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Robust uniform persistence and competitive exclusion in a nonautonomous multi-strain SIR epidemic model with disease-induced mortality.
MedLine Citation:
PMID:  23277451     Owner:  NLM     Status:  Publisher    
Abstract/OtherAbstract:
A nonautonomous version of the SIR epidemic model in Ackleh and Allen (2003) is considered, for competition of [Formula: see text] infection strains in a host population. The model assumes total cross immunity, mass action incidence, density-dependent host mortality and disease-induced mortality. Sufficient conditions for the robust uniform persistence of the total population, as well as of the susceptible and infected subpopulations, are given. The first two forms of persistence depend entirely on the rate at which the population grows from the extinction state, respectively the rate at which the disease is vertically transmitted to offspring. We also discuss the competitive exclusion among the [Formula: see text] infection strains, namely when a single infection strain survives and all the others go extinct. Numerical simulations are also presented, to account for the situations not covered by the analytical results. These simulations suggest that the nonautonomous nature of the model combined with the disease induced mortality allow for many strains to coexist. The theoretical approach developed here is general enough to apply to other nonautonomous epidemic models.
Authors:
Azmy S Ackleh; Paul L Salceanu
Publication Detail:
Type:  JOURNAL ARTICLE     Date:  2013-1-1
Journal Detail:
Title:  Journal of mathematical biology     Volume:  -     ISSN:  1432-1416     ISO Abbreviation:  J Math Biol     Publication Date:  2013 Jan 
Date Detail:
Created Date:  2013-1-1     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  7502105     Medline TA:  J Math Biol     Country:  -    
Other Details:
Languages:  ENG     Pagination:  -     Citation Subset:  -    
Affiliation:
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, 70504-1010, USA, ackleh@louisiana.edu.
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