Stability analysis of an influenza virus model with disease resistance

We study a new model describing the transmission of influenza virus with disease resistance in human. Mathematical analysis shows that dynamics of the spread is determined by the basic reproduction number R0. If R0 ≤ 1, the disease free equilibrium is globally asymptotically stable, and if R0 > 1, the endemic equilibrium is globally asymptotically stable under some conditions. The change of stability of equilibria is explained by transcritical bifurcation. Lyapunov functional method and geometric approach are used for proving the global stability of equilibria. A numerical investigation is carried out to confirm the analytical results. Some effective strategies for eliminating virus are suggested.