TY - GEN

T1 - Simulation of an epidemic model with nonlinear cross-diffusion

AU - Berres, Stefan

AU - Ruiz-Baier, Ricardo

PY - 2013/1/1

Y1 - 2013/1/1

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.

UR - http://www.scopus.com/inward/record.url?scp=84870571151&partnerID=8YFLogxK

M3 - Conference Paper

AN - SCOPUS:84870571151

SN - 9780415621502

T3 - 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.

SP - 331

EP - 338

BT - Numerical Methods for Hyperbolic Equations

T2 - International Conference on Numerical Methods for Hyperbolic Equations: Theory and Applications

Y2 - 4 July 2011 through 9 July 2011

ER -