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Global stability for a class of HIV virus-to-cell dynamical model with Beddington-DeAngelis functional response and distributed time delay

Xinran Zhou Long Zhang Tao Zheng Hong-li Li Zhidong Teng

*Corresponding author: Long Zhang longzhang_xj@sohu.com

MBE2020,5,4527doi:10.3934/mbe.2020250

A HIV virus-to-cell dynamical model with distributed delay and Beddington-DeAngelis functional response is proposed in this paper. Using the characteristic equations and analytical means, the principle reproduction number R0 on the local stability of infection-free and chronic-infection equilibria is established. Furthermore, by constructing suitable Lyapunov functionals and using LaSalle invariance principle, we show that if R0 ≤ 1 the infection-free equilibrium is globally asymptotically stable, while if R0 > 1 the chronic-infection equilibrium is globally asymptotically stable. Numerical simulations are presented to illustrate the theoretical results. Comparing the effects between discrete and distributed delays on the stability of HIV virus-to-cell dynamical models, we can see that they could be same and different even opposite.

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