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

Berres Stefan (1) , Ricardo Ruiz Baier (2)

1 Departamento de Ciencias Matem\'{a}tica y F\'{\i}sica
2 EPFL - Ecole Polytechnique Fédérale de Lausanne

An epidemic model is formulated by a reaction-diffusion system where the spatial pattern formation is driven by cross-diffusion. 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.

Mots clés: Epidemic model; reaction-diffusion equation; cross-diffusion; fully adaptive multiresolution

Domaines: Analyse numérique [math.NA]; Formation de Structures et Solitons [nlin.PS]

Berres Stefan, Ricardo Ruiz Baier. A fully adaptive numerical approximation for a two-dimensional epidemic model with nonlinear cross-diffusion. 2010. ⟨hal-00462460⟩