Extinction and positive recurrence of a regime-switching HIV/AIDS model with treatment and standard incidence

In this paper, we investigate the dynamics of a high-dimensional human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome (AIDS) model with treatment and standard incidence, which is perturbed by telegraph noise. The switching is formulated by a continuous time Markov chain. Firstly, we show the existence and uniqueness of the global positive solution. Then, conditions for extinction of the disease are established. Moreover, through constructing suitable Lyapunov functions, we derive sufficient conditions for the existence of positive recurrence of the solutions. Positive recurrence implies all the individuals can coexist and persist in the long term. Finally, numerical experiments are performed for supporting the theoretical results.