EpiDynamics (version 0.3.1)

SIRSinusoidalForcing: SIR model with sinusoidal forcing (P 5.1).

Description

Solves a SIR model with sinusoidal forcing of the transmission rate.

Usage

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

Arguments

pars

list with 4 values: the death rate, the mean transmission rate, a scalar (or a vector to create bifurcations) with the amplitude of sinusoidal forcing, the frequency of oscillations and the recovery rate. The names for these values must be: "mu", "beta0", "beta1", "omega" and "gamma", respectively.

init

vector with 3 values: initial proportion of proportion of susceptibles, infectious and recovered. The names of these values must be "S", "I" and "R", respectively. All parameters must be positive and S + I <= 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.

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.

Details

This is the R version of program 5.1 from page 160 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

When beta1 is a vector in pars, it must be a sequence between 0 and 1.

References

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

See Also

ode.

Examples

# NOT RUN {
# Parameters and initial conditions.
parameters <- list(beta0 = 17 / 13, beta1 = 0.1, gamma = 1 / 13,
                   omega = 2 * pi / 365, mu = 1 / (50 * 365))

initials <- c(S = 1 / 17, I = 1e-4, 
              R = 1 - 1 / 17 - 1e-4)

# Solve and plot.
sir.sinusoidal.forcing <- SIRSinusoidalForcing(pars = parameters, 
                                               init = initials, 
                                               time = 0:(60 * 365))
PlotMods(sir.sinusoidal.forcing)

# Solve bifurcation dynamics for 20 years.
# If max(time) < 3650, bifurcation dynamics are solved for 3650 time-steps.
parameters2 <- list(beta0 = 17 / 13, beta1 = seq(0.001, 0.251, by = 0.001),
                   gamma = 1 / 13, omega = 2 * pi / 365, mu = 1 / (50 * 365))
# Uncomment the following lines (running it takes more than a few seconds):
# bifur <- SIRSinusoidalForcing(pars = parameters2, 
#                               init = initials,
#                               time = 0:(20 * 365))
# PlotMods(bifur, bifur = TRUE)

# }