DYNAMICS OF A STOCHASTIC HIV/AIDS MODEL WITH TREATMENT UNDER REGIME SWITCHING

This paper focuses on the spread dynamics of an HIV/AIDS model with multiple stages of infection and treatment, which is disturbed by both white noise and telegraph noise. Switching between different environmental states is governed by Markov chain. Firstly, we prove the existence and uniqueness of the global positive solution. Then we investigate the existence of a unique ergodic stationary distribution by constructing suitable Lyapunov functions with regime switching. Furthermore, sufficient conditions for extinction of the disease are derived. The conditions presented for the existence of stationary distribution improve and generalize the previous results. Finally, numerical examples are given to illustrate our theoretical results.

Automated summary

This paper focuses on the spread dynamics of an HIV/AIDS model with multiple stages of infection and treatment, disturbed by white noise and telegraph noise, and governed by Markov chain for switching between different environmental states. It proves the existence and uniqueness of the global positive solution, investigates the existence of a unique ergodic stationary distribution, and derives sufficient conditions for disease extinction. The conditions for the existence of stationary distribution improve and generalize previous results, and numerical examples are provided to illustrate the theoretical findings.