Journal of Guangxi Normal University(Natural Science Edition) ›› 2023, Vol. 41 ›› Issue (2): 106-117.doi: 10.16088/j.issn.1001-6600.2022033102

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Stability of an HIV Immune Model with Saturation Incidence and Distributed Delays

SONG Bing, ZHANG Yuru, SANG Yuan, ZHANG Long*   

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi Xinjiang 830046, China
  • Received:2022-03-31 Revised:2022-05-20 Online:2023-03-25 Published:2023-04-25

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Abstract: A delayed HIV model of intracellular infection with saturated infection rate and antibody immune response is presented here. Including uninfected cells, latently infected cells, infected cells, free HIV virus, and CTLs. The following four delays are considered: latently infected delay, intracellular delay, the time lag between an infected cell and a virus, and CTL response delay. Two threshold conditions are defined: infection reproduction number R0 and CTL immunity-activated reproduction number R1. It obtains three equilibria of this model: disease-free equilibrium, immune-free infection equilibrium and immune-activated equilibrium. By analyzing the characteristic equation, Lyapunov function and LaSalle's invariance principle, the locally and globally asymptotic stable criteria of each equilibrium are established.

Key words: CTL immune response, distributed delay, globally asymptotically stable, Lyapunov function, saturated infection rate

CLC Number: 

  • O175
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