The Effect of Cross-Immunity in a Multi-Strain Epidemic Model

Authors

  • Pornpan Theprungsimankul Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand.
  • Supaporn Junsank Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand.
  • Aksarapak Abdulloh Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand.
  • Wirawan Chinviriyasit Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand.

Keywords:

multi-strain SIR model, cross-immunity, stability

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 R0) 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.

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Published

2011-06-30

How to Cite

Pornpan Theprungsimankul, Supaporn Junsank, Aksarapak Abdulloh, and Wirawan Chinviriyasit. 2011. “The Effect of Cross-Immunity in a Multi-Strain Epidemic Model”. Agriculture and Natural Resources 45 (3). Bangkok, Thailand:563-70. https://li01.tci-thaijo.org/index.php/anres/article/view/245333.

Issue

Vol. 45 No. 3 (2011): May-June

Section

Research Article

License

online 2452-316X print 2468-1458/Copyright © 2022. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/),
production and hosting by Kasetsart University of Research and Development Institute on behalf of Kasetsart University.