Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Fisher waves in an epidemic model

Pages: 1117 - 1128, Volume 4, Issue 4, November 2004      doi:10.3934/dcdsb.2004.4.1117

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Xiao-Qiang Zhao - Department of Mathematics and Statistics, Memorial University of Newfoundland, St. Johns, NF A1C 5S7, Canada (email)
Wendi Wang - Department of Mathematics, Southwest Normal University, Chongqing, 400715, China (email)

Abstract: 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:  Epidemic model, traveling waves, upper and lower solutions, monotone iterations.
Mathematics Subject Classification:  35K57, 92D30.

Received: January 2003;      Revised: December 2003;      Available Online: August 2004.