American Institute of Mathematical Sciences

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November  2004, 4(4): 1117-1128. doi: 10.3934/dcdsb.2004.4.1117

Fisher waves in an epidemic model

Xiao-Qiang Zhao 1, and  Wendi Wang 2,

1. 

Department of Mathematics and Statistics, Memorial University of Newfoundland, St. Johns, NF A1C 5S7, Canada
2. 

Department of Mathematics, Southwest Normal University, Chongqing, 400715

Received  January 2003 Revised  December 2003 Published  August 2004

The existence of Fisher type monotone traveling waves and the minimal wave speed are established for a reaction-diffusion system modeling man-environment-man epidemics via the method of upper and lower solutions as applied to a reduced second order ordinary differential equation with infinite time delay.
Keywords: monotone iterations., traveling waves, Epidemic model, upper and lower solutions.
Mathematics Subject Classification: 35K57, 92D3.
Citation: Xiao-Qiang Zhao, Wendi Wang. Fisher waves in an epidemic model. Discrete and Continuous Dynamical Systems - B, 2004, 4 (4) : 1117-1128. doi: 10.3934/dcdsb.2004.4.1117
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