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

Pages: 3303 - 3324, Volume 32, Issue 9, September 2012

doi:10.3934/dcds.2012.32.3303       Abstract        References        Full Text (471.0K)       Related Articles

Xiang-Sheng Wang - 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, Canada (email)
Haiyan Wang - Division of Mathematical and Natural Sciences, Arizona State University, Phoenix, AZ 85069-7100, United States (email)
Jianhong Wu - 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, Canada (email)

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.

Keywords:  Traveling waves, SIR model, Schauder fixed point theorem, Laplace transform.
Mathematics Subject Classification:  Primary: 92D30, 35K57; Secondary: 34B40.

Received: January 2012;      Revised: March 2012;      Published: April 2012.

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