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```
#' Stochastic simulation of an SEIR-type model
#'
#' @description Simulation of a stochastic SEIR type model with the following
#' compartments: Susceptibles (S), Infected and pre-symptomatic/exposed (E),
#' Infected and Symptomatic (I), Recovered and Immune (R)
#'
#' @param S : initial number of susceptible hosts : numeric
#' @param I : initial number of infected, symptomatic hosts : numeric
#' @param bE : level/rate of infectiousness for hosts in the E compartment : numeric
#' @param bI : level/rate of infectiousness for hosts in the I compartment : numeric
#' @param gE : rate at which a person leaves the E compartment : numeric
#' @param gI : rate at which a person leaves the I compartment : numeric
#' @param w : rate at which recovered lose immunity and return to susceptible : numeric
#' @param m : the rate at which new individuals enter the model (are born) : numeric
#' @param n : the rate of natural death (the inverse is the average lifespan) : numeric
#' @param tmax : maximum simulation time : numeric
#' @param rngseed : seed for random number generator to allow reproducibility : numeric
#' @return The function returns a list. The list has one element, a data frame ts
#' which contains the time series of the simulated model,
#' with one column per compartment/variable. The first column is time.
#' @details A compartmental ID model with several states/compartments is
#' simulated. Initial conditions for the E and R variables are 0. Units of
#' time depend on the time units chosen for model parameters. The simulation
#' runs as a stochastic model using the adaptive-tau algorithm as implemented
#' by ssa.adaptivetau() in the adpativetau package. See the manual of this
#' package for more details.
#' @section Warning: This function does not perform any error checking. So if
#' you try to do something nonsensical (e.g. specify negative parameter values
#' or fractions > 1), the code will likely abort with an error message.
#' @examples
#' # To run the simulation with default parameters, just call the function:
#' result <- simulate_seir_stochastic()
#' # To choose parameter values other than the standard one, specify them like this:
#' result <- simulate_seir_stochastic(S = 2000, tmax = 200, bE = 0.01)
#' # You can display or further process the result, like this:
#' plot(result$ts[,'time'],result$ts[,'S'],xlab='Time',ylab='Number Susceptible',type='l')
#' print(paste('Max number of infected: ',max(result$ts[,'I'])))
#' @seealso See the Shiny app documentation corresponding to this simulator
#' function for more details on this model. See the manual for the adaptivetau
#' package for details on the stochastic algorithm.
#' @author Andreas Handel
#' @export
simulate_seir_stochastic <- function(S = 1000, I = 10, bE = 0, bI = 1e-3, gE = 0.5, gI = 0.5, w = 0, m = 0, n = 0, tmax = 100, rngseed = 100)
{
#this specifies the rates used by the adapativetau routine
stochasticSEIRfunc <- function(y, parms, t)
{
with(as.list(c(y, parms)),
{
#specify each rate/transition/reaction that can happen in the system
rates=c( m,
n * S,
n * E,
n * I,
n * R,
S * bE * E,
S * bI * I,
gE * E,
gI * I,
w * R
) #end specification of each rate/transition/reaction
return(rates)
})
} #end function specifying rates used by adaptivetau
Y0 = c(S = S, E = 0, I = I, R = 0); #combine initial conditions into a vector
dt = tmax / 1000; #time step for which to get results back
timevec = seq(0, tmax, dt); #vector of times for which solution is returned (not that internal timestep of the integrator is different)
#combining parameters into a parameter vector
pars = c(bE = bE, bI = bI, gE = gE, gI = gI, w = w, m = m, n = n);
#specify for each reaction/rate/transition how the different variables change
#needs to be in exactly the same order as the rates listed in the rate function
transitions = list(c(S = +1), #births of susceptible
c(S = -1), #deaths of susceptible
c(E = -1), #deaths of E
c(I = -1), #deaths of I
c(R = -1), #deaths of R
c(S = -1, E = +1), #infection of S by E
c(S = -1, E = +1), #infection of S by I
c(E = -1, I = +1), #move of E to I (becoming symptomatic)
c(I = -1, R = +1), #move of I to R (recovery)
c(R = -1, S = +1) #move of R to S (waning immunity)
) #end list of transitions
#this line runs the simulation using the SSA algorithm in the adaptivetau package
set.seed(rngseed) # to allow reproducibility
simres = adaptivetau::ssa.adaptivetau(init.values = Y0, transitions = transitions, rateFunc = stochasticSEIRfunc, params = pars, tf = tmax)
result <- list()
result$ts <- as.data.frame(simres)
return(result)
}
```

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