SIRBirthDeath: SIR model with births and deaths (P 2.2).
In oswaldosantos/EpiDynamics: Dynamic Models in Epidemiology

Description Usage Arguments Details Value References See Also Examples

Solves a simple SIR model with equal births and deaths.

1	SIRBirthDeath(pars = NULL, init = NULL, time = NULL, ...)

`pars`	`vector` with 3 values: the per capita death rate (equal to the population level birth rate), the transmission rate, and the recovery rate. The names of these values must be "mu", "beta", and "gamma", respectively.
`init`	`vector` with 3 values: the initial proportion of proportion of susceptibles, infectious and recovered. The names of these values must be "S", "I" and "R", respectively.
`time`	time sequence for which output is wanted; the first value of times must be the initial time.
`...`	further arguments passed to ode function.

This is the R version of program 2.2 from page 27 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

All parameters must be positive and S + I + R <= 1.

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.

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

ode.

# Parameters and initial conditions.
parameters <- c(mu = 1 / (70 * 365),
                       beta = 520 / 365, gamma = 1 / 7)
initials <- c(S = 0.1, I = 1e-4, R = 1 - 0.1 - 1e-4)

# Solve and plot.
sir.birth.death <- SIRBirthDeath(pars = parameters, init = initials, 
                                 time = 0:(60 * 365))
PlotMods(sir.birth.death)