epistep {amei} | R Documentation |
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
epistep(SIR, 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 ) |
true |
a list containing scalar entries indicating
the true parameters according to which the SIR model evolves
stochastically: $b , $k , $nu , and $mu
representing the transmission probability, clumpiness parameter,
the recovery probability, and the mortality probability, respectively |
This function is intended to be passed as an argument to the
manage
function, to describe the default evolution
of an epidemic under the SIR model. Other, user-defined, functions
undergoing different disease dynamics should follow the protocol (i.e.,
inputs and outputs) prototyped by this function. Similarly, this
function may be used as input to MCmanage
which
depends on the manage
function.
The epidemic described by the default parameterization ({tt true}) is an approximation of an influenza epidemic in a British boarding school described by Murray (see references below).
For more details on the parameterization and simulation of the
SIR model, etc., see vignette("amei")
epistep
returns a list
containing the
scalar integer components listed below indicating the number of
individuals which are
rem |
newly removed |
rec |
newly recovered |
infect |
newly infected |
dead |
newly dead |
Daniel Merl <dan@stat.duke.edu>, Leah R. Johnson <leah@statslab.cam.ac.uk>, Robert B. Gramacy <bobby@statslab.cam.ac.uk>, and Mark S. Mangel <msmangl@ams.ucsc.edu>
A statistical framework for the adaptive management of epidemiological interventions (2008). Daniel Merl, Leah R. Johnson, Robert B. Gramacy, and Marc S. Mangel. Duke Working Paper 08-29. http://ftp.stat.duke.edu/WorkingPapers/08-29.html
Murray, J. D. (2002) Mathematical Biology I: An Introduction. Springer Verlag
## parameters to epistep (similar default except mu != 0) true <- list(b = 0.00218, k = 0.1, nu = 0.4, mu = 0.1) SIR <- list(S=700, I=200, R=100) ## examine the distribution of the outputs of epistep T <- 1000 na <- rep(NA, T) out <- data.frame(rem=na, rec=na, infect=na, dead=na) for(t in 1:T) { out[t,] <- epistep(SIR=SIR, true=true) } ## make histograms of the output par(mfrow=c(2,2)) hist(out$rem) hist(out$rec) hist(out$infect) hist(out$dead)