Traveling waves of diffusive predator-prey systems: Disease outbreak propagation

Xiang-Sheng Wang; Haiyan Wang; Jianhong Wu

doi:10.3934/dcds.2012.32.3303

Article Contents

2012, Volume 32, Issue 9: 3303-3324. Doi: 10.3934/dcds.2012.32.3303

This issue Previous Article Symbolic dynamics for the $N$-centre problem at negative energies Next Article

Traveling waves of diffusive predator-prey systems: Disease outbreak propagation

1.
Mprime Centre for Disease Modelling, York Institute for Health Research, Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics, York University, Toronto, M3J 1P3
2.
Division of Mathematical and Natural Sciences, Arizona State University, Phoenix, AZ 85069-7100

Received: December 31, 2011

Revised: February 29, 2012

Published: August 2012

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Abstract

We study the traveling waves of reaction-diffusion equations for a diffusive SIR model. The existence of traveling waves is determined by the basic reproduction number of the corresponding ordinary differential equations and the minimal wave speed. Our proof is based on Schauder fixed point theorem and Laplace transform.

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Mathematics Subject Classification: Primary: 92D30, 35K57; Secondary: 34B40.

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