| In this paper, based on the basic process of viral infection and previous knowledge about the virus dynamics, we establish a mathematical model of viral infection with the general incidence rate and a latent delay. Then we study its dynamical behavior.The first chapter introduces the development of viral dynamics and some relevant theoretical knowledge.In recent years, depending on the actual background, a considerable number of pa-pers are committed to changing the incidence of virus functions to improve the basic models, including bilinear incidence, standardized incidence, Holling Ⅰ/Ⅱ incidence rate and so on. The second chapter will combine these incidences to create a model with general incidence of the virus and contains a recovery rate. The dynamic behavior of the model is completely determined by the basic reproduction number Ro by analysis. When R0≤1, by means of Lyapunov function and Lasalle invariant principle, we established the global stability of the disease-free equilibrium. When R0>1, there exist the unique infection equilibrium, using the Poincare-Bendixson property for three dimensional com-petitive systems, we obtained the global stability of the infection equilibrium.In the third chapter, we introduce a time delay from susceptible cells been infected to a free virus released, and we construct a virus dynamical model with general incidence and intercellular delay. As the same, the dynamics behavior of this model is determined by the basic reproduction number R1. Lyapunov functions are constructed and LaSalle invariance principle for delay differential equation, we have the result: When R1≤ 1, infection-free equilibrium is global asymptotically stable; When R1>1, infection equilibrium is global asymptotically stable.In the last chapter, we make a brief review of the above conclusion, and present the epidemic dynamic point of view and practical meaning for these models. And we analyze some shortcomings of this paper and point out some questions and future work. |
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