Abstract
In this paper, we analyze a higher-order stochastically perturbed multigroup staged-progression model for the transmission of HIV with saturated incidence rate. We obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system by establishing a suitable stochastic Lyapunov function. In addition, we make up adequate conditions for complete eradication and wiping out the infectious disease. In a biological interpretation, the existence of a stationary distribution implies that the disease will prevail and persist in the long term. Finally, examples and numerical simulations are introduced to validate our theoretical results.
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