{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The SIR model without spatial heterogeneity\n",
    "\n",
    "We consider the dynamics of susceptibles, $S(t)$, infectives, $I(t)$ and removeds, $R(t)$, to evolve according to\n",
    "\n",
    "\\begin{eqnarray}\n",
    "\\frac{\\text{d}S}{\\text{d}t}&=&-rIS,\\\\\n",
    "\\frac{\\text{d}I}{\\text{d}t}&=&rIS-aI,\\\\\n",
    "\\frac{\\text{d}R}{\\text{d}t}&=&aI,\n",
    "\\end{eqnarray}\n",
    "\n",
    "subject to\n",
    "\n",
    "\\begin{equation}\n",
    "S(0)=S_0,\n",
    "\\quad\n",
    "I(0)=I_0,\n",
    "\\quad\n",
    "R(0)=0.\n",
    "\\end{equation}\n",
    "\n",
    "Note that\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{\\text{d}}{\\text{d}t}(S+I+R)=0 \\quad \\Longrightarrow \\quad S+I+R=S_0+I_0.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import integrate\n",
    "from scipy import optimize\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "\n",
    "#set the plotting parameters\n",
    "plt.rcParams.update({\n",
    "    \"text.usetex\": True,\n",
    "    \"font.family\": \"serif\",\n",
    "    \"font.serif\": [\"Times New Roman\"],\n",
    "    \"font.size\": 18,\n",
    "    \"axes.linewidth\": 1.5,\n",
    "})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ode_system(t,y,args):\n",
    "    \n",
    "    pa,pr=args\n",
    "    \n",
    "    derivs=np.zeros(2)\n",
    "    \n",
    "    derivs[0]=-pr*y[0]*y[1]\n",
    "    derivs[1]=pr*y[0]*y[1]-pa*y[1]\n",
    "    \n",
    "    return derivs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# model parameters\n",
    "pr=0.01\n",
    "pa=0.25\n",
    "N0=100.0;\n",
    "\n",
    "tpp_final=1e4; # final time\n",
    "tpp=np.linspace(0,tpp_final,10*int(tpp_final)+1)\n",
    "dtpp=tpp[1]-tpp[0]\n",
    "args=[pa,pr]\n",
    "\n",
    "# set up the ODE solver\n",
    "r=integrate.ode(ode_system)\n",
    "r.set_integrator('dopri5');\n",
    "r.set_f_params(args);\n",
    "\n",
    "# initial conditions -  trajectory 1\n",
    "y_pp1=np.empty((len(tpp),2),dtype=np.float)\n",
    "r.set_initial_value([N0-10,10],tpp[0]);\n",
    "# solve the ODE\n",
    "idx=0\n",
    "while r.successful() and r.t<=tpp_final:\n",
    "    y_pp1[idx,:]=r.y\n",
    "    r.integrate(r.t+dtpp)\n",
    "    idx+=1\n",
    "    \n",
    "# initial conditions -  trajectory 2\n",
    "y_pp2=np.empty((len(tpp),2),dtype=np.float)\n",
    "r.set_initial_value([N0-30,30],tpp[0]);\n",
    "# solve the ODE\n",
    "idx=0\n",
    "while r.successful() and r.t<=tpp_final:\n",
    "    y_pp2[idx,:]=r.y\n",
    "    r.integrate(r.t+dtpp)\n",
    "    idx+=1\n",
    "    \n",
    "# initial conditions -  trajectory 3\n",
    "y_pp3=np.empty((len(tpp),2),dtype=np.float)\n",
    "r.set_initial_value([N0-50,50],tpp[0]);\n",
    "# solve the ODE\n",
    "idx=0\n",
    "while r.successful() and r.t<=tpp_final:\n",
    "    y_pp3[idx,:]=r.y\n",
    "    r.integrate(r.t+dtpp)\n",
    "    idx+=1\n",
    "    \n",
    "# initial conditions -  trajectory 4\n",
    "y_pp4=np.empty((len(tpp),2),dtype=np.float)\n",
    "r.set_initial_value([N0-70,70],tpp[0]);\n",
    "# solve the ODE\n",
    "idx=0\n",
    "while r.successful() and r.t<=tpp_final:\n",
    "    y_pp4[idx,:]=r.y\n",
    "    r.integrate(r.t+dtpp)\n",
    "    idx+=1\n",
    "    \n",
    "# initial conditions -  trajectory 5\n",
    "y_pp5=np.empty((len(tpp),2),dtype=np.float)\n",
    "r.set_initial_value([N0-90,90],tpp[0]);\n",
    "# solve the ODE\n",
    "idx=0\n",
    "while r.successful() and r.t<=tpp_final:\n",
    "    y_pp5[idx,:]=r.y\n",
    "    r.integrate(r.t+dtpp)\n",
    "    idx+=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the results\n",
    "fig,ax=plt.subplots(figsize=(6,5))\n",
    "fig.tight_layout(pad=3.0)\n",
    "\n",
    "# create a quiver plot to see where the trajectory directions\n",
    "x,y=np.meshgrid(np.arange(0.0,N0,N0/20.0),np.arange(0.0,N0,N0/20.0))\n",
    "u=-pr*x*y\n",
    "v=pr*x*y-pa*y\n",
    "n=-2\n",
    "color=np.sqrt(((u-n)/2)**2+((v-n)/2)**2) \n",
    "ax.quiver(x,y,u,v,color,width=0.002)\n",
    "\n",
    "# plot a trajectory \n",
    "ax.plot(y_pp1[:,0],y_pp1[:,1])\n",
    "ax.plot(y_pp2[:,0],y_pp2[:,1])\n",
    "ax.plot(y_pp3[:,0],y_pp3[:,1])\n",
    "ax.plot(y_pp4[:,0],y_pp4[:,1])\n",
    "ax.plot(y_pp5[:,0],y_pp5[:,1])\n",
    "\n",
    "xplot=np.arange(0,N0,N0/100.0)\n",
    "ax.plot(xplot,N0-xplot,color='black',linestyle='--');\n",
    "# ax.plot(xplot,np.zeros(len(xplot)),color='black',linestyle=':');\n",
    "# ax.plot(np.zeros(len(yplot)),yplot,color='black')\n",
    "\n",
    "ax.set_xlabel(\"$S$\")\n",
    "ax.set_ylabel(\"$I$\")\n",
    "ax.set_xlim(0,N0)\n",
    "ax.set_ylim(0,N0)\n",
    "ax.set_yticks(np.arange(0,N0*1.2,N0/5));\n",
    "ax.set_yticks(np.arange(0,N0*1.2,N0/5));\n",
    "\n",
    "# to save the figure\n",
    "outputpath='../Lecture Notes/Chapter_TravellingWaves/figures/SIR_ODEs.pdf'\n",
    "plt.savefig(outputpath,bbox_inches=\"tight\", pad_inches=0.1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SIR model with spatial heterogeneity\n",
    "We consider the dynamics of susceptibles, $S(x,t)$, infectives, $I(x,t)$ and removeds, $R(x,t)$, to evolve according to\n",
    "\n",
    "\\begin{eqnarray}\n",
    "\\frac{\\partial{S}}{\\partial{t}}&=&-rIS,\\\\\n",
    "\\frac{\\partial{I}}{\\partial{t}}&=&D\\frac{\\partial^2{I}}{\\partial{x^2}}+rIS-aI,\\\\\n",
    "\\end{eqnarray}\n",
    "\n",
    "subject to\n",
    "\n",
    "\\begin{equation}\n",
    "S(0)=S_0(x),\n",
    "\\quad\n",
    "I(0)=I_0(x),\n",
    "\\end{equation}\n",
    "\n",
    "with zero flux boundary conditions as $x\\to\\pm\\infty$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set up the ODE system - discretised PDE using central differences \n",
    "def f(t,y,args):\n",
    "    \n",
    "    pa,pr,pD,dx,n_odes=args\n",
    "    \n",
    "    derivs=np.zeros(2*n_odes)\n",
    "    \n",
    "    # convert the diffusion coefficient for the infectives\n",
    "    pd=pD/dx**2\n",
    "    \n",
    "    # derivatives for the S equations\n",
    "    for ii in range(0,n_odes):\n",
    "        derivs[ii]=-pr*y[ii]*y[ii+n_odes]\n",
    "    \n",
    "    # derivatives for the I equations\n",
    "    derivs[n_odes]=pd*(-y[n_odes]+y[n_odes+1])+pr*y[0]*y[n_odes]-pa*y[n_odes]\n",
    "    for ii in range(n_odes+1,2*n_odes-1):\n",
    "                derivs[ii]=pd*(y[ii-1]-2.0*y[ii]+y[ii+1])+pr*y[ii-n_odes]*y[ii]-pa*y[ii]\n",
    "    derivs[2*n_odes-1]=pd*(y[2*n_odes-2]-y[2*n_odes-1])+pr*y[n_odes-1]*y[2*n_odes-1]-pa*y[2*n_odes-1]\n",
    "    \n",
    "    return derivs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# model parameters\n",
    "\n",
    "L=150.0 # domain length\n",
    "dx=0.2 # spatial discretistion\n",
    "n_odes=int(L/dx)-1; # number of ODEs to solve for each species\n",
    "xmesh=np.linspace(dx,L-dx,n_odes)\n",
    "\n",
    "t_final=100.0; # final time\n",
    "t=np.linspace(0,t_final,int(t_final)+1)\n",
    "dt=t[1]-t[0]\n",
    "\n",
    "pr=0.01\n",
    "pa=0.25\n",
    "pD=1.0;\n",
    "\n",
    "args=[pa,pr,pD,dx,n_odes]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initial conditions\n",
    "y0=np.zeros(2*n_odes)\n",
    "S0=100\n",
    "I0=25\n",
    "y0[0:n_odes]=S0*np.ones(n_odes);\n",
    "y0[n_odes:2*n_odes]=I0*0.5*(1.0-np.tanh((xmesh-5.0)))*0.5*(1.0-np.tanh(-(xmesh-5.0)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set up the ODE solver\n",
    "y=np.empty((len(t),len(y0)),dtype=np.float)\n",
    "r=integrate.ode(f)\n",
    "r.set_integrator('dopri5');\n",
    "r.set_initial_value(y0,t[0]);\n",
    "r.set_f_params(args);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# solve the ODE\n",
    "idx=0\n",
    "while r.successful() and r.t<=t_final:\n",
    "    y[idx,:]=r.y\n",
    "    r.integrate(r.t+dt)\n",
    "    idx+=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=plt.subplots(1,2,figsize=(12,5))\n",
    "fig.tight_layout(pad=3.0)\n",
    "\n",
    "ax[0].plot(xmesh,y0[0:n_odes])\n",
    "ax[0].plot(xmesh,y0[n_odes:2*n_odes])\n",
    "ax[0].set_xlabel(\"$x$\")\n",
    "ax[0].set_ylabel(\"$S(x,0)$ and $I(x,0)$\")\n",
    "ax[0].set_yticks(np.arange(0, 120, 20))\n",
    "\n",
    "for pp in range(20,80,10):\n",
    "    ax[1].plot(xmesh,y[pp,0:n_odes])\n",
    "    ax[1].plot(xmesh,y[pp,n_odes:2*n_odes])\n",
    "    plt.gca().set_prop_cycle(None)\n",
    "\n",
    "ax[1].set_xlabel(\"$x$\")\n",
    "ax[1].set_ylabel(\"$S(x,t)$ and $I(x,t)$\")\n",
    "ax[1].set_yticks(np.arange(0, 120, 20))\n",
    "\n",
    "# to save the figure\n",
    "outputpath='../Lecture Notes/Chapter_TravellingWaves/figures/SIR_tw.pdf'\n",
    "plt.savefig(outputpath,bbox_inches=\"tight\", pad_inches=0.1);"
   ]
  }
 ],
 "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
