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Global stability analysis and permanence for an HIV-1 dynamics model with distributed delays
Yongqi Liu,Qigui Yang
Keywords:Global stability analysis, Beddington-DeAngelis functional response, Distributed intracellular delays, uniformly persistent
      This paper investigates the global asymptotic stability of an HIV dynamics model with two distributed intracellular delays incorporating Beddington-DeAngelis functional response infection rate. An eclipse stage of infected cells (i.e. latently infected cells), not yet producing virus, is included in our models. It is proven that if the basic reproduction number R0 is less than unity, then the disease-free equilibrium is globally asymptotically stable, and if R0 is greater than unity, then the infected equilibrium is globally asymptotically stable. The authors also obtain that the disease is always present when R0 is greater than unity by using a permanence theorem for infinite dimensional systems. What is more, an n-stage-structured HIV model is developed and analyzed. The authors also prove the global asymptotical stabilities of two equilibria by constructing suitable Lyapunov functionals.