Authors: Symon Bilesi Chibaya; Farai Nyabadza
Addresses: Department of Mathematics and Applied Mathematics, University of Johannesburg, Johannesburg, South Africa; Applied Studies Department, Malawi University of Science and Technology, Thyolo, Malawi ' Department of Mathematics and Applied Mathematics, University of Johannesburg, Johannesburg, South Africa
Abstract: Poverty continues to impact people living with HIV/AIDS negatively and it drives HIV/AIDS epidemics mostly in poor resource countries such as Malawi. In this paper, a mathematical model for HIV/AIDS that provides linkages between HIV/AIDS and poverty is formulated and analysed using nonlinear ordinary differential equations. The theoretical evaluations identified four equilibria namely; an equilibrium in which there is no disease and per capita income is zero, disease-free, an equilibrium in which per capita income is zero and endemic. An epidemic threshold value, RM, called the reproduction number is determined using the next-generation matrix method. The analysis of the model shows that the disease-free and endemic equilibria are globally stable for RM < 1 and RM > 1 respectively. Sensitivity analysis of RM is performed in order to determine how the parameters affect the dynamics of HIV/AIDS epidemics. Numerical simulations are done to show the role of some key model parameters on HIV/AIDS as well as to verify some analytical results. The results of the model suggest that income has the propensity to control the spread of HIV/AIDS because it has the capacity of decreasing unemployed people's vulnerability to sexually transmitted diseases such as HIV/AIDS.
Keywords: reproduction number; equilibria; HIV/AIDS; poverty; simulation.
International Journal of Mathematical Modelling and Numerical Optimisation, 2021 Vol.11 No.2, pp.168 - 195
Received: 02 Mar 2020
Accepted: 20 May 2020
Published online: 10 Feb 2021 *