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
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
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
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