Some examples of mathematical modeling and simple MCMC in R, including some Rcpp examples

ModelingWithR.ipynb

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    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
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     },
     "source": [
      "# Modeling with R"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%load_ext rmagic"
     ],
     "language": "python",
     "metadata": {
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       "slide_type": "skip"
      }
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     "outputs": [],
     "prompt_number": 1
    },
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     "cell_type": "markdown",
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       "slide_type": "fragment"
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     "source": [
      "\\begin{align}\n",
      "\\label{eq:sir}\n",
      "\\frac{dS(t)}{dt} & = -\\beta S(t) I(t)\\\\\n",
      "\\frac{dI(t)}{dt} & = \\beta S(t) I(t)- \\mu I(t)\\\\\n",
      "\\frac{dR(t)}{dt} & = \\mu I(t)\n",
      "\\end{align}"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "library(deSolve)\n",
      "sir.ode <- function(times,init,parms){\n",
      "  with(as.list(c(parms,init)), {\n",
      "  # ODEs\n",
      "  dS <- -beta*S*I\n",
      "  dI <- beta*S*I-gamma*I\n",
      "  dR <- gamma*I\n",
      "  list(c(dS,dI,dR))\n",
      "  })\n",
      "}\n",
      "parms <- c(beta=0.1,gamma=0.05)\n",
      "init <- c(S=0.99,I=0.01,R=0) \n",
      "times <- seq(0,200,by=0.01)\n",
      "sir.out <- ode(init,times,sir.ode,parms,method=\"rk4\")\n",
      "print(head(sir.out))"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "     time         S          I            R\n",
        "[1,] 0.00 0.9900000 0.01000000 0.000000e+00\n",
        "[2,] 0.01 0.9899901 0.01000490 5.001225e-06\n",
        "[3,] 0.02 0.9899802 0.01000980 1.000490e-05\n",
        "[4,] 0.03 0.9899703 0.01001471 1.501103e-05\n",
        "[5,] 0.04 0.9899604 0.01001962 2.001961e-05\n",
        "[6,] 0.05 0.9899504 0.01002453 2.503065e-05\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "# Plotting"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "library(ggplot2)\n",
      "p <- ggplot(as.data.frame(sir.out),aes(x=time,y=I))+geom_line()\n",
      "print(p)"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "fragment"
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     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "Use suppressPackageStartupMessages to eliminate package startup messages.\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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6glmf6/WXoykkOPcC8fWFARQWvLOVfi6LQoK/Oh+cieVFYcFssf5CeIUEXwNO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\nzLtS9z3RpzIAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "# Stochastic simulations"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "fragment"
      }
     },
     "source": [
      "\\begin{align}\n",
      "{\\rm Transition} & \\quad {\\rm Rate} \\cr\n",
      "S,I \\rightarrow S-1,I+1 & \\quad \\beta S(t) I(t) \\cr\n",
      "I  \\rightarrow I-1  & \\quad \\gamma I(t)\n",
      "\\end{align}"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "sir <- function(beta, gamma, N, S0, I0, R0, tf) {\n",
      "    time <- 0\n",
      "    S <- S0\n",
      "    I <- I0\n",
      "    R <- R0\n",
      "    ta <- numeric(0)\n",
      "    Sa <- numeric(0)\n",
      "    Ia <- numeric(0)\n",
      "    Ra <- numeric(0)\n",
      "    while (time < tf) {\n",
      "        ta <- c(ta, time)\n",
      "        Sa <- c(Sa, S)\n",
      "        Ia <- c(Ia, I)\n",
      "        Ra <- c(Ra, R)\n",
      "        pf1 <- beta * S * I\n",
      "        pf2 <- gamma * I\n",
      "        pf <- pf1 + pf2\n",
      "        dt <- rexp(1, rate = pf)\n",
      "        time <- time + dt\n",
      "        if (time > tf) {\n",
      "            break\n",
      "        }\n",
      "        ru <- runif(1)\n",
      "        if (ru < (pf1/pf)) {\n",
      "            S <- S - 1\n",
      "            I <- I + 1\n",
      "        } else {\n",
      "            I <- I - 1\n",
      "            R <- R + 1\n",
      "        }\n",
      "        if (I == 0) {\n",
      "            break\n",
      "        }\n",
      "    }\n",
      "    results <- data.frame(time = ta, S = Sa, I = Ia, R = Ra)\n",
      "    return(results)\n",
      "}"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(system.time(replicate(100,sir(0.1/10000, 0.05, 10000, 9999, 1, 0, 1000))))"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "   user  system elapsed \n",
        " 87.156   0.096  87.484 \n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "library(Rcpp)\n",
      "cppFunction('\n",
      "  List csir(double beta, double gamma, double N, double S0, double I0, double R0, double tf){\n",
      "    double t = 0;\n",
      "    double S = S0;\n",
      "    double I = I0;\n",
      "    double R = R0;\n",
      "    std::vector<double> ta;\n",
      "    std::vector<double> Sa;\n",
      "    std::vector<double> Ia;\n",
      "    std::vector<double> Ra;\n",
      "    do{\n",
      "      ta.push_back(t);\n",
      "      Sa.push_back(S);\n",
      "      Ia.push_back(I);\n",
      "      Ra.push_back(R);\n",
      "      double pf1 = beta*S*I;\n",
      "      double pf2 = gamma*I;\n",
      "      double pf = pf1+pf2;\n",
      "      double dt = rexp(1,pf)[0];\n",
      "      t += dt;\n",
      "      double r = runif(1)[0];\n",
      "      if(r<pf1/pf){\n",
      "        S--;\n",
      "        I++;\n",
      "      }else{\n",
      "        I--;\n",
      "        R++;\n",
      "      }\n",
      "      if(I==0){break;}\n",
      "    } while (t<=tf && (I>0));\n",
      "  return List::create(_[\"time\"] = ta, _[\"S\"] = Sa, _[\"I\"] = Ia, _[\"R\"]=Ra);\n",
      "  }'\n",
      ")"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(system.time(replicate(100,csir(0.1/10000, 0.05, 10000, 9999, 1, 0, 1000))))"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "subslide"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "   user  system elapsed \n",
        "  0.408   0.008   0.417 \n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "# MCMC"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "norm <-function (n, alpha) \n",
      "{\n",
      "        vec <- vector(\"numeric\", n)\n",
      "        x <- 0\n",
      "        vec[1] <- x\n",
      "        for (i in 2:n) {\n",
      "                innov <- runif(1, -alpha, alpha)\n",
      "                can <- x + innov\n",
      "                aprob <- min(1, dnorm(can)/dnorm(x))\n",
      "                u <- runif(1)\n",
      "                if (u < aprob) x <- can\n",
      "                vec[i] <- x\n",
      "        }\n",
      "        vec\n",
      "}"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "subslide"
      }
     },
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(system.time(norm(1000000,1)))"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "subslide"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "   user  system elapsed \n",
        " 16.056   0.008  16.158 \n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "library(Rcpp)\n",
      "library(inline)\n",
      "gslnorm <- '\n",
      "  long n = Rcpp::as<long>(c_n);\n",
      "  double alpha = Rcpp::as<double>(c_alpha);\n",
      "  long i;\n",
      "  double x,can,u,aprob;\n",
      "  gsl_rng *r = gsl_rng_alloc(gsl_rng_mt19937);\n",
      "  x=0.0;\n",
      "  std::vector<double> vec(n);\n",
      "  vec[0]=x;\n",
      "  for (i=1;i<n;i++)\n",
      "  {\n",
      "    can=x+gsl_ran_flat(r,-alpha,alpha);\n",
      "    aprob=min(1.0, gsl_ran_ugaussian_pdf(can)/gsl_ran_ugaussian_pdf(x));\n",
      "    u=gsl_ran_flat(r,0.0,1.0);\n",
      "    if (u < aprob) x=can;\n",
      "    vec[i]=x;\n",
      "  }\n",
      "  return Rcpp::wrap(vec) ;\n",
      "'\n",
      "helperfn <- '\n",
      "  double min(double a, double b)\n",
      "  {\n",
      "  if (a < b)\n",
      "    return(a);\n",
      "  else\n",
      "    return(b);   \n",
      "  }\n",
      "'\n",
      "rcppnorm <- cfunction(signature(c_n=\"numeric\",c_alpha=\"numeric\"), gslnorm,\n",
      "                   includes=c(\"#include <gsl/gsl_rng.h>\",\n",
      "                   \"#include <gsl/gsl_randist.h>\",\n",
      "                   \"#include <cmath>\",\n",
      "                   \"using namespace Rcpp;\",\n",
      "                   \"using namespace std;\",\n",
      "                   helperfn),\n",
      "                   Rcpp=TRUE,\n",
      "                   cppargs=\"-I/usr/include\",\n",
      "                   libargs=\"-lgsl -lgslcblas\")"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\n",
        "Attaching package: \u2018inline\u2019\n",
        "\n",
        "The following object is masked from \u2018package:Rcpp\u2019:\n",
        "\n",
        "    registerPlugin\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "print(system.time(rcppnorm(1000000,1)))"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "subslide"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "   user  system elapsed \n",
        "  0.084   0.008   0.111 \n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "source": [
      "# epicookbook"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "library(devtools)\n",
      "install_github(\"epicookbook\",\"sdwfrost\")\n",
      "library(epicookbook)"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "subslide"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "Installing github repo(s) epicookbook/master from sdwfrost\n",
        "Installing epicookbook.zip from https://github.com/sdwfrost/epicookbook/archive/master.zip\n",
        "Installing epicookbook\n",
        "'/usr/local/lib/R/bin/R' --vanilla CMD INSTALL  \\\n",
        "  '/tmp/RtmpT8zicr/epicookbook-master'  \\\n",
        "  --library='/home/simon/R/x86_64-unknown-linux-gnu-library/3.0'  \\\n",
        "  --with-keep.source \n",
        "\n",
        "Loading required package: simecol\n",
        "Loading required package: lattice\n",
        "Loading required package: GillespieSSA\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "demo(package=\"epicookbook\")"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "R demosDemos in package \u2018epicookbook\u2019:\n",
        "\n",
        "acutehiv                A model of HIV infection with acute and chronic\n",
        "                        infection stages\n",
        "hivmodel                A simple model of HIV infection\n",
        "hivmodelage             The simple HIV model, with age considered\n",
        "                        explicitly\n",
        "hivmodeldiffrisk        A model of HIV infection with differential\n",
        "                        contact rates and mixing patterns\n",
        "reedfrost               A Reed-Frost chain binomial model\n",
        "sirabc                  Fitting an SIR model using approximate Bayesian\n",
        "                        computation (rejection method)\n",
        "sircn                   An edge-based SIR model on a configuration\n",
        "                        network\n",
        "sirdiscrete             A discrete-time SIR model\n",
        "sirforced               An SIR model with seasonal forcing of infection\n",
        "sirfunction             An example of how different functions can be\n",
        "                        used for transmission in an SIR model\n",
        "sirode                  A susceptible-infected-recovered differential\n",
        "                        equation model using simecol\n",
        "sirpa                   A pair approximation for an SIR model on a\n",
        "                        k-regular network\n",
        "sirstochastic           A stochastic SIR model simulated using the SSA\n",
        "                        algorithm\n",
        "siuniformized           Simulation of a stochastic SI model using\n",
        "                        uniformization\n",
        "wnv                     A model of West Nile Virus in birds and\n",
        "                        mosquitoes\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "library(reshape2)\n",
      "demo(acutehiv)"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\n",
        "\n",
        "\tdemo(acutehiv)\n",
        "\t---- ~~~~~~~~\n",
        "\n",
        "> acutehiv <- new(\"odeModel\",\n",
        "+   main = function(time, init, parms, ...){\n",
        "+     with(as.list(c(init,parms)),{\n",
        "+     # ODEs\n",
        "+     N <- S+I1+I2\n",
        "+     dS <- lambd-beta1*c*S*I1/N-beta2*c*S*I2/N-mu*S\n",
        "+     dI1 <- beta1*c*S*I1/N+beta2*c*S*I2/N-alpha*I1-mu*I1\n",
        "+     dI2 <- alpha*I1-mu*I2-gamma*I2\n",
        "+     list(c(dS,dI1,dI2))\n",
        "+    })},\n",
        "+   parms = c(beta1=1./50,beta2=1./200,c=1,alpha=1./8,gamma=1./520,mu=1./(70*52),lambd=10000./(70*52)),\n",
        "+   times = c(from=0,to=60*52,by=1),\n",
        "+   init = c(S=9999,I1=1,I2=0),\n",
        "+   solver = \"lsoda\"\n",
        "+ )\n",
        "\n",
        "> acutehiv <- sim(acutehiv)\n",
        "\n",
        "> acutehiv.out <- out(acutehiv)\n",
        "\n",
        "> acutehiv.out.long <- melt(as.data.frame(acutehiv.out),\"time\")\n",
        "\n",
        "> # Now plot\n",
        "> ggplot(acutehiv.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\")\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Odm502MJ6IM8goAFmJLJitcnxFxum6TjyiaXlQF5BQAPMiOlyK0uSp0/6lMl4aAXSAwEN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\nAQAAAIBB/tbT2FEQwZSgAaYEDTAVhn5Ex8SrKz4AAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "demo(siuniformized)"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "slide"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\n",
        "\n",
        "\tdemo(siuniformized)\n",
        "\t---- ~~~~~~~~~~~~~\n",
        "\n",
        "> # Set population size\n",
        "> N <- 100\n",
        "\n",
        "> # Initial number of infecteds\n",
        "> Iinit <- 1\n",
        "\n",
        "> # Set infectivity parameter\n",
        "> beta <- 1\n",
        "\n",
        "> # Set maximum time (approximately)\n",
        "> maxt <- 20\n",
        "\n",
        "> # Set the number of runs\n",
        "> numruns <- 10\n",
        "\n",
        "> # Calculate the maximum rate and number of timepoints\n",
        "> maxrate <- beta*N/2*N/2*(1/N)\n",
        "\n",
        "> numt <- floor(maxt*maxrate)\n",
        "\n",
        "> # Main loop\n",
        "> results <- list()\n",
        "\n",
        "> for(r in 1:numruns){\n",
        "+   # Generate vector of times\n",
        "+   tvec <- cumsum(c(0,rexp(numt-1,maxrate)))\n",
        "+   ivec <- c(Iinit,rep(NA,numt-1))\n",
        "+   for(i in 2:numt){\n",
        "+     p <- (beta*ivec[i-1]*(N-ivec[i-1])/N)/maxrate\n",
        "+     u <- runif(1,0,1)\n",
        "+     if(u<p){\n",
        "+       ivec[i] <- ivec[i-1]+1\n",
        "+     }\n",
        "+     else{\n",
        "+       ivec[i] <- ivec[i-1]\n",
        "+     }\n",
        "+   }\n",
        "+   results[[r]] <- data.frame(time=tvec,I=ivec)\n",
        "+ }\n",
        "\n",
        "> # Plot simulation runs\n",
        "> mycols <- rainbow(numruns)\n",
        "\n",
        "> siplot <- ggplot(results[[1]],aes(x=time,y=I))+geom_line(lwd=1,col=mycols[1])+xlab(\"Time\")+ylab(\"Number\")\n",
        "\n",
        "> for(i in 2:numruns){\n",
        "+   siplot <- siplot + geom_line(lwd=1,col=mycols[i],data=results[[i]])\n",
        "+ }\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "siplot"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_type": "subslide"
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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CX/cG3v5/1d5BZ9rl83rqUYn2vEAfqZxrQrYDAhFTFQNO5QVatncyLgoMZUF3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\n2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      }
     ],
     "prompt_number": 16
    }
   ],
   "metadata": {}
  }
 ]
}