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@FranckBoyer
Last active October 3, 2022 14:22
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Simulations interactives pour un modèle SRI
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{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"from ipywidgets import interact, interactive, fixed\n",
"from IPython.display import display"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from scipy import integrate\n",
"import matplotlib.pyplot as plt\n",
"#from matplotlib import animation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Le système SRI"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Présentation du modèle\n",
"\n",
"$$\\begin{equation}\\label{SIR}\n",
"\\left\\{\n",
"\\begin{split}\n",
"S'(t) & = - \\beta I(t) S(t) + \\gamma R(t),\\\\\n",
"R'(t) & = \\nu I(t) - \\gamma R(t),\\\\\n",
"I'(t) & = -\\nu I(t) + \\beta I(t) S(t),\n",
"\\end{split}\n",
"\\right.\n",
"\\end{equation}$$\n",
"\n",
"Ce système décrit l'évolution selon le temps (l'unité de temps étant {\\em le jour}) d'une population soumise à une maladie contagieuse. Les hypothèses et les notations sont les suivantes:\n",
"\n",
" * La population totale est constante au cours du temps : on ne tient pas compte dans ce modèle des effets de la natalité et de la mortalité, dont on suppose qu'ils se compensent exactement.\n",
" * $I(t)\\in [0,1]$ représente la proportion au temps $t$ des individus qui sont {\\em Infectés} par la maladie. Ces individus sont par ailleurs contagieux et sont le vecteur de la propagation de la maladie.\n",
" * $R(t)\\in [0,1]$ représente la proportion au temps $t$ des individus qui sont {\\em Résistants}, c'est-à-dire qui ont contracté la maladie, en ont guéri et en sont maintenant immunisés.\n",
" * $S(t)\\in [0,1]$ représente la proportion au temps $t$ des individus qui sont {\\em Susceptibles} de contracter la maladie. Il s'agit donc de tous les individus qui ne sont pas malades et qui ne sont pas immunisés.\n",
"\n",
"La signification des paramètres (tous positifs) est la suivante:\n",
"\n",
" * $1/\\nu$ est le temps moyen de guérison d'un patient infecté.\n",
" * $\\beta$ est le facteur de contamination, c'est-à-dire la probabilité que, si un individu {\\em Infecté} est en contact avec un individu {\\em Susceptible} pendant 1 unité de temps, alors ce dernier va contracter la maladie.\n",
" * $1/\\gamma$ est le temps moyen durant lequel un individu ayant contracté la maladie va en être immunisé.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Résolution numérique du modèle et tracé\n",
"\n",
"La fonction qui suit fait tout le travail : calcul de la solution approché et tracé. "
]
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {},
"outputs": [],
"source": [
"def resolution_SRI(t_max=40.0, gamma=0.6, beta=0.8, nu=0.4, I0=0.04, t_fleches=6.,fichier=None, deux_figs=False, N_calc=50):\n",
" \"\"\"Calcul et tracé des solutions du système SRI\n",
" \n",
" Paramètres :\n",
" t_max = temps final du calcul\n",
" t_fleches = reel ou tuple contenant les instants ou on souhaite tracer le champ de vecteurs\n",
" gamma, beta, nu = paramètres du modèle\n",
" I0 = proportion intiale d'individus infectés, on suppose R0=0\n",
" fichier = nom du fichier de sauvegarde de l'image au format png si on le souhaite\n",
" deux_figs : est-ce qu'on sort les résultats en un ou deux fichiers PNG\n",
" N_calc = nombre de points de calcul par unité de temps.\n",
" \"\"\"\n",
"\n",
" if not isinstance(t_fleches,tuple):\n",
" t_fleches=(t_fleches,)\n",
" \n",
" if deux_figs:\n",
" fig = plt.figure(figsize=(6,6))\n",
" fig2 = plt.figure(figsize=(6,6))\n",
" ax = fig.subplots(1,1)\n",
" ax2 = fig2.subplots(1,1)\n",
" else:\n",
" fig = plt.figure(figsize=(12,6))\n",
" ax,ax2 = fig.subplots(1,2)\n",
"\n",
" # préparation des axes\n",
" ax.set_xlim((0, t_max))\n",
" ax.set_xlabel('temps $t$')\n",
" ax.set_ylim((-0.1, 1.1))\n",
" \n",
" ax2.set_xlim((-0.1,1.1))\n",
" ax2.set_xlabel('Infectés')\n",
" ax2.set_ylim((-0.1,1.1))\n",
" ax2.set_ylabel('Susceptibles')\n",
" \n",
" def SRI_champ(SRI, t, gamma=gamma, beta=beta, nu=nu):\n",
" \"\"\"Definition du champ de vecteur pour le système SRI\n",
" Même si le champ est autonome il doit dépendre de la variable t\n",
" qui est ici la seconde variable !!\"\"\"\n",
" \n",
" # SRI est un triplet, on sépare les valeurs\n",
" S, R, I = SRI\n",
" \n",
" # On retourne les trois composantes du champ\n",
" return [ -beta*I*S + gamma*R, \n",
" nu*I - gamma*R, \n",
" -nu*I +beta*I*S ]\n",
"\n",
" # On suppose qu'il n'y a aucun individu résistant au départ\n",
" R0=0.\n",
" S0=1.0-I0 \n",
" \n",
" x0 = [S0,R0,I0]\n",
"\n",
" # On résout la trajectoire en calculant d'abord les temps t ou la solution doit être évaluée\n",
" N=int(N_calc*t_max)\n",
" t = np.linspace(0, t_max, N)\n",
" \n",
" # Ensuite on appelle la fonction de résolution numérique de l'EDO proposée par le module scipy\n",
" x = integrate.odeint(SRI_champ, x0, t)\n",
" \n",
" # On donne un nom aux trois composantes de x pour la suite\n",
" S,R,I=x.T\n",
" # On fait le tracé des trois courbes t-->S(t) t--> R(t) et t--> I(t) sur le graphique de gauche\n",
" lines=ax.plot(t,S,'-')\n",
" plt.setp(lines,linewidth=2)\n",
"\n",
" lines=ax.plot(t,R,'-')\n",
" plt.setp(lines,linewidth=2)\n",
" \n",
" lines=ax.plot(t,I,'-')\n",
" plt.setp(lines,linewidth=2)\n",
" \n",
" ax.legend(['S','R','I'])\n",
" ax.set_title('Evolution de S,R et I au cours du temps')\n",
" ax.axhline(0,linestyle='--',color='black',zorder=-10)\n",
" ax.axhline(1,linestyle='--',color='black',zorder=-10)\n",
" \n",
" # On trace la trajectoire dans le plan de phases (I,S)\n",
" lines=ax2.plot(I,S,'-',c='black')\n",
" plt.setp(lines,linewidth=2)\n",
" \n",
" # On trace des vecteurs tangents\n",
"\n",
" for t_fleche in t_fleches:\n",
" if t_fleche<t_max:\n",
" Nt=int(N*t_fleche/t_max)\n",
" temps_t=t[Nt]\n",
" It=I[Nt]\n",
" St=S[Nt]\n",
" Rt=R[Nt]\n",
" dS,dR,dI=SRI_champ([St,Rt,It],temps_t)\n",
" ax2.quiver(It,St,dI,dS)\n",
" \n",
" # On affiche les points d'équilibre en rouge\n",
" lines=ax2.plot(0,1,'o',c='red')\n",
" plt.setp(lines,markersize=10)\n",
" \n",
" if gamma==0:\n",
" lines=ax2.plot(0*np.linspace(0,1,40),np.linspace(0,1,40),c='red',linewidth=5)\n",
" elif beta>=nu:\n",
" lines=ax2.plot(gamma*(beta-nu)/(beta*(nu+gamma)),nu/beta,'o',c='red')\n",
" plt.setp(lines,markersize=10) \n",
" \n",
" # Point initial du calcul en bleu\n",
" lines=ax2.plot(x[0,2],x[0,0],'o',c='blue')\n",
" plt.setp(lines,markersize=5) \n",
" \n",
" # Les axes de coordonnées pour agrémenter \n",
" ax2.axhline(0,linestyle='--',color='black',zorder=-10)\n",
" ax2.axvline(0,linestyle='--',color='black',zorder=-10)\n",
" ax2.set_title('Trajectoire dans le plan de phase (I,S)')\n",
"\n",
" if fichier:\n",
" if deux_figs:\n",
" fig.tight_layout()\n",
" fig2.tight_layout()\n",
" fig.savefig(fichier+'_temps.png',format='png',dpi=300)\n",
" fig2.savefig(fichier+'_phases.png',format='png',dpi=300)\n",
" pass\n",
" else:\n",
" fig.savefig(fichier+'.png',format='png',dpi=300)\n",
" \n",
" return t, x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Quelques exemples de simulations\n",
"\n",
"### Extinction d'une épidémie de force modérée :\n",
"\n",
"On suppose que : \n",
" * la moitié de la population est infectée à l'instant initial \n",
" * La durée moyenne d'infection est de 2 jours : $\\nu=1/2$\n",
" * La probabilité de contagion est $\\beta=1/30$\n",
" * L'immunité disparaît au bout d'une dizaine de jours : $\\gamma=1/10$"
]
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x432 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"t,x=resolution_SRI(t_max=100,beta=1/30,gamma=1/10,nu=1/2,I0=0.5,t_fleches=(2.0,5.),fichier='epidemie_moderee')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On observe que l'épidémie s'éteint au bout de quelques dizaines de jours\n",
"\n",
"### Déclenchement d'une épidémie de grippe à New-York dans les années 60\n",
"\n",
"Cette grippe très virulente a démarré avec 10 individus infectés sur une population totale de 8 millions d'habitants, ce qui donne $I_0=1.25\\, 10^{-6}$.\n",
"\n",
"La durée moyenne d'infection constatée était de $3$ jours et la probabilité de contagion était de $1/2$. On suppose que l'immunité acquise est permanente, i.e. $\\gamma=0$"
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Proportion maximale de personnes infectées 0.063024063429098\n",
"Proporition total d'invidus ayant contracté la maladie durant l'épidémie : 0.5828128433110361\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x432 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"t,x=resolution_SRI(t_max=200,beta=1/2,gamma=0,nu=1/3,I0=1.25e-6,t_fleches=(65,80),fichier='epidemie_newyork')\n",
"S,R,I=x.T\n",
"print(f'Proportion maximale de personnes infectées {np.max(I)}')\n",
"print(f'Proporition total d\\'invidus ayant contracté la maladie durant l\\'épidémie : {np.max(R)}')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On observe que l'épidémie a mis presque 50 jours a devenir réellement importante.\n",
"\n",
"Elle a duré environ 150 jours et à la fin, près des $2/3$ de la population de New-York aura été infectée.\n",
"\n",
"### Prise en compte de la mutation du virus\n",
"\n",
"Supposons que le virus de la grippe New-Yorkaise ait eu la capacité de muter. Cela implique que l'immunité des personnes infectées va finir par disparaître car petit à petit le virus va s'adapter. \n",
"\n",
"Reprenons la simulation précédente et supposons que $\\gamma$ est très petit, par exemple $\\gamma=1/365$, ce qui modélise le fait que le virus mettra environ 1 an à muter."
]
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/fboyer/miniconda3_new/lib/python3.7/site-packages/ipykernel_launcher.py:120: UserWarning: Creating legend with loc=\"best\" can be slow with large amounts of data.\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Limite de I = 0.002470428721697746\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x432 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"t,x=resolution_SRI(t_max=2000,beta=1/2,gamma=1/365,nu=1/3,I0=1.25e-6,t_fleches=(65,80),fichier=\"epidemie_newyork_mutation\")\n",
"S,R,I=x.T\n",
"print(f'Limite de I = {I[-1]}')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Le cas $\\beta=\\nu$\n",
"\n",
"Dans ce cas, nous sommes capables de prouver la stabilité asymptotique globale de l'équilibre mais pas la stabilité exponentielle. On va faire une simulation qui montre que cette propriété est fausse."
]
},
{
"cell_type": "code",
"execution_count": 83,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x432 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"t,x=resolution_SRI(t_max=1000,beta=1/3,gamma=0.1,nu=1/3,I0=0.7,t_fleches=(2.0,5.),N_calc=2,fichier='epidemie_beta=nu',deux_figs=not True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On observe bien le retour vers l'équilibre mais il semble en effet moins rapide que prévu.\n",
"\n",
"Il est possible de montrer (avec des méthodes hors de portée de ce cours) que la convergence a lieu à la vitesse suivante\n",
"$$I(t)\\sim_{t\\to +\\infty} \\frac{cte}{t}, \\quad 1-S(t) \\sim_{t\\to +\\infty} \\frac{cte}{t}.$$\n",
"\n",
"Ceci est confirmé par la figure ci-dessous qui montre l'évolution des quantités $t*I(t)$ et $t*(1-S(t))$ en fonction du temps."
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"S,R,I=x.T\n",
"beta=1/3\n",
"gamma=0.1\n",
"fig3=plt.figure(figsize=(6,6))\n",
"ax3=fig3.subplots(1,1)\n",
"ax3.plot(t,t*I,'r',label='$t*I$')\n",
"ax3.plot(t,t*(1-S),'b',label='$t*(1-S)$')\n",
"ax3.set_xlabel('temps $t$')\n",
"ax3.legend();\n",
"fig3.savefig('epidemie_beta=nu_vitesse.png',dpi=300)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Utilisation des possibilités interactives de Jupyter"
]
},
{
"cell_type": "code",
"execution_count": 79,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "448e185d4aab4034affedeba02ee70be",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"interactive(children=(IntSlider(value=40, description='t_max', max=50, min=4), FloatSlider(value=0.6, descript…"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"w = interactive(resolution_SRI, \n",
" t_max=(4,50),\n",
" t_fleches=(1,50),\n",
" gamma=(0.0,5.0,0.05), \n",
" nu=(0.0,5.0,0.05), \n",
" beta=(0.0,5.0,0.05), \n",
" I0=(0.0,1.0,0.01),\n",
" fichier=fixed(None),deux_figs=fixed(False),N_calc=fixed(10))\n",
"\n",
"display(w)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*Auteur* : F. Boyer, Université Paul Sabatier - Toulouse 3\n",
"\n",
"*Date* : 21 Février 2020"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"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": "3.7.4"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
@Bertinho
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Bertinho commented Oct 3, 2022

Thanks !!!
Please, I need also to perform that modelling by using the Non-Standard Difference Scheme. Can I have a help?

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