A STOCHASTIC MODEL FOR HIV EPIDEMIC WITH
TREATMENT AND INFLOW OF INFECTIVES
Mozart Umba Nsuami1, Peter Joseph Witbooi2
1,2Department of Mathematics and Applied Mathematics
University of the Western Cape
Robert Sobukwe Rd, Bellville 7530, SOUTH AFRICA

Abstract

We present a stochastic model of the population dynamics of HIV/AIDS with treatment and inflow of infectives. Starting with a deterministic compartmental model, each of the four ordinary differential equations are stochastically perturbed. An invariant ${\cal R}_{\sigma}$ similar to the basic reproduction number of an ordinary differential equation system is introduced. Under conditions which permit the existence of a disease-free equilibrium point, we prove almost sure exponential stability of the disease-free equilibrium for ${\cal R}_{\sigma}<1$. We also investigate asymptotic behaviour of the solutions to the stochastic model around the endemic equilibrium of the underlying deterministic model. Our theoretical results are illustrated by simulations with parameters applicable to South Africa.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 31
Issue: 5
Year: 2018

DOI: 10.12732/ijam.v31i5.2

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