An accelerated hybrid framework for stochastic simulations of reaction–diffusion epidemic models

Reaction–diffusion models have been widely used in mathematical epidemiology as a powerful tool for describing the spatiotemporal dynamics of an infectious disease. This paper presents a novel hybrid stochastic algorithm to simulate such models. Unlike existing hybrid methods, which are based on spatial coupling, our method temporally couples reactive multiparticle collision (RMPC) dynamics—a particle-based method—and the inhomogeneous stochastic simulation algorithm (ISSA)—a compartment-based method. The advantage of our hybrid algorithm is demonstrated on three benchmark epidemic models, with a focus on accuracy and computational cost. While the hybrid method has comparable accuracy, it is faster than full RMPC as long as the ISSA grid is not too refined. It is also found that the speed can be improved by either using a coarser ISSA grid or a smaller infectious switching threshold I*. Coupling RMPC with a spatial tau-leaping algorithm further improves the simulation times.