId": "22c2f7d8-e9d0-49f6-bc72-fa42b17067a3"
      },
      "source": [
        "print(\"plotting - No vaccination strategy\")\n",
        "\n",
        "plt.plot(results[0][3][0], results[0][3][1], label = \"Susceptible\")\n",
        "plt.plot(results[0][3][0], results[0][3][2], label = \"Infected\")\n",
        "plt.plot(results[0][3][0], results[0][3][3], label = \"Recovered/Vaccinated\")\n",
        "plt.xlabel(\"$t$\")\n",
        "plt.ylabel(\"Number of invididuals\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "id": "okzYqT2vGeBI",
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "plotting - No vaccination strategy\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "df758a58",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        },
        "outputId": "b567d70b-298f-40a3-ae3f-a7d6a7016330"
      },
      "source": [
        "print(\"plotting - Topology-based vaccination strategy\")\n",
        "\n",
        "plt.plot(results[0][4][0], results[0][4][1], label = \"Susceptible\")\n",
        "plt.plot(results[0][4][0], results[0][4][2], label = \"Infected\")\n",
        "plt.plot(results[0][4][0], results[0][4][3], label = \"Recovered/Vaccinated\")\n",
        "plt.xlabel(\"$t$\")\n",
        "plt.ylabel(\"Number of invididuals\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "id": "df758a58",
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "plotting - Topology-based vaccination strategy\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "R7yaOU9KCQBT",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        },
        "outputId": "f3a79ab4-5573-496c-863b-4284821fb7a4"
      },
      "source": [
        "print(\"plotting - Random vaccination strategy\")\n",
        "\n",
        "plt.plot(results[0][5][0], results[0][5][1], label = \"Susceptible\")\n",
        "plt.plot(results[0][5][0], results[0][5][2], label = \"Infected\")\n",
        "plt.plot(results[0][5][0], results[0][5][3], label = \"Recovered/Vaccinated\")\n",
        "plt.xlabel(\"$t$\")\n",
        "plt.ylabel(\"Number of invididuals\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "id": "R7yaOU9KCQBT",
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "plotting - Random vaccination strategy\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "27MSPExE1zeV",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        },
        "outputId": "0c731854-b357-4aaa-8951-6f1ec8b1ccf2"
      },
      "source": [
        "print(\"plotting\")\n",
        "\n",
        "plt.plot(results[0][3][0], results[0][3][2], label = \"No vaccination\")\n",
        "plt.plot(results[0][4][0], results[0][4][2], label = \"Degree-based\")\n",
        "plt.plot(results[0][5][0], results[0][5][2], label = \"Random-based\")\n",
        "plt.xlabel(\"$t$\")\n",
        "plt.ylabel(\"Number infected\")\n",
        "plt.legend()\n",
        "plt.show\n",
        "plt.savefig(\"Degree_1.svg\")\n"
      ],
      "id": "27MSPExE1zeV",
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "plotting\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}