A stochastic SICA model for HIV/AIDS transmission. (December 2022)

• Record Type: Journal Article
• Authors: Tan, Yiping; Cai, Yongli; Sun, Xiaodan; Wang, Kai; Yao, Ruoxia; Wang, Weiming; Peng, Zhihang
• Is Part Of: Chaos, solitons and fractals. Volume 165:Part 1(2022)
• Publication Date: 2022-12
• Subjects: Stochastic SICA model -- HIV/AIDS transmission -- White noise -- Extinction -- Stationary distribution; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.112768
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: In this paper, we present a stochastic HIV/AIDS model with standard incidence rate to investigate the impact of random fluctuations on the HIV viral dynamics. Firstly, the sufficient conditions for the stochastic extinction of the disease are obtained. Secondly, after defining the threshold parameter R s, we prove that the model has a unique ergodic stationary distribution when R s > 1, which reveals that the disease will persist almost surely. Subsequently, we give the exact expression of the probability density function around a quasi-equilibrium point by applying four-dimensional Fokker–Planck equation. Finally, through the numerical simulations of several examples, we not only verify the correctness of the theoretical results, but also explore how the disease goes for the case of not giving clear results theoretically. Epidemiologically, we find that increasing the noise intensities may be conducive to control the spread of the HIV. Highlights: A stochastic SICA model for HIV/AIDS transmission is developed. The sufficient conditions for the stochastic extinction of the disease is established. The existence of a unique ergodic stationary distribution of the model is displayed. The probability density function of the stationary distribution is given. The noise intensity may be conducive to control the spread of the HIV.