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

บทคัดย่อ

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.