{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Network SIR model with pair approximation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "library(deSolve)\n",
    "library(simecol)\n",
    "library(reshape2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "sir_pa_ode <- new(\"odeModel\",\n",
    "  main = function(time, init, parms, ...){\n",
    "    with(as.list(c(init,parms)),{\n",
    "      # Closure\n",
    "      SSI <- (k-1)*SS*SI/(k*S)\n",
    "      ISS <- (k-1)*SI*SS/(k*S)\n",
    "      ISI <- (k-1)*SI*SI/(k*S)\n",
    "      # ODEs\n",
    "      dS <- -beta*SI\n",
    "      dI <- beta*SI-gamma*I\n",
    "      dSS <- -beta*(SSI+ISS)\n",
    "      dSI <- beta*(SSI-ISI)-beta*SI-gamma*SI\n",
    "      dII <- beta*(2*ISI)+2*beta*SI-2*gamma*II\n",
    "      list(c(dS,dI,dSS,dSI,dII))\n",
    "    })},\n",
    "  parms = c(beta=3,gamma=1.0,k=5),\n",
    "  times = c(from=0,to=20,by=0.01),\n",
    "  init = c(S=0.999,I=0.001,SS=0.999*0.999,SI=0.999*0.001,II=0.001*0.001),\n",
    "  solver = \"lsoda\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "sir_pa_ode <- sim(sir_pa_ode)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "sir_pa_out <- out(sir_pa_ode)\n",
    "sir_pa_out_long <- melt(as.data.frame(sir_pa_out),\"time\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualisation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "library(ggplot2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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aqtgxmRTCgkwyaqGgyqCgnTXVCZqNo6mBHJhEIybKKqwaCqkDDdBZWJqq2DGZFM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\nIVBIEQL/D1Gm9YD9cNEmAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(sir_pa_out_long,aes(x=time,y=value,colour=variable,group=variable))+\n",
    "  # Add line\n",
    "  geom_line(lwd=2)+\n",
    "  #Add labels\n",
    "  xlab(\"Time\")+ylab(\"Number\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.4.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}