optvac: Optimal (Static) Vaccination Policy
In amei: Adaptive Management of Epidemiological Interventions

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

A Monte Carlo method is used to calculate the expected costs of a range of static vaccination policies for an epidemic with a known parameterization and initialization

1 2	optvac(init, params, vacgrid, costs, T = 40, MCvits = 100, 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
`vacgrid`	a `list` containing vector entries `$fracs` and `$stops` indicating the permissible fractions (in [0,1]) of the population to be vaccinated and the (positive integer) of stopping thresholds having a maximum of `init$S0`
`costs`	a `list` containing scalar entries `$vac`, `$death`, and `$infect` depicting the costs associated with a single vaccination, death, or the daily cost of maintaining an infected individual, respectively
`T`	the maximum number of time steps during which the epidemic is allowed to evolve
`MCvits`	the number of Monte Carlo iterations of forward epidemic evolution used to determine the optimal vaccination policy
`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

This function use a Monte Carlo experiment to calculate the expected costs over a range of vaccination policies specified by permissible fractions of individuals to be vaccinated and stopping thresholds. These policies are constructed by simulating SIR-modeled epidemics that evolve according to params starting in the initial configuration provided. The output is an object of class "optvac", so the cost grid, or matrix, can be visualized with the plot.optvac generic method. The getpolicy function can be used to select out the best (and worst) one(s).

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

optvac returns an object of class "optvac", which is a list containing the following components.

`vacgrid`	a copy of the input `vacgrid`
`C`	a matrix of expected costs estimated for each combination of `vacgrid$fracs` and `vacgrid$stops`

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.optvac, getpolicy, MCepi

## same inputs as in the MCepi example
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)

## construct a grid of valid vaccination strategies
vacgrid <- list(fracs=seq(0,1.0,0.1), stops=seq(2,init$S0-50,50))

## calculate the cost surface of all combinations in vacgrid
out.optvac <- optvac(init, truth, vacgrid, costs)

## extract the best and worst (static) policy
best <- getpolicy(out.optvac)
worst <-  getpolicy(out.optvac, which="worst")
rbind(best, worst)

## plot the cost surface along with the best and worst policy
plot(out.optvac)

## now return to MCepi for a cost comparison to no vaccination
## using these values
vac.opt <- best[3:4]
vac.opt