The effect of cross-immunity in a multi-strain epidemic model
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Author list: Theprungsimankul P., Junsank S., Abdulloh A., Chinviriyasit W.
Publication year: 2011
Journal: Kasetsart Journal - Natural Science (0075-5192)
Volume number: 45
Issue number: 3
Start page: 563
End page: 570
Number of pages: 8
ISSN: 0075-5192
Languages: English-Great Britain (EN-GB)
Abstract
A multi-strain SIR (susceptible-infected-recovered) epidemiological model was studied and rigorously analyzed. A new parameter called cross-immunity among strains played a key role in the dynamic behavior of the model. The model had a local, asymptotically stable, disease-free equilibrium (DFE) whenever the maximum of the associated reproduction numbers of the two strains (denoted by R 0) was less than unity. It was shown that the model could have infinitely many co-existence equilibria if infection with one strain conferred complete cross-immunity against the other strain and the associated reproduction number of each strain exceeded unity. On the other hand, if infection with one strain conferred partial cross-immunity against the other strain, disease elimination, competitive exclusion or co-existence of the two strains could occur.
Keywords
Cross-immunity, Multi-strain sir model
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