# Linear Chain System (Cao et al., 2004) In GillespieSSA: Gillespie's Stochastic Simulation Algorithm (SSA)

set.seed(1)
knitr::opts_chunk\$set(fig.width = 8, fig.height = 6)

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)

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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GillespieSSA documentation built on March 18, 2022, 7:55 p.m.