A stochastic delay model of HIV pathogenesis with reactivation of latent reservoirs

• Published in: Chaos, solitons and fractals solitons and fractals, 2020-03, Vol.132, p.109594, Article 109594
• Main Authors: Qesmi, Redouane, Hammoumi, Aayah
• Format: Article
• Language: English
• Subjects: Delay; Differential equation; HIV; In-host; Latency; Stochastic; Therapy
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2019.109594

•We developed a stochastic HIV model that includes latent reservoir.•We performed stochastic analysis and simulations of the model.•We considered Pharmacokinetic effects of taking different drug therapies.•Locking in latency therapy cannot eradicate the latent reservoir.•Lytic Therapy combined with drugs treatment  may eradicate the virus. In this paper, we propose a stochastic HIV model with latency to describe the factors that are responsible for extinction and persistence of the infection. This model incorporates latent period of reservoirs that inhibits the eradication of the virus. It is shown that this model leads naturally to a stochastic system of differential delay equations. We derived the global existence, positivity and boundedness properties of solutions of the proposed stochastic system. Analyzing the model, sufficient conditions for the eradication and the persistence of the disease are also obtained. Furthermore, numerical simulations are performed to study the impact of several strategies of drug therapy on the persistence and the extinction of HIV virus. Our results constitute an important step towards control strategies to reduce HIV infection.