A two-strain epidemic model with uncertainty in the interaction

Mick Roberts

Abstract


Annual epidemics of influenza A typically involve two subtypes, with a degree of cross-immunity. We present a model of an epidemic of two interacting viruses, where the degree of cross-immunity may be unknown. We treat the unknown as a second independent variable, and expand the dependent variables in orthogonal functions of this variable. The resulting set of differential equations is solved numerically. We show that if the population is initially more susceptible to one variant, if that variant invades earlier, or if it has a higher basic reproduction number than the other variant, then its dynamics are largely unaffected by cross-immunity. In contrast, the dynamics of the other variant may be considerably restricted.

doi:10.1017/S1446181112000326

Keywords


epidemics, influenza, SIR model, immunity



DOI: http://dx.doi.org/10.21914/anziamj.v54i0.5882



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.