{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start with a population of uninfected susceptible cells ($T$). The initial number of uninfected susceptible cells is $T_0$. Uninfected cells become infected ($I_1$) at a rate that is dependent on the amount of extracellular virus ($V$) and the infectivity of the virus ($\\beta$).\n",
    "\n",
    "$\\frac{dT}{dt}=-\\beta T V$ \n",
    "\n",
    "$\\frac{dI_1}{dt}=\\beta T V$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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foToplFcZ2X8uv9Y0GKKNKsmB0xvh9AY4s8l0d29jOHuBrj/oBkCH/hDazzTKR4g2yOGS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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import tellurium as te\n",
    "model_string = '''\n",
    "    //Equations\n",
    "    E1: T -> I1 ; beta*T*V ; //Infection rate\n",
    "    \n",
    "    //Parameters\n",
    "    beta = 6.2E-5 ; // 1.0/(TCID*day)\n",
    "    \n",
    "    //Inputs\n",
    "    V = 10000.0\n",
    "    \n",
    "    //Initial Conditions\n",
    "    T0 = 1E7\n",
    "    T = T0\n",
    "'''\n",
    "m = te.loada(model_string)\n",
    "s = m.simulate(0,10,100)\n",
    "m.plot(title = \"Cell population\",xtitle=\"time (days)\", ytitle=\"variable\",linewidth=3.5)"
   ]
  },
  {
   "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
