Program 7.5 - Individual based SIR model

Individual-based models can encompass a wide range of model forms, and can be designed to include a variety of complex and detailed host behavior that could not be readily expressed within the other model types. As the name suggests, these models consider the dynamics of individuals that occupy a spatial landscape. Here, as an example of this methodology, we formulate a general stochastic individual-based model based on the simple SIR model in which only two events are possible: recovery which occurs at rate γ for any infected individual and transmission which is a spatial process. The rate of transmission (or force of infection) to a susceptible individual, i, is given by:
where the sum is over all infectious individuals (labelled j), d_ij is the distance between individuals i and j, and K_T is the transmission kernel. In these programs the kernel is a power-law decay: K_T(d) = d^-α.