Simulation of an epidemic model with nonlinear cross-diffusion

A spatially two-dimensional epidemic model is formulated by a reaction-diffusion system. The spatial pattern formation is driven by a cross-diffusion corresponding to a non-diagonal, uppertriangular diffusion matrix. Whereas the reaction terms describe the local dynamics of susceptible and infected species, the diffusion terms account for the spatial distribution dynamics. For both self-diffusion and cross-diffusion nonlinear constitutive assumptions are suggested. To simulate the pattern formation two finite volume formulations are proposed, which employ a conservative and a non-conservative discretization, respectively. Numerical examples illustrate the impact of the cross-diffusion on the pattern formation. © 2013 Taylor & Francis Group, London.