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Stability analysis of an influenza virus model with disease resistance. (English) Zbl 1339.34056
Summary: We study a new model describing the transmission of influenza virus with disease resistance. Mathematical analysis shows that dynamics of the spread is determined by the basic reproduction number $$R_{0}$$. If $$R_{0}\leq 1$$, the disease free equilibrium is globally asymptotically stable, and if $$R_{0} > 1$$, 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 illustrate the analytical results. Some effective strategies for eliminating the virus are suggested.

##### MSC:
 34C60 Qualitative investigation and simulation of ordinary differential equation models 34D23 Global stability of solutions to ordinary differential equations 92D30 Epidemiology 92C60 Medical epidemiology 34D05 Asymptotic properties of solutions to ordinary differential equations 34C23 Bifurcation theory for ordinary differential equations
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