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Global properties of a class of virus infection models with multitarget cells. (English) Zbl 1254.92064
Summary: We propose a class of virus infection models with multitarget cells and study their global properties. We first study three models with specific forms of incidence rate functions, and then study a model with a more general nonlinear incidence rate. The basic model is a (2n+1)-dimensional nonlinear ODE that describes the population dynamics of the virus, n classes of uninfected target cells, and n classes of infected target cells. Models with exposed state and models with saturated infection rate are also studied. For these models, Lyapunov functions are constructed to establish the global asymptotic stability of the uninfected and infected steady states of these models. We have proven that if the basic reproduction number is less than unity then the uninfected steady state is globally asymptotically stable, and if the basic reproduction number is greater than unity then the infected steady state is globally asymptotically stable. For the model with general nonlinear incidence rate, we construct suitable Lyapunov functions and establish sufficient conditions for the global stability of the uninfected and infected steady states of this model.
MSC:
92C60Medical epidemiology
34D23Global stability of ODE
37N25Dynamical systems in biology
34D05Asymptotic stability of ODE
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