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

Stefan Berres, Ricardo Ruiz-Baier

Research output: Contribution to journalArticleResearchpeer-review

24 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)2888-2903
Number of pages16
JournalNonlinear Analysis: Real World Applications
Volume12
Issue number5
DOIs
Publication statusPublished - 1 Oct 2011
Externally publishedYes

Keywords

  • Cross-diffusion
  • Epidemic model
  • Fully adaptive multiresolution
  • Reaction-diffusion equation

Cite this

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A fully adaptive numerical approximation for a two-dimensional epidemic model with nonlinear cross-diffusion. / Berres, Stefan; Ruiz-Baier, Ricardo.

In: Nonlinear Analysis: Real World Applications, Vol. 12, No. 5, 01.10.2011, p. 2888-2903.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Ruiz-Baier, Ricardo

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AB - 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.

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