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.