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

doi:10.3934/mbe.2020250

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 4527-4543. doi: 10.3934/mbe.2020250

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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

College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China

Received: 03 March 2020 Accepted: 16 June 2020 Published: 29 June 2020

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.
- distributed delay,
- principle reproduction number,
- Beddington-DeAngelis functional response,
- Lyapunov functional,
- globally asymptotical stability
Citation: Xinran Zhou, Long Zhang, Tao Zheng, Hong-li Li, Zhidong Teng. Global stability for a class of HIV virus-to-cell dynamical model with Beddington-DeAngelis functional response and distributed time delay[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 4527-4543. doi: 10.3934/mbe.2020250

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Abstract

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.

References

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