American Institute of Mathematical Sciences

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May  2005, 5(2): 175-188. doi: 10.3934/dcdsb.2005.5.175

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, United States
2. 

Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, United States

Received  September 2003 Revised  August 2004 Published  February 2005

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.
Keywords: competitive exclusion., Epidemic models, cross immunity.
Mathematics Subject Classification: 34D05, 34D23, 92D3.
Citation: Azmy S. Ackleh, Linda J. S. Allen. Competitive exclusion in SIS and SIR epidemic models with total cross immunity and density-dependent host mortality. Discrete & Continuous Dynamical Systems - B, 2005, 5 (2) : 175-188. doi: 10.3934/dcdsb.2005.5.175
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