Global analysis of multi-strains SIS, SIR and MSIR epidemic models

We consider SIS, SIR and MSIR models with standard mass action and varying population, with n different pathogen strains of an infectious disease. We also consider the same models with vertical transmission. We prove that under generic conditions a competitive exclusion principle holds. To each stra...

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Bibliographic Details
Published in:Journal of applied mathematics & computing 2014-02, Vol.44 (1-2), p.273-292
Main Authors: Bichara, D., Iggidr, A., Sallet, G.
Format: Article
Language:English
Subjects:
Applied mathematics
Computational Mathematics and Numerical Analysis
Dynamical Systems
Epidemiology
Equilibrium
Human health and pathology
Infectious diseases
Life Sciences
Mathematical analysis
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Original Research
Pathogens
Population
Santé publique et épidémiologie
Studies
Theory of Computation
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Summary:We consider SIS, SIR and MSIR models with standard mass action and varying population, with n different pathogen strains of an infectious disease. We also consider the same models with vertical transmission. We prove that under generic conditions a competitive exclusion principle holds. To each strain a basic reproduction ratio can be associated. It corresponds to the case where only this strain exists. The basic reproduction ratio of the complete system is the maximum of each individual basic reproduction ratio. Actually we also define an equivalent threshold for each strain. The winner of the competition is the strain with the maximum threshold. It turns out that this strain is the most virulent, i.e., this is the strain for which the endemic equilibrium gives the minimum population for the susceptible host population. This can be interpreted as a pessimization principle.
ISSN:1598-5865
1865-2085
1865-2085
DOI:10.1007/s12190-013-0693-x