Dynamic analysis of an HIV model with CTL immune response and logarithmic Ornstein–Uhlenbeck process

Qiuyue Dong, Yan Wang and Daqing Jiang

Chaos, Solitons & Fractals, 2025, vol. 191, issue C

Abstract: In this paper, we present a stochastic HIV model, including logistic growth, CTL immune response and logarithmic mean–reverting Ornstein–Uhlenbeck process. Firstly, we certify that there exists a unique global positive solution by rigorous mathematical analysis. Then, by constructing a suitable Lyapunov function and using the strong law of large numbers and Fatou’s lemma, we obtain the existence of the stationary distribution when stochastic reproduction number is greater than one. Moreover, we derive an approximate expression for the probability density function of the stochastic model around the infected equilibrium of its corresponding deterministic model. In addition, a critical condition for virus extinction is established. Finally, through numerical simulations, we investigate the effects of noise intensity and the logistic growth on model behavior, and we also explore the influence of key parameters on virus persistence and extinction.

Keywords: Stochastic differential equation; CTL immune response; Ornstein–Uhlenbeck process; Stationary distribution; Probability density function (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:191:y:2025:i:c:s0960077924013419

DOI: 10.1016/j.chaos.2024.115789

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