primer (version 0.1)

SIRbd: The S-I-R epidemilogical disease model with births and deaths

Description

The S-I-R epidemilogical disease model with births and deaths (population dynamics), for use with ode in the deSolve package. This model uses mass action transmission.

Usage

SIRbd(t, y, p)

Arguments

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

Value

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

Details

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

References

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

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

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

See Also

ross, SIRf, SIR

Examples

library(deSolve)
N <- 10^6; R <- 0; I <- 1; S <- N - I - R
g <- 1/(13/365); b <- 1/50; 
age <- 5; R0 <- 1 + 1/(b*age)
B <- R0 * (g + b) / N
parms <- c(B = B, g = g, b = b, m=b)
years <- seq(0,30, by=.1)
SIRbd.out <- data.frame(ode(c(S=S,I=I,R=R), years, SIRbd, parms, hmax=.01)) 
matplot(SIRbd.out[,1], sqrt(SIRbd.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')