{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Logistic population growth model\n", "\n", "This example shows how the [Logistic model](http://pints.readthedocs.io/en/latest/toy/logistic_model.html) can be used.\n", "\n", "This model describes the [growth of a population](https://en.wikipedia.org/wiki/Population_growth#Logistic_equation), from an initial starting point up to a maxium carrying capacity $k$. The rate of growth is given by a second parameter, $r$.\n", "\n", "$$ y(t) = \\frac{k}{1 + (k / p_0 - 1) e^{-r t}} $$\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import pints\n", "import pints.toy\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "p0 = 2 # initial population; initial value\n", "model = pints.toy.LogisticModel(p0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Parameters are given in the order ``(r, k)``." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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XVIqIiIiIXAwFPDmrbM7pG5uge3iCruEkXVPL5CmBbmTaJZSTGitLph438PaN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\nKOCJiIiIiIgsEv8f30YwMTJL0EwAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "times = np.linspace(0, 100, 100)\n", "r = 0.1\n", "k = 50\n", "values = model.simulate((r, k), times)\n", "\n", "plt.figure(figsize=(15,2))\n", "plt.xlabel('t')\n", "plt.ylabel('y (Population)')\n", "plt.plot(times, values)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that, starting from ``p0 = 2`` the model quickly approaches the carrying capacity ``k = 50``." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can test that, if we wait long enough, we get very close to $k$:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 34.73246508]\n", "[ 49.60065997]\n", "[ 49.99262803]\n", "[ 49.99986496]\n", "[ 49.99999753]\n", "[ 49.99999995]\n", "[ 50.]\n" ] } ], "source": [ "print(model.simulate((r, k), [40]))\n", "print(model.simulate((r, k), [80]))\n", "print(model.simulate((r, k), [120]))\n", "print(model.simulate((r, k), [160]))\n", "print(model.simulate((r, k), [200]))\n", "print(model.simulate((r, k), [240]))\n", "print(model.simulate((r, k), [280]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This model also provides sensitivities: derivatives $\\frac{\\partial y}{\\partial p}$ of the output $y$ with respect to the parameters $p$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "values, sensitivities = model.simulateS1((r, k), times)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can plot these sensitivities, to see where the model is sensitive to each of the parameters:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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39hy59RPA7/VQmpNMWU4Ky2fkUZabQnlOCmW5KRSmB/B4NBCMiIiIiMiJKBhK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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(15,7))\n", "\n", "plt.subplot(3, 1, 1)\n", "plt.ylabel('y (Population)')\n", "plt.plot(times, values)\n", "\n", "plt.subplot(3, 1, 2)\n", "plt.ylabel(r'$\\partial y/\\partial r$')\n", "plt.plot(times, sensitivities[:, 0])\n", "\n", "plt.subplot(3, 1, 3)\n", "plt.xlabel('t')\n", "plt.ylabel(r'$\\partial y/\\partial k$')\n", "plt.plot(times, sensitivities[:, 1])\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For $\\frac{\\partial y}{\\partial r}$ (middle plot), we see that the model reacts most strongly to changes in $r$ at $t \\approx 35$, just when the population size is changing fastest. This makes a lot of sense: since $r$ determines the rate of growth it is most clearly visible during the period of greatest growth.\n", "\n", "For $\\frac{\\partial y}{\\partial k}$ (bottom plot) the result is very similar to the graph of $y$ itself: The carrying capacity is hard to tell at the very beginning, as the population hasn't begun to grow much yet. As growth increases it becomes easier to predict what the final population size will be. Finally, when the carrying capacity has been reached the value of $y \\approx k$, so that the derivative is almost 1." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For parameter estimation, this tells us something interesting: Namely that we need to know about the final stages of the process to get an accurate estimate of $k$, while estimating $r$ requires the period of greatest growth to be present in the signal." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 2 }