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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 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.
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Dates and versions

hal-00462460 , version 1 (09-03-2010)

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  • HAL Id : hal-00462460 , version 1

Cite

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

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