epistep {amei}R Documentation

Evolve One Step of an Epidemic in Time

Description

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

Usage

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

Arguments

SIR a list with the current scalar values of the number of susceptibles ($S), infecteds ($I) and recovereds ($R)
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

Details

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 ({tt 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")

Value

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

Author(s)

Daniel Merl <dan@stat.duke.edu>, Leah R. Johnson <leah@statslab.cam.ac.uk>, Robert B. Gramacy <bobby@statslab.cam.ac.uk>, and Mark S. Mangel <msmangl@ams.ucsc.edu>

References

A statistical framework for the adaptive management of epidemiological interventions (2008). Daniel Merl, Leah R. Johnson, Robert B. Gramacy, and Marc S. Mangel. Duke Working Paper 08-29. http://ftp.stat.duke.edu/WorkingPapers/08-29.html

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

See Also

manage, MCmanage

Examples

## 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)

[Package amei version 1.0 Index]