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Message-ID: <51758F69.6060706@TU-Dresden.de>
Date: 2013-04-22T19:28:41Z
From: Thomas Petzoldt
Subject: [R-sig-dyn-mod] metapopulation SIR model
In-Reply-To: <1366623995.60039.YahooMailNeo@web171503.mail.ir2.yahoo.com>

Hi,

I would suggest to use an interaction matrix approach
similar to the multi-species Lotka-Volterra example, cf.:

http://desolve.r-forge.r-project.org/slides/tutorial.pdf#91

or the example below.

thpe


##----------------------------------------------------------
library(deSolve)

model <- function(t, n, parms) {
   with(parms, {
     dn <- r * n  + n * (A %*% n)
     list(dn)
   })
}

parms <- list(
   r = c(r1 = 0.1, r2 = 0.1, r3 = -0.1, r4 = -0.1),
   A = matrix(c(
     0.0, 0.0, -0.2, 0.0, # prey 1
     0.0, 0.0, 0.0, -0.1, # prey 2
     0.2, 0.0, 0.0, 0.0,  # predator 1; eats prey 1
     0.0, 0.1, 0.0, 0.0), # predator 2; eats prey 2
     nrow = 4, ncol = 4, byrow = TRUE)
)

times = seq(0, 500, 0.1)
n0  = c(n1 = 1, n2 = 1, n3 = 2, n4 = 2)

out <- ode(n0, times, model, parms)
plot(out)