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We demonstrate how direct simulation of stochastic, individual-based modelscan be combined with continuum numerical analysis techniques to study thedynamics of evolving diseases. % Sidestepping the necessity of obtainingexplicit population-level models, the approach analyzes the (unavailable inclosed form) `coarse' macroscopic equations, estimating the necessaryquantities through appropriately initialized, short `bursts' ofindividual-based dynamic simulation. % We illustrate this approach by analyzinga stochastic and discrete model for the evolution of disease agents caused bypoint mutations within individual hosts. % Building up from classical SIR andSIRS models, our example uses a one-dimensional lattice for variant space, andassumes a finite number of individuals. % Macroscopic computational tasksenabled through this approach include stationary state computation, coarseprojective integration, parametric continuation and stability analysis.Comment: 16 pages, 8 figure

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