epistep: Evolve One Step of an Epidemic in Time
In amei: Adaptive Management of Epidemiological Interventions

Description Usage Arguments Details Value Author(s) References See Also Examples

This function takes the current state of an epidemic, described by the values of SIR, and evolves the epidemic by one time step, stochastically, according to the parameterization provided

1	epistep(SIR, last = NULL, true = list(b = 0.00218, k = 10, nu = 0.4, mu = 0))

`SIR`	a `list` with the current scalar values of the number of susceptibles (`$S`), infecteds (`$I`) and recovereds (`$R`)
`last`	a (dummy) argument used to pass additional information necessary for the sampling the dynamics of the epidemic; the return-value of a user-defined `epistep` function would be automatically passed in here by the `manage` function. This is not required by the simple SIR model implemented here in the default version
`true`	a `list` containing scalar entries indicating the true parameters according to which the SIR model evolves stochastically: `$b`, `$k`, `$nu`, and `$mu` representing the transmission probability, clumpiness parameter, the recovery probability, and the mortality probability, respectively

This function is intended to be passed as an argument to the manage function, to describe the default evolution of an epidemic under the SIR model. Other, user-defined, functions undergoing different disease dynamics should follow the protocol (i.e., inputs and outputs) prototyped by this function. Similarly, this function may be used as input to MCmanage which depends on the manage function.

The epidemic described by the default parameterization (given by true) is an approximation of an influenza epidemic in a British boarding school described by Murray (see references below).

For more details on the parameterization and simulation of the SIR model, etc., see vignette("amei")

epistep returns a list containing the scalar integer components listed below indicating the number of individuals which are

`rem`	newly removed
`rec`	newly recovered
`infect`	newly infected
`dead`	newly dead

Daniel Merl <danmerl@gmail.com>
Leah R. Johnson <lrjohnson@uchicago.edu>
Robert B. Gramacy <rbgramacy@chicagobooth.edu>
and Mark S. Mangel <msmangl@ams.ucsc.edu>

D. Merl, L.R. Johnson, R.B. Gramacy, and M.S. Mangel (2010). “amei: An R Package for the Adaptive Management of Epidemiological Interventions”. Journal of Statistical Software 36(6), 1-32. http://www.jstatsoft.org/v36/i06/

D. Merl, L.R. Johnson, R.B. Gramacy, M.S. Mangel (2009). “A Statistical Framework for the Adaptive Management of Epidemiological Interventions”. PLoS ONE, 4(6), e5807. http://www.plosone.org/article/info:doi/10.1371/journal.pone.0005807

Murray, J. D. (2002) Mathematical Biology I: An Introduction. Springer Verlag

manage, MCmanage

## parameters to epistep (similar default except mu != 0)
true <- list(b = 0.00218, k = 0.1, nu = 0.4, mu = 0.1)
SIR <- list(S=700, I=200, R=100)

## examine the distribution of the outputs of epistep
T <- 1000
na <- rep(NA, T)
out <- data.frame(rem=na, rec=na, infect=na, dead=na)
for(t in 1:T) {
  out[t,] <- epistep(SIR=SIR, true=true)
}

## make histograms of the output
par(mfrow=c(2,2))
hist(out$rem)
hist(out$rec)
hist(out$infect)
hist(out$dead)