A stochastic HIV model based on population mobility

This paper established a stochastic HIV model that incorporates population mobility to analyze the role of stochastic noise in HIV dynamics. First, the existence and uniqueness of a globally positive solution for the stochastic system were proven, and sufficient conditions for the stochastic extinction of the disease were derived. Second, by constructing a Lyapunov function, it was demonstrated that the stochastic system possesses a unique ergodic stationary distribution when $\widehat{R_0^s}>1$. Finally, theoretical findings were illustrated through numerical simulations. From an epidemiological perspective, our study reveals that an increased response to infection risks and higher white noise intensity appear advantageous for limiting HIV transmission.