Radioactive Decay model • GillespieSSA2

This model is also known as the irreversible isomerization reaction set (Gillespie 1977). 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)

## Loading required namespace: ggplot2

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)

References

Gillespie, Daniel T. 1977. “Exact Stochastic Simulation of Coupled Chemical Reactions.” The Journal of Physical Chemistry 81 (25): 2340–61. https://doi.org/10.1021/j100540a008.