American Institute of Mathematical Sciences

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March  2007, 7(2): 251-273. doi: 10.3934/dcdsb.2007.7.251

Travelling wave solutions for a scalar age-structured equation

A. Ducrot 1,

1. 

UMR CNRS 5466 & INRIA Futurs Anubis, case 26, Université Victor Segalen Bordeaux 2, 146, rue Léo Saignat, F 33076 Bordeaux Cedex, France

Received  May 2006 Revised  November 2006 Published  December 2006

This paper is devoted to the study of travelling wave solutions for a simple epidemic model. This model consists in a single scalar equation with age-dependence and spatial structure. We prove the existence of travelling waves for a continuum of admissible wave speeds as well as some qualitative properties, like exponential decay and monotonicity with respect to the direction of front's propagation. Our proofs extensively use the comparison principle that allows us to construct suitable sub and super-solutions or to use the classical sliding method to obtain qualitative properties of the wave front.
Keywords: SI epidemic model- age-dependence- spatial structure-travelling waves..
Mathematics Subject Classification: Primary: 35K60, 92D30; Secondary: 35B50, 37N2.
Citation: A. Ducrot. Travelling wave solutions for a scalar age-structured equation. Discrete and Continuous Dynamical Systems - B, 2007, 7 (2) : 251-273. doi: 10.3934/dcdsb.2007.7.251
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