Equation-free modelling of evolving diseases: Coarse-grained computations with individual-based models

We demonstrate how direct simulation of stochastic, individual-based models can be combined with continuum numerical-analysis techniques to study the dynamics of evolving diseases. Sidestepping the necessity of obtaining explicit population-level models, the approach analyses the (unavailable in closed form) 'coarse' macroscopic equations, estimating the necessary quantities through appropriately initialized short 'bursts' of individual-based dynamic simulation. We illustrate this approach by analysing a stochastic and discrete model for the evolution of disease agents caused by point mutations within individual hosts. Building up from classical susceptible- infected recovered and susceptible infected-recovered-susceptible models, our example uses a one-dimensional lattice for variant space, and assumes a finite number of individuals. Macroscopic computational tasks enabled through this approach include stationary-state computation, coarse projective integration, parametric continuation and stability analysis.