# [R] How to apply a system of ordinary differential equations to a cell grid?

David Winsemius dwinsemius at comcast.net
Wed Jun 21 22:30:39 CEST 2017

```> On Jun 21, 2017, at 12:48 PM, Marine Regis <marine.regis at 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?
>
> 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.

>
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