Kermack-McKendrick SIR 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)

The Kermack-McKendrick SIR model [@Brown1993] is defined as

dS/dt = -beta*N*S
dI/dt = beta*N*S - gamma*I
dR/dt = gamma*I

Note that simulations of this model can generate in all zero propensity, if the first reaction is a recovery of the single 'Infected' individual.

Define parameters

library(GillespieSSA2)
sim_name <- "Kermack-McKendrick SIR model"
params <- c(beta = .001, gamma = .1)
final_time <- 100
initial_state <- c(S = 500, I = 1, R = 0)

Define reactions

reactions <- list(
  reaction("beta * S * I", c(S = -1, I = +1), name = "transmission"),
  reaction("gamma * I", c(I = -1, R = +1), name = "recovery")
)

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(),
  sim_name = sim_name
) 
plot_ssa(out)

Run simulations with the Binomial tau-leap method

set.seed(2)
out <- ssa(
  initial_state = initial_state,
  reactions = reactions,
  params = params,
  final_time = final_time,
  method = ssa_btl(),
  sim_name = sim_name
) 
plot_ssa(out)