SISinusoidalTransmBrith {EpiDynamics}

Rabbit Hemorrhagic Disease model with sinusoidal transmission rate and per capita birth rate (P 5.4).

Description

Solves the Rabbit Hemorrhagic Disease, in which both transmission rate and birth rates can be seasonally forced.

Usage

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

Arguments

pars

list with: the mean transmission rate, the amplitude of sinuoidal forcing (transmission), the mean birth rate, the amplitude of sinuoidal forcing for the birth rate, the frequency of the oscillations, the recovery rate, the per capita death rate, the mortality rate due to infection, and the carrying capacity. The names of these values must be "beta0", "beta1", "alpha0", "alpha1", "w", "gamma", "mu", "m" and "K", respectively. All parameters must be positive, alpha1, beta1 <= 1.

init

vector with 3 values: the initial numbers of susceptible hosts (rabbits), infectious hosts (rabbits) and total population size. The names of these values must be "X", "Y" and "N", respectively. All initial values must be positive and X(0) + Y(0) <= N(0).

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 5.4 from page 186 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

Value

list. The first element, *$model, is the model function. The second element is a list with the *$pars argument. The third and fourth elements are the vectors *$init and *$time, containing the 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 number 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 <- list(beta0 = 0.936, beta1 = 0.1, alpha0 = 0.02, alpha1 = 0.1,
                   w = 2 * pi / 365, gamma = 0.025,  mu = 0.01, m = 0.475,
                   K = 10000)
initials <- c(X = 0.5, Y = 0.01, N = 0.6)

# Solve and plot.
sis.rhdm <- SISinusoidalTransmBrith(pars = parameters,
                                    init = initials,
                                    time = 0:(60 * 365))
PlotMods(sis.rhdm)