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

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Autor:
Berres, Stefan - Ruiz-Baier, Ricardo
URI:
http://repositoriodigital.uct.cl/handle/10925/2997
Datos de publicación:
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS,Vol.12,2888-2903,2011
Temas:
Epidemic model - Reaction-diffusion equation - Cross-diffusion - Fully adaptive multiresolution
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Resumen:
An epidemic model is formulated by a reaction-diffusion system where the spatial pattern formation is driven by cross-diffusion. The reaction terms describe the local dynamics of susceptible and infected species, whereas 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. (c) 2011 Elsevier Ltd. All rights reserved.

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