Article

Stochastic dynamics of an HIV/AIDS epidemic model with treatment

Published in: Quaestiones Mathematicae
Volume 42, issue 5, 2019 , pages: 605–621
DOI: 10.2989/16073606.2018.1478908
Author(s): Mozart U. NsuamiDepartment of Mathematics and Applied Mathematics, South Africa, Peter J. WitbooiDepartment of Mathematics and Applied Mathematics, South Africa

Abstract

We investigate a stochastic HIV/AIDS epidemic model with treatment. The model allows for two stages of infection namely the asymptomatic phase and the symptomatic phase. We prove existence of global positive solutions. We show that the solutions are stochastically ultimately bounded and stochastically permanent. We also study asymptotic behaviour of the solution to the stochastic model around the disease-free equilibrium of the underlying deterministic model. Our theoretical results are illustrated by way of numerical simulations.

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