A fully adaptive numerical approximation for a two-dimensional epidemic model with nonlinear cross-diffusion

Abstract

An epidemic model is formulated by a reaction-diffusion system where the spatial pattern formation is driven by crossdiffusion. 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. An efficient simulation is obtained by a fully adaptive multiresolution strategy. Numerical examples illustrate the impact of the cross-diffusion on the pattern formation.