A Thesis On Mathematical Modeling Of Hiv/Aids Transmission From Mother To Children With Treatment.

Abstract

In this research work we developed a mathematical model which describes the dy namic transmission of HIV/AIDS from mother to children with treatment. A non linear deterministic mathematical model for the problem is proposed and analyzed qualitatively using the stability theory of differential equations. Local stability of the disease free equilibrium point of the model was established using next gener ation method. The results show that the disease free equilibrium point is locally asymptotically stable when the threshold parameter is less than unity and unstable at threshold parameter greater than unity. Globally, the disease free equilibrium point is not stable due to existence of forward bifurcation at threshold parameter equal to unity. The endemic equilibrium point is locally asymptotically stable when the threshold parameter is greater than unity, unstable at threshold parameter less than unity and globally asymptotically stable under certain conditions. However, it is shown that using treatment measures (ARVs) and control of the rate of vertical transmission have the effect of reducing the transmission of the disease significantly. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the spread of the disease.