Abstract:
The spread of the Human Immunodeficiency Virus (HIV) and the resulting Acquired Immune Deficiency
syndrome (AIDS) is a major health concern. Mathematical models are therefore commonly applied to understand the spread of
the HIV epidemic. In this study, HIV dynamics is analyzed using a Stochastic Discrete-Time Markov Chain Mathematical Model.
Demographic and epidemiological parameters that affect the model population dynamics were investigated. Well posedness of
the model determined and the conditions for the existence and stability of disease-free and endemic equilibrium points proved,
using the next generation matrix technique. The effect of various intervention strategies, were simulated by varying the parameters
representing the possible strategies and comparing the respective values of the reproductive ratio . The numerical simulation
results using intervention transition matrix showed that vertical transmission is the most sensitive parameter standing at 0.6
followed by the use of HAART at 0.4. This indicates the strategy which requires much effort to avert progression of infected individuals to AIDS
