# Radioactive Decay model

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)

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.