Dynamics of Two-Strain Influenza with Isolation and Partial Cross-Immunity
Department of Biostatistics, Harvard University
(May 25, 2004 3:30 PM - 4:30 PM)
The time evolution of influenza A virus is linked to a non-fixed landscape driven by tight co-evolutionary interactions between hosts and competing influenza strains. Herd-immunity, cross-immunity and age-structure are among the factors that have been shown to support strain coexistence and/or disease oscillations. In this study, we put two influenza strains under various levels of (interference) competition. We establish that cross-immunity and host isolation lead to periodic epidemic outbreaks (sustained oscillations) in this multi-strain system. We compute the basic reproductive number for each strain independently, as well as for the full system and show that when the basic reproductive number of both strains is less than 1, the disease dies out. Sub-threshold coexistence driven by cross-immunity is possible even when the basic reproductive number of one strain is below one. Conditions that guarantee a winning type or coexistence are established in general. Oscillatory coexistence is established via Hopf-bifurcation theory and numerical simulations using realistic parameter values.