Dynamics of Two-Strain Influenza with Isolation and Partial Cross-Immunity
Abstract
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 ($\Re_i$) independently, as well as for the full system ($\Re_q$), and show that when $\Re_q < 1$, 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.
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SIAM Journal on Applied Mathematics
Pages: 964 - 982
ISSN (online): 1095-712X
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Copyright © 2005 Society for Industrial and Applied Mathematics.
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Published online: 31 July 2006
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