Qualitative analysis and travelling wave solutions for the SI model with vertical transmission

Arnaud Ducrot; Michel Langlais; Pierre Magal

doi:10.3934/cpaa.2012.11.97

Article Contents

2012, Volume 11, Issue 1: 97-113. Doi: 10.3934/cpaa.2012.11.97

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Qualitative analysis and travelling wave solutions for the SI model with vertical transmission

1.
UMR CNRS 5251, I.M.B. and INRIA Bordeaux Sud-ouest Anubis, case 36, UFR Sciences et Modélisation, Université Victor Segalen Bordeaux 2, 3 ter, place de la Victoire - 33076 Bordeaux cedex
2.
Institut de Mathématiques de Bordeaux, UMR CNRS 5251, INRIA Bordeaux sud-ouest, EPI Anubis, UFR Sciences de la Vie, Université Victor Segalen Bordeaux 2, 3 ter Place de la Victoire, 33076 Bordeaux

Received: January 2010

Revised: August 2010

Published: January 2012

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Abstract

In this note we analyze a spatially structured SI epidemic model with vertical transmission, a logistic effect on vital dynamics and a density dependent incidence. For a bounded spatial domain we show global stability of the endemic state when it is feasible. Then we look at the existence of travelling wave solutions connecting the endemic and the disease free states.

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Mathematics Subject Classification: Primary: 35A18, 35B35, 35B40, 35K57; Secondary: 92D30.

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