Simulation of an epidemic model with nonlinear cross-diffusion

Stefan Berres, Ricardo Ruiz-Baier

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

2 Citations (Scopus)

Abstract

A spatially two-dimensional epidemic model is formulated by a reaction-diffusion system. The spatial pattern formation is driven by a cross-diffusion corresponding to a non-diagonal, uppertriangular diffusion matrix. 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. Numerical examples illustrate the impact of the cross-diffusion on the pattern formation.

Original languageEnglish
Title of host publicationNumerical Methods for Hyperbolic Equations
Subtitle of host publicationTheory and Appl., An Int. Conf. to Honour Professor E.F. Toro - Proc. of the Int. Conf. on Numerical Methods for Hyperbolic Equations: Theory and Appl.
Pages331-338
Number of pages8
Publication statusPublished - 1 Jan 2013
Externally publishedYes
EventInternational Conference on Numerical Methods for Hyperbolic Equations: Theory and Applications - Santiago de Compostela, Spain
Duration: 4 Jul 20119 Jul 2011

Publication series

NameNumerical Methods for Hyperbolic Equations: Theory and Appl., An Int. Conf. to Honour Professor E.F. Toro - Proc. of the Int. Conf. on Numerical Methods for Hyperbolic Equations: Theory and Appl.

Conference

ConferenceInternational Conference on Numerical Methods for Hyperbolic Equations: Theory and Applications
CountrySpain
CitySantiago de Compostela
Period4/07/119/07/11

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