{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "b11b704f", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy.integrate import solve_ivp\n", "import matplotlib.pyplot as plt\n", "\n", "# Définition des équations différentielles du modèle SIR\n", "\n", "\n", "def deriv(t, y, N, beta, gamma, delta):\n", " \"\"\"\n", " N : population totale\n", " beta : taux de contamination\n", " gamma :taux de guérison, \n", " delta : taux de mortalité\n", " \"\"\"\n", "\n", " S, I, R, D = y\n", " dSdt = -beta * S * I / N\n", " dIdt = beta * S * I / N - gamma * I - delta * I\n", " dRdt = gamma * I\n", " dDdt = delta * I\n", " return dSdt, dIdt, dRdt, dDdt" ] }, { "cell_type": "code", "execution_count": 18, "id": "d3ed8946", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Nombre maximum de personnes infectées: 121713\n", "Conservation de la population: 6.111804395914078e-10\n" ] } ], "source": [ "def sird(N=1000000, duree=730, beta=0.2, gamma=0.1, delta=0.01):\n", " # Nombre initial d'individus infectés, rétablis et décédés, le reste est sain\n", " I0, R0, D0 = 1, 0, 0\n", " S0 = N - I0 - R0 - D0\n", " # Vecteur des conditions initiales\n", " y0 = S0, I0, R0, D0\n", " # Vecteur des temps 2 ans\n", " t = np.linspace(0, duree, duree)\n", " # Résolution des équations différentielles du modèle SIR\n", " sol = solve_ivp(deriv, [0, duree], y0, t_eval=t,\n", " args=(N, beta, gamma, delta))\n", " S, I, R, D = sol.y\n", " # Traçage des résultats\n", " plt.plot(t, S, 'b', label='Sains')\n", " plt.plot(t, I, 'r', label='Infectés')\n", " plt.plot(t, R, 'g', label='Rétablis')\n", " plt.plot(t, D, 'k', label='Décédés')\n", " plt.xlabel('temps (jours)')\n", " plt.ylabel('Nombre d\\'individus (millions)')\n", " # calcul du R_0\n", " R_0 = beta*S0/(N*(gamma + delta))\n", " plt.title(r'$R_0=%.2f$' % (R_0, )) # affiche le R_0\n", " # affiche les valeurs finales\n", " plt.text(0.4*duree, 0.95*N, r'$Infectés=%.1i$' % (I[-1],))\n", " plt.text(0.4*duree, 0.85*N, r'$Rétablis=%.1i$' % (R[-1],))\n", " plt.text(0.4*duree, 0.75*N, r'$Décédés=%.1i$' % (D[-1],))\n", " plt.legend()\n", " plt.grid(True)\n", " plt.savefig('sir.png')\n", " plt.show()\n", " print('Nombre maximum de personnes infectées:', int(np.max(I)))\n", " # verifie que S+I+R+D = N au cours du temps\n", " print('Conservation de la population:', np.max(np.abs(N-S-I-R-D)))\n", "\n", " return\n", "\n", "\n", "sird()" ] }, { "cell_type": "markdown", "id": "95b1f84f", "metadata": {}, "source": [ "On définit $R_0 = \\dfrac{\\beta S_0}{N(\\gamma + \\delta)}.$\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "1fd0c51b", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Widget Javascript not detected. It may not be installed or enabled properly. Reconnecting the current kernel may help.\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "bd520d807a13482f91dd0bb5acc0e552" } }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# pour jouer facilement avec les paramètres\n", "from ipywidgets import interact\n", "interact(sird, duree=(30,720,30), beta=(0.1, 0.4, 0.01), gamma=(\n", " 0.1, 0.5, 0.01), delta=(0.01, 0.2, 0.01))" ] }, { "cell_type": "markdown", "id": "3004dcf8", "metadata": {}, "source": [ "Lorsqu'on augmente le paramètre $\\delta$ on constate que l'épidémie s'arrête! Le virus est pourtant beaucoup plus virulent. Mais les personnes infectées décèdent trop vite et n'ont pas le temps de contaminer d'autres personnes." ] }, { "cell_type": "code", "execution_count": 6, "id": "c03b9188", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Nombre maximum de personnes infectées: 1\n", "Conservation de la population: 2.710294211283326e-10\n" ] } ], "source": [ "sird(N=1000000,duree=100000, beta=0.2, gamma=0.1, delta=0.1)" ] }, { "cell_type": "code", "execution_count": 8, "id": "64527351", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Nombre maximum de personnes infectées: 1\n", "Conservation de la population: 1.2170175978098996e-10\n" ] } ], "source": [ "sird(N=1000000,duree=10000, beta=0.12, gamma=0.1, delta=0.02)" ] }, { "cell_type": "markdown", "id": "c3f426ac", "metadata": {}, "source": [ "Lorsque $R_0 = 1$ on retrouve le même phénomène, l'épidémie ne se déclenche pas. Le nombre d'infectés n'augmente pas suffisamment.\n", "\n", "***On remarque aussi que le ratio limite Rétablis/Décédés vaut approximativement $\\gamma/\\delta$.*** On peut établir ce fait, voir les compléments." ] }, { "cell_type": "markdown", "id": "e29b5a46", "metadata": {}, "source": [ "### Compléments facultatifs: régime asymptotique\n", "\n", "On intègre $R(t) = \\gamma \\int_0^t I(s) ds$, \n", "$D(t) = \\delta \\int_0^t I(s) ds$ et \n", "$$S(t) = S_0 \\exp{-\\frac{\\beta}{N} \\int_0^t I(s) ds }.$$\n", "\n", "Quand $t\\to +\\infty$ $R(t) \\to \\gamma \\int_0^\\infty I(s) ds.$\n", "Quand $t\\to +\\infty$ $D(t) \\to \\delta \\int_0^\\infty I(s) ds.$\n", "\n", "Posons $I^\\star = \\int_0^\\infty I(s) ds$ intégrale convergente sinon $R(t)$ et $D(t)$ ne sont pas bornées.\n", "\n", "On trouve donc les valeurs limites\n", "$ S_{lim} = S_0 \\exp{-\\frac{\\beta}{N} I^\\star},$\n", "$R_{lim} = \\gamma I^\\star,$\n", "$D_{lim} = \\delta I^\\star,$\n", "tandis que $I_{lim} = 0$ puisque l'équilibre est atteint.\n", "On démontre ainsi que les valeurs limites $R_{lim}/ D_{lim} = \\gamma/\\delta$ ***respectent les proportions entre $\\gamma$ et $\\delta$***, ce qu'on voit sur les simulations.\n", "\n", "On peut calculer directement $I^\\star$ en résolvant l'équation non linéaire \n", "$$S_{lim} + R_{lim} + D_{lim} = S_0 \\exp{(-\\frac{\\beta}{N} I^\\star)}+(\\gamma + \\delta) I^\\star = N\n", "$$ " ] }, { "cell_type": "code", "execution_count": 9, "id": "b68eb833", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "from scipy.optimize import fsolve\n", "\n", "N = 1000000\n", "beta = 0.2\n", "gamma = 0.1\n", "delta = 0.01\n", "\n", "\n", "def func(x, args=(N, beta, gamma, delta)):\n", "\n", " return (N-1)*np.exp(-beta*x/N) + (gamma + delta)*x - N\n", "\n", "#il faut chercher une racine au voisinage de +l'infini\n", "#car la fonction s'annule deux fois, une fois pour une valeur négative\n", "# et une fois pour une valeur positive. Pour que le solveur retourne\n", "#cette valeur, il faut l'initialiser avec une grande valeur\n", "root = fsolve(func, 10*N)" ] }, { "cell_type": "code", "execution_count": 10, "id": "9b738fc4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([6719997.97578123])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "root" ] }, { "cell_type": "markdown", "id": "a22a2005", "metadata": {}, "source": [ "### On retrouve les populations limites!" ] }, { "cell_type": "code", "execution_count": 11, "id": "50465e6c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "population limite guéris = 671999.8.\n", "population limite décédés = 67200.0.\n" ] } ], "source": [ "# populations limites guéris, décédés\n", "Rlim= root[0]*gamma\n", "Dlim = root[0]*delta\n", "print(f'population limite guéris = {Rlim :.1f}.')\n", "print(f'population limite décédés = {Dlim :.1f}.')" ] }, { "cell_type": "code", "execution_count": 12, "id": "f13f3b75", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#tracé de la fonction\n", "x=np.linspace(-N,10*N,1000)\n", "plt.plot(x,func(x,args=(N,beta,gamma,delta) ))\n", "plt.plot(x,x*0,'r')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "261d47ed", "metadata": {}, "source": [ "Attention on est tenté de linéariser l'équation non linéaire.\n", "Si on le fait, on obtient des résultats aberrants, car on sélectionne la racine négative de la fonction. En effet $\\exp{(-\\frac{\\beta}{N} I^\\star)} \\approx 1 -\\frac{\\beta}{N} I^\\star$ et l'équation non linéaire donne\n", "$$(N-1)( 1 -\\frac{\\beta}{N} I^\\star) + (\\gamma + \\delta) I^\\star =N$$\n", "cela donne $$I^\\star= \\frac{1}{(\\gamma+ \\delta - \\beta (N-1)/N)} = \n", "\\frac{1}{(\\gamma+ \\delta)(1 - R_0)}$$\n", "qui est négative. Cela signifie que $\\beta I^\\star$ n'est pas négligeable devant $N$. " ] }, { "cell_type": "code", "execution_count": 13, "id": "b05a8212", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "On obtient la valeur aberrante Istar =-11.111.\n" ] } ], "source": [ "Istar= 1/(gamma+ delta - (N-1)*beta/N)\n", "print(f'On obtient la valeur aberrante Istar ={Istar:.3f}.')" ] }, { "cell_type": "code", "execution_count": null, "id": "08060d14", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.12" } }, "nbformat": 4, "nbformat_minor": 5 }