# Decaying-Dimerization Reaction Set

The Decaying-Dimerization Reaction Set (Gillespie 2001) consists of three species and four reaction channels.

          S1 --c1--> 0
     S1 + S1 --c2--> S2
          S2 --c3--> S1 + S1
          S2 --c4--> S3

Define parameters

    library(GillespieSSA2)
    sim_name <- "Decaying-Dimerizing Reaction Set"
    final_time <- 10
    params <- c(c1 = 1.0, c2 = 0.002, c3 = 0.5, c4 = 0.04)
    initial_state <- c(s1 = 10000, s2 = 0, s3 = 0)

Define reactions

    reactions <- list(
      reaction("c1 * s1",        c(s1 = -1)),
      reaction("c2 * s1 * s1",   c(s1 = -2, s2 = +1)),
      reaction("c3 * s2",        c(s1 = +2, s2 = -1)),
      reaction("c4 * s2",        c(s2 = -1, s3 = +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 = 0.003),
      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. 2001. “Approximate Accelerated Stochastic Simulation of Chemically Reacting Systems.” The Journal of Chemical Physics 115 (4): 1716–33. https://doi.org/10.1063/1.1378322.