Radioactive Decay model
In GillespieSSA2: Gillespie's Stochastic Simulation Algorithm for Impatient People

set.seed(1)
knitr::opts_chunk$set(fig.width = 6, fig.height = 4)
if("package:GillespieSSA" %in% search()) detach("package:GillespieSSA", unload=TRUE)

This model is also known as the irreversible isomerization reaction set [@Gillespie1977]. It consists of a single species and single reaction channels,

X --c--> 0

Define parameters

library(GillespieSSA2)
sim_name <- "Radioactive Decay model"
params <- c(k = 0.5)
final_time <- 20
initial_state <- c(N = 1000)

Define reactions

reactions <- list(
  reaction("k * N", c(N = -1))
)

Run simulations with the Exact method

set.seed(1)
out <- ssa(
  initial_state = initial_state,
  reactions = reactions,
  params = params,
  final_time = final_time,
  method = ssa_exact(),
  sim_name = sim_name
) 
plot_ssa(out)

Run simulations with the Explict tau-leap method

set.seed(1)
out <- ssa(
  initial_state = initial_state,
  reactions = reactions,
  params = params,
  final_time = final_time,
  method = ssa_etl(tau = .003),
  sim_name = sim_name
) 
plot_ssa(out)

Run simulations with the Binomial tau-leap method

set.seed(1)
out <- ssa(
  initial_state = initial_state,
  reactions = reactions,
  params = params,
  final_time = final_time,
  method = ssa_btl(),
  sim_name = sim_name
) 
plot_ssa(out)