Simulation of an epidemic model with nonlinear cross-diffusion

Stefan Berres; Ricardo Ruiz-Baier

Simulation of an epidemic model with nonlinear cross-diffusion

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

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 language	English
Title of host publication	Numerical Methods for Hyperbolic Equations
Subtitle of host publication	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.
Pages	331-338
Number of pages	8
Publication status	Published - 1 Jan 2013
Externally published	Yes
Event	International Conference on Numerical Methods for Hyperbolic Equations: Theory and Applications - Santiago de Compostela, Spain Duration: 4 Jul 2011 → 9 Jul 2011

Publication series

Name	Numerical 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

Conference	International Conference on Numerical Methods for Hyperbolic Equations: Theory and Applications
Country/Territory	Spain
City	Santiago de Compostela
Period	4/07/11 → 9/07/11

Cite this

Berres, S., & Ruiz-Baier, R. (2013). Simulation of an epidemic model with nonlinear cross-diffusion. In Numerical 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. (pp. 331-338). (Numerical 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.).

Berres, Stefan ; Ruiz-Baier, Ricardo. / Simulation of an epidemic model with nonlinear cross-diffusion. Numerical 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.. 2013. pp. 331-338 (Numerical 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.).

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title = "Simulation of an epidemic model with nonlinear cross-diffusion",

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.",

author = "Stefan Berres and Ricardo Ruiz-Baier",

year = "2013",

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note = "International Conference on Numerical Methods for Hyperbolic Equations: Theory and Applications ; Conference date: 04-07-2011 Through 09-07-2011",

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Berres, S & Ruiz-Baier, R 2013, Simulation of an epidemic model with nonlinear cross-diffusion. in Numerical 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.. Numerical 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., pp. 331-338, International Conference on Numerical Methods for Hyperbolic Equations: Theory and Applications, Santiago de Compostela, Spain, 4/07/11.

Simulation of an epidemic model with nonlinear cross-diffusion. / Berres, Stefan; Ruiz-Baier, Ricardo.

Numerical 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.. 2013. p. 331-338 (Numerical 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.).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

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AU - Ruiz-Baier, Ricardo

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N2 - 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.

AB - 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.

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Berres S, Ruiz-Baier R. Simulation of an epidemic model with nonlinear cross-diffusion. In Numerical 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.. 2013. p. 331-338. (Numerical 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.).

Simulation of an epidemic model with nonlinear cross-diffusion

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