MultiStrainPartialImmunity: Partial immunity model that cycles (P 4.2).

In EpiDynamics: Dynamic Models in Epidemiology

Description

Solves multi-strain where the strains are arranged in a circle and each strain offers partial immunity (in terms of reduced transmission) to its neighbours.

Usage

MultiStrainPartialImmunity(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars	vector with 2 vectors and 2 values in the following order: beta, gamma, mu and a. The first element of each vector corresponds to the first strain, the second element to the second strain and so on. mu is the per capita death rate and alpha is the modified transmission rate due to partial immunity.
init	vector with 3 vectors in the following order: S, P and L. The first element of each vector corresponds to the first strain, the second element to the second strain and so on. Si + Pi + Li = 1 but sum(Si) could be greater than 1.
time	time sequence for which output is wanted; the first value of times must be the initial time.
...	further arguments passed to ode function.

Details

This is the R version of program 4.2 from page 123 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

Value

list. The first element, *$model, is the model function. The second, third and fourth elements are the vectors (*$pars, *$init, *$time, containing the pars, init and time arguments of the function. The fifth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. Second, third and fourth columns contain the proportion of susceptibles, infectious and recovered.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

See Also

ode.

Examples

# Parameters and initial conditions.
parameters <- c(beta = rep(40, 4), gamma = rep(9.98, 4),
                       mu = 0.02, a = 0.4 )

initials <- c(S = c(0.08, 0.1, 0.1, 0.11),
                       P = c(0.4, 0.3, 0.3, 0.29),
                       L = c(0.15, 0.02, 0.1, 0.01))

# Solve and plot.
mlti.strain.pi <- MultiStrainPartialImmunity(pars = parameters, 
                                             init = initials, 
                                             time = 0:200)
PlotMods(mlti.strain.pi, variables = c('L1', 'L2', 'L3', 'L4'), grid = FALSE)
                                 

Example output

EpiDynamics documentation built on March 26, 2020, 6:33 p.m.