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Abstract
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It is well known that the mathematical biology and dynamical systems give very important information for the study and research of viral infection models such as HIV, HBV, HCV, Ebola and Influenza. This paper deals with the global dynamics of generalized virus model with logistic growth rate for target cells, general incidence rate and cellular immunity. The results will be obtained by using Lyapunov's second method and LaSalle's invariance principle. We prove the global stability of the rest points of the system by the value of basic reproduction number $(\mathbf{R_0})$ and the immune response reproduction number $(\mathbf{R_{CTL}})$. We have found that if $\mathbf{R_0}<1$, then the infection-free equilibrium is globally asymptotically stable. For $\mathbf{R_0}>1$ and $\mathbf{R_{CTL}}<1$, under certain conditions on incidence rate function, immune-free equilibrium is globally asymptotically stable. Finally, we prove that if $\mathbf{R_0}>1$ and $\mathbf{R_{CTL}}>1$, then under certain conditions on incidence rate function the endemic equilibrium is globally asymptotically stable.
Since the logistic growth rate for target cells and general incidence rate have been included in this manuscript, our obtained results are the generalization of those in the previous literatues. Moreover, the results have been obtained with weaker assumptions in comparison with the previous ones.
Numerical simulations are presented to support and illustrate our analytical results.
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