MCepi: Monte Carlo Epidemic Simulation with Static Vaccination
In amei: Adaptive Management of Epidemiological Interventions

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

This function performs a Monte Carlo simulation of epidemic trajectories under a static vaccination strategy. Statistics are collected for a collection of characteristics including the state of the epidemic (evolution of susceptibles (S), infecteds (I), recovereds (R), and deads) and the cost of the vaccination strategy employed

1 2	MCepi(init, params, vac, costs, T = 40, MCreps = 1000, quant = c(0.025, 0.975), midepi = FALSE, start = 7, ...)

`init`	a `list` containing scalar entries `$S0`, `$I0`, `$R0`, `$D0` depicting the initial number of susceptibles, infecteds, recovereds, and deads in the outbreak
`params`	a `list` containing scalar entries `$b`, `$k`, `$nu`, and `$mu` depicting the true parameters of the SIR model representing the transmission probability, clumpiness parameter, the recovery probability, and the mortality probability, respectively; optionally `params` may be an `epistep` function
`vac`	a `list` containing scalar entries `$frac` and `$stop` depicting the fraction to be vaccinated at each time step, and the vaccination (stopping) threshold, respectively
`costs`	a `list` containing scalar entries `$vac`, `$death`, and `$infect` depicting the costs associated with a single vaccination, death, or daily cost of maintaining an infected individual, respectively
`T`	the maximum number of time steps during which the epidemic is allowed to evolve
`MCreps`	the number of times to repeat the Monte Carlo experiment, each time starting with the state in `init` and collecting characteristics of the epidemic trajectories and (vaccination/death) costs
`quant`	a 2-vector of quantiles to use in order to capture the spread in the density of characteristics of the epidemic trajectory and costs
`midepi`	a debugging `logical` indicating whether to signal that a trajectory is unlikely to be an epidemic
`start`	at what time, after time 1 where the state is given by `init`, should vaccinations be allowed to start
`...`	additional arguments passed to a user-defined `epistep` function that may be passed in via `params`

This function simulates many (MCreps) trajectories of an epidemic starting out in a particular state (init) and evolving according to a particular (true) parameterization under a fixed vaccination strategy (vac). It returns a summary of characteristics of the state trajector(y/ies) and the associated costs. The output can be visualized with the generic plot.MCepi method and costs can be extracted with getcost.

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

MCepi returns an object of class "MCepi", which is a list containing the components listed below.

`Q1`	a `data.frame` containing 6 columns (`S`, `I`, `R`, `D`, `V`, `C`) depicting the first quantile (`quant[1]`) of the distribution of the evolution of the state of the epidemic (SIRD), the number of vaccinations (V), and the cost (C), at each time point
`Mean`	same as `Q1` except the mean rather than a quantile
`Q3`	same as `Q1` except the third quantile (`quant[2]`)

These quantities can be visually inspected using the plot.MCepi method

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

plot.MCepi, optvac

## true epidemic parameters, initial values, and
## vaccination costs
truth <- list(b=0.00218, k=10, nu=0.4, mu=0) 
init <- list(S0=762, I0=1, R0=0, D0=0) 
costs <- list(vac=2, death=4, infect=1)

## trivial vaccination strategy -- dont vaccinate
vac <- list(frac=0, stop=0)

## simulate the resulting trajectories
init.MCepi <- MCepi(init, truth, vac, costs)

## plot the distribution of trajectories and costs
## under no vaccination
plot(init.MCepi, main="no vaccination")
plot(init.MCepi, type="costs")

## Now try the optimal strategy.
## See the optvac function for more info
vac.opt <- list(frac=0.7, stop=502)
opt.MCepi <- MCepi(init, truth, vac.opt, costs)

## plot the distribution of trajectories and costs
## under the optimal (static) vaccination
plot(opt.MCepi, main="optimal static vaccination")
plot(opt.MCepi, type="costs")

## show the total number of vaccinations
## median and quantiles
getvac(opt.MCepi)

## compare the median costs of the the initial
## (no vaccination) strategy versus the optimal
## (static) policy
T <- length(opt.MCepi$Median$C)
optC <- getcost(opt.MCepi)
initC <- getcost(init.MCepi)
rbind(initC,optC)

  q0.025    mean median q0.975
1      0 352.756  417.5    515
    q0.025     mean median   q0.975
1 2155.975 2295.795 2296.5 2433.000
2 1506.975 1847.815 1790.0 2377.125