Thank you very much for your answer. I'm not sure if I can use the function
ode.2 because it's a solver for 2-D partial differential equation problems. My
equations don't contain diffusion parameters.
Thank you for your help
Marine
________________________________
De : David Winsemius <dwinsem...@comcast.net>
Envoyé : mercredi 21 juin 2017 22:30
À : Marine Regis
Cc : r-help@r-project.org
Objet : Re: [R] How to apply a system of ordinary differential equations to a
cell grid?
> On Jun 21, 2017, at 12:48 PM, Marine Regis <marine.re...@hotmail.fr> wrote:
>
> Hello,
>
> I am developing an agent-based model to simulate the spread of infectious
> diseases in heterogeneous landscapes composed of habitat polygons (or clumps
> of connected cells). To simplify the model, I consider a habitat grid (or
> raster) containing the polygon ID of each cell. In addition, I have
> epidemiological parameters associated with each polygon ID. At each time
> step, the parameter values change in the polygon. Thus, the data frame
> �landscape� (see below) is updated at each time step. Here is an example at t
> = 0:
>
> landscape <- data.frame(polygon_ID = seq(1, 10, by = 1),
> beta = sample(c(100, 200, 400, 600), 10, replace =
> TRUE),
> gamma = sample(c(25, 26, 27, 28), 10, replace = TRUE))
>
> To study the disease dynamics, I also am developing a compartmental model
> based on a system of ordinary differential equations (ODEs). Here is an
> example to represent the system of ODEs:
>
> solve_sir_model <- function (times, parameters) {
>
> sir_model <- function (times, states, parameters) {
>
> with(as.list(c(states, parameters)), {
>
> dSdt <- -beta*S*I
> dIdt <- beta*S*I-gamma*I
> dRdt <- gamma*I
> dNdt <- dSdt + dIdt + dRdt
>
> return(list(c(dSdt, dIdt, dRdt, dNdt)))
>
> })
> }
>
> states <- c(S = 99, I = 1, R = 0, N = 100)
> return(ode(y = states, times = times, func = sir_model, parms = parameters))
> }
>
> require(deSolve)
> output <- as.data.frame(solve_sir_model(times = seq(0, 5, by = 1), parameters
> = c(beta = 400, gamma = 28)))
>
> Here is my question: at each time step, is it possible to apply the system of
> ODEs to each habitat polygon (thus each row) in the data frame �landscape�? I
> am using lsoda as an ODE solver. Do I need to use another solver to apply the
> ODEs at each time step?
>
> Thank you very much for your advice.
> Have a nice day
> Marine
>
There's also ode.2D in the same package {deSolve} and it's help page has a 2-d
diffusion example that might be cognate.
>
> [[alternative HTML version deleted]]
>
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David Winsemius
Alameda, CA, USA
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