Existence of traveling wave solutions for a nonlocal reaction-diffusionmodel of influenza a drift

Joaquin Riviera; Yi Li

doi:10.3934/dcdsb.2010.13.157

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2010, Volume 13, Issue 1: 157-174. Doi: 10.3934/dcdsb.2010.13.157

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Existence of traveling wave solutions for a nonlocal reaction-diffusion model of influenza a drift

Joaquin Riviera^1, and
Yi Li^2,

1.
Department of Mathematics, Colgate University, Hamilton, NY 13346
2.
Department of Mathematics, The University of Iowa, Iowa City, IA 52242

Received: November 2008

Revised: July 2009

Published: July 2010

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Abstract

In this paper we discuss the existence of traveling wave solutions for a nonlocal reaction-diffusion model of Influenza A proposed in Lin et. al. (2003). The proof for the existence of the traveling wave takes advantage of the different time scales between the evolution of the disease and the progress of the disease in the population. Under this framework we are able to use the techniques from geometric singular perturbation theory to prove the existence of the traveling wave.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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