Dynamics of a type HIV-1 infection model with cell-to-cell transmission and immune impairment
Based on the two mechanisms of virus-to-cell infection and cell-to-cell transmissions,a dynamic model of HIV-1 infection with the intracellular delay,CTL immune response and immune impairment is studied.The basic reproduction ratio of virus infection is calculated.By analyzing the distribution of roots of the corresponding characteristic equations,the local stability of the infection-free and chronic-infection equilibria of the model is discussed.By constructing appropriate Lyapunov functionals and using LaSalle's invariance principle,it is proved that the global dynamics of the model can be completely determined by the basic reproduction ratio of virus infection:if the basic reproduction ratio of virus infection is less than unity,the infection-free equilibrium is globally asymptotically stable;If the basic reproduction ratio of virus infection is greater than unity,the chronic-infection equilibrium is globally asymptotically stable.Furthermore,numerical simulations are carried out to illustrate the theoretical results,the sensitivity analysis is performed to determined the the degree of influence of the basic reproduction ratio of virus infection on parameters.
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