SIRmod: The S-I-R Epidemilogical Disease Model
In primer: Functions and Data for the Book, a Primer of Ecology with R

Description Usage Arguments Details Value Author(s) References See Also Examples

The S-I-R epidemiological disease model with births and deaths (population dynamics), for use with ode in the deSolve package. This model uses scaled transmission, where z controls the degree of density- and frequency-dependence.

1	SIRmod(t, y, p)

`t`	times points for which values will be returned
`y`	the vector of disease states of hosts (S, I, R)
`p`	a vector of parameters

The user does not put these directly into this function, but rather uses ode in the deSolve package.

Returns of list of one component (required by ode).

Hank Stevens <Hank.Stevens@miamioh.edu>

Ellner, S.P. and Guckenheimer, J. (2006) Dynamic Models in Biology, Princeton University Press.

Kermack, W.O. and McCormick, W.G. (1927) A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society, Series A, 115, 700–721.

Stevens, M.H.H. (2009) A Primer of Ecology with R, Use R! Series. Springer.

ross, SIRf, SIRd

library(deSolve)
N <- 10^6; R <- 0; I <- 1; S <- N - I - R
g <- 1/(13/365); b <- 1/50; z <- 0;
age <- 5; R0 <- 1 + 1/(b*age)
B <- R0 * (g + b) / N
parms <- c(B = B, g = g, b = b, mu=b)
years <- seq(0,30, by=.1)
SIR.out <- data.frame(ode(c(S=S,I=I,R=R), years, SIRmod, parms, hmax=.01))
matplot(SIR.out[,1], sqrt(SIR.out[,-1]), type='l',
        lty=1:3, ylab="sqrt(No. of Individuals)", xlab='Years')
legend('right', c('S','I','R'), lty=1:3, col=1:3, bty='n')