A reaction-diffusion system modeling direct and indirect transmission of diseases

W. E. Fitzgibbon; M. Langlais; J.J. Morgan

doi:10.3934/dcdsb.2004.4.893

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2004, Volume 4, Issue 4: 893-910. Doi: 10.3934/dcdsb.2004.4.893

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A reaction-diffusion system modeling direct and indirect transmission of diseases

1.
Department of Mathematics, University of Houston, Houston, Texas, 77204-3476
2.
UMR CNRS 5466, Mathématiques Appliquées de Bordeaux, case 26, Université Victor Segalen Bordeaux 2, 146, rue Léo Saignat, 33076 Bordeaux Cedex
3.
Department of Mathematics, University of Houston, Houston, Texas 77204

Received: November 30, 2002

Revised: May 31, 2004

Published: October 2004

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Abstract

We study the global existence and approximation of the solutions to a reaction diffusion system coupled with an ordinary differential equation modeling direct transmission between individuals and indirect transmission via a contaminated environment of an epidemic disease.

Keywords:

Reaction diffusion equations,
global existence.

Mathematics Subject Classification: 35K57, 35R05, 35B40, 92D30.

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