Abstract
Nutrition and household per capita income are important determinants in the HIV transmission. In this research, three mathematical models for HIV transmission dynamics with a focus on modelling the impact of supplementary feeding and per capita income were developed and analysed. Using the next-generation matrix technique, the reproduction numbers were calculated. Numerical simulations and sensitivity analysis for each of the models were carried out to support the analyti-cal results and to determine the parameters influencing the dynamics of the disease in each respective model. Analytical results of the first model showed two equi-librium points namely: the disease-free and endemic equilibria. The disease-free and endemic equilibria are asymptotically stable when the reproduction number is smaller than 1 and more than 1 respectively. Each of the other two models has four equilibrium states. These are disease-free, disease and per capita income free, per capita income free and endemic equilibria. It was shown that the disease-free equilibria are asymptotically stable when the per capita income reproduction num-ber is less than 1. The endemic equilibria are stable when the per capita income reproduction number is greater than 1. The simulations highlighted that both sup-plementary feeding and per capita income are crucial in the management of HIV. The relationship between HIV and poverty in Malawi is also established. It was shown that there is a positive relationship between HIV and poverty in Malawi.
Ph.D. (Applied Mathematics)