Exploring the linkages between HIV/AIDS and poverty: insights through a mathematical model

摘要

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, R_(M) , 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 R_(M) < 1 and R_(M) > 1 respectively. Sensitivity analysis of R_(M) 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.