Dynamics of a Stochastic HIV Infection Model with Logistic Growth and CTLs Immune Response under Regime Switching

Lin Hu () and Lin-Fei Nie
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Lin Hu: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
Lin-Fei Nie: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China

Mathematics, 2022, vol. 10, issue 19, 1-20

Abstract: Considering the influences of uncertain factors on the reproduction of virus in vivo, a stochastic HIV model with CTLs’ immune response and logistic growth was developed to research the dynamics of HIV, where uncertain factors are white noise and telegraph noise. which are described by Brownian motion and Markovian switching, respectively. We show, firstly, the existence of global positive solutions of this model. Further, by constructing suitable stochastic Lyapunov functions with regime switching, some sufficient conditions for the existence and uniqueness of the stationary distribution and the conditions for extinction are obtained. Finally, the main results are explained by some numerical examples. Theoretical analysis and numerical simulation show that low-intensity white noise can maintain the persistence of the virus, and high intensity white noise can make the virus extinct after a period of time with multi-states.

Keywords: HIV model; logistic growth; Brownian motion and Markovian switching; stationary distribution; extinction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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