Competitive exclusion in SIS and SIR epidemic models with total cross immunity  and density-dependent host mortality

Azmy S. Ackleh; Linda J. S. Allen

doi:10.3934/dcdsb.2005.5.175

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2005, Volume 5, Issue 2: 175-188. Doi: 10.3934/dcdsb.2005.5.175

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Competitive exclusion in SIS and SIR epidemic models with total cross immunity and density-dependent host mortality

Azmy S. Ackleh^1, and
Linda J. S. Allen^2,

1.
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010
2.
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042

Received: August 31, 2003

Revised: July 31, 2004

Published: April 2008

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Abstract

We study SIR and SIS epidemic models with multiple pathogen strains. In our models we assume total cross immunity, standard incidence, and density-dependent host mortality. We derive conditions on the models parameters which guarantee competitive exclusion between the n strains. An example is given to show that if these conditions are not satisfied then coexistence between the strains is possible. Furthermore, numerical results are presented to indicate that our conditions on the parameters are sufficient but not necessary for competitive exclusion.

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Mathematics Subject Classification: 34D05, 34D23, 92D30.

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