The Effect of Cross-Immunity in a Multi-Strain Epidemic Model - Pornpan Theprungsimankul; Supaporn Junsank; Aksarapak Abdulloh; Wirawan Chinviriyasit (Agriculture and Natural Resources, 2011)
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.