This article examines the transmission dynamics of HIV/AIDS with treatment effects. The total population ( ) was grouped into four compartments namely susceptible individuals at time t ( ), infected humans at time t ( ), individuals on treatment at time t ( ), and the AIDS carriers at time t ). A first order deterministic mathematical model for the case is formulated and analyzed to gain insight into the qualitative features of the local stability and disease free equilibrium which enable us to understand the transmission dynamics of the disease. The numerical simulation of the model was carried out to investigate the sensitivity of some threshold parameters on spread rate of the disease. We also investigated the impact of early detection of HIV cases and compliant behavior of patients on treatment. Our results from numerical simulation and early detection of HIV case/ compliant behavior of patients on treatment show that early detection of HIV case and compliant behavior of patients on treatment reduce spread of the disease and minimize rate at which people develop AIDS.
Keywords: HIV/AIDS, Modeling, Transmission dynamics, Treatment., mathematical assessment
