SIRInducedMortality: SIR model with disease induced mortality: Density-dependent...

In EpiDynamics: Dynamic Models in Epidemiology

Description

Solves a SIR model with a probability of mortality, and unequal births and deaths.

Usage

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

Arguments

pars	vector with 5 values: the probability that an infected individual dies from the disease before recovering, the per capita death rate from natural causes, the population level birth rate, the transmission rate, and the recovery rate. The name of these values must be: "rho", "mu", "nu", "beta", and "gamma", respectively. All parameters must be positive.
init	vector with 3 values: the initial number of susceptibles, infectious and recovered. The names of these values must be "X", "Y" and "Z", 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.

Details

This is the R version of program 2.3 from page 35 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, *$init and *$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 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 <- c(rho = 0.5, mu = 1 / (70 * 365), nu = 1 / (70 * 365),
                      beta = 520 / 365.0, gamma = 1 / 7)
initials <- c(X = 0.2, Y = 1e-4, Z = 1 - 0.2 - 1e-4)

# Solve and plot.
# Uncomment the following lines (running it takes more than a few seconds):
# sir.induced.mortality <- SIRInducedMortality(pars = parameters, 
#                                  init = initials, 
#                                  time = 0:1e5)
# PlotMods(sir.induced.mortality)
                                 

Example output

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