Open AccessGlobal stability for a class of HIV virus-to-cell dynamical model with Beddington-DeAngelis functional response and distributed time delay
Author(s) -
Xin Zhou,
Long Zhang,
Tao Zheng,
Hongli Li,
Zhidong Teng
Publication year - 2020
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2020250
Subject(s) - stability (learning theory) , human immunodeficiency virus (hiv) , class (philosophy) , functional response , control theory (sociology) , computer science , mathematics , virology , biology , artificial intelligence , ecology , control (management) , machine learning , predation , predator
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 R 0 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 R 0 ≤ 1 the infection-free equilibrium is globally asymptotically stable, while if R 0 > 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.