Dynamics of two-strain influenza with isolation and partial cross-immunity

The time evolution of the influenza A virus is linked to a nonfixed landscape driven by 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 multistrain system. We compute the isolation reproductive number for each strain (R-i) independently, as well as for the full system (R-q), and show that when R-q < 1, both strains die out. Subthreshold coexistence driven by cross-immunity is possible even when the isolation reproductive number of one strain is below 1. Conditions that guarantee a winning type or coexistence are established in general. Oscillatory coexistence is established via Hopf bifurcation theory and confirmed via numerical simulations.