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Linear Chain System (Cao et al., 2004)

The Linear Chain System consists of M chain reactions with M+1 species as follows:

  S_1 --c1--> S_2
  S_2 --c2--> S_3
       ...
  S_M --cM--> S_(M+1)

Load package

library(GillespieSSA)

Define parameters

parms <- c(c = 1)                # Rate parameter
M <- 50                          # Number of chain reactions
simName <- "Linear Chain System" # Simulation name
tf <- 5                          # Final time

Define initial state vector

x0 <- c(1000, rep(0, M)) 
names(x0) <- paste0("x", seq_len(M+1))

Define state-change matrix

nu <- matrix(rep(0, M * (M+1)), ncol = M)
nu[cbind(seq_len(M), seq_len(M))] <- -1
nu[cbind(seq_len(M)+1, seq_len(M))] <- 1

Define propensity functions

a <- paste0("c*x", seq_len(M))

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 = .1),
  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(f = 50),
  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)

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They may not be fully stable and should be used with caution. We make no claims about them.
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