[R-sig-dyn-mod] Individual-based modelling

[Sibylle Mohr]

Dear all,

I want to implement an individual-based model and am unsure how to go about this - here’s to hoping someone can point me in the right direction..

I created a simple model (predator-prey like equations) which predicts the number of scab mites from serological data (i.e. immune response) on a **single** animal (see code below).
Immune response grows with mite count here.
Now I would like to extend the model from a single sheep towards an individual-based model representing the flock of animals with two initial states, “clinical” and "sub-clinical” depending on the how large the immune response is (i.e. small immune response = infested but no clinical signs).
So I guess I have to questions:

(a) How can I go from a single animal model to an individual-based population model?
(b) How can I integrate this into a two-stage model?

Any thoughts are most welcome.

Many thanks & best wishes,

Sibylle

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The code:

## Immune response model 

require(simecol)
require(deSolve)

# P = number of scab mites,
# E = ‘amount’ of protective immunity,
# W = mites in environment
# nu = intrinsic mite growth rate,
# mu*E = per-capita mite death rate,
# epsilon*P = per-capita growth of the immune response
# alpha =  rate of decline of the immune response in the absence of antigenic stimulation
# lambda = parasite environmental production
# gamma= = parasite environmental death
# beta = transmission rate

ImmRespode <- {new("odeModel",
                     main = function(time, init, parms){
                       with(as.list(c(init, parms)),{

                         dP <- P*(nu - mu*E)
                         dE <- -E*(alpha - epsilon*P)
                         dW <- (lambda*E) - (gamma*W) - (beta*W*P)

                         list(c(dP, dE, dW))
                       })
                     },
                     times = c(from = 0, to = 365, by = 0.01),
                     init = c(P = 2, E = 2, W = 0),
                     
                     parms = c(nu = .11, mu = .01, epsilon = .00024, alpha = .00024, lambda = .05, gamma = .05, beta=.05),
                     solver = "lsoda")
}
ImmRespode <- sim(ImmRespode)

print(ImmRespode, all=TRUE)
ImmRespodedata <- out(ImmRespode)	# ?simecol::out

par(mfrow = c(1, 3))
plot(ImmRespodedata[,1], ImmRespodedata[,3], type="l", xlab = "Time Period", ylab = "Immune response", col=2)
plot(ImmRespodedata[,1], ImmRespodedata[,2], type="l", xlab = "Time Period", ylab = "Mite Density")
plot(ImmRespodedata[,1], ImmRespodedata[,4], type="l", xlab = "Time Period", ylab = "Environment")



--
Sibylle Mohr, Ph.D.
Institute of Biodiversity, Animal Health, and Comparative Medicine
College of Medical, Veterinary and Life Sciences
University of Glasgow
464 Bearsden Rd. Glasgow G61 1QH