# Radioactive decay model (Gillespie, 1977)

This model is also known as the irreversible isomerization reaction set. It consists of a single species and single reaction channels,

    X --c--> 0

Load package

    library(GillespieSSA)

Define parameters

    parms <- c(k = 0.5)
    tf <- 20                                       # Final time
    simName <- "Radioactive decay model"

Define initial state vector

    x0 <- c(N=1000)

Define state-change matrix

    nu <- matrix(c(-1),nrow=1,byrow=TRUE)

Define propensity functions

    a <- c("k*N")

Run simulations with the Direct method

    set.seed(1)
    out <- ssa(
      x0 = x0,
      a = a,
      nu = nu,
      parms = parms,
      tf = tf,
      method = ssa.d(),
      simName = simName,
      verbose = FALSE,
      consoleInterval = 1
    )
    ssa.plot(out, show.title = TRUE, show.legend = FALSE)

Run simulations with the Explict tau-leap method

    set.seed(1)
    out <- ssa(
      x0 = x0,
      a = a,
      nu = nu,
      parms = parms,
      tf = tf,
      method = ssa.etl(tau = .003),
      simName = simName,
      verbose = FALSE,
      consoleInterval = 1
    )
    ssa.plot(out, show.title = TRUE, show.legend = FALSE)

Run simulations with the Binomial tau-leap method

    set.seed(1)
    out <- ssa(
      x0 = x0,
      a = a,
      nu = nu,
      parms = parms,
      tf = tf,
      method = ssa.btl(),
      simName = simName,
      verbose = FALSE,
      consoleInterval = 1
    )
    ssa.plot(out, show.title = TRUE, show.legend = FALSE)

Run simulations with the Optimized tau-leap method

    set.seed(1)
    out <- ssa(
      x0 = x0,
      a = a,
      nu = nu,
      parms = parms,
      tf = tf,
      method = ssa.otl(),
      simName = simName,
      verbose = FALSE,
      consoleInterval = 1
    )
    ssa.plot(out, show.title = TRUE, show.legend = FALSE)