Abstract

This research presents a Mathematical Modelling and the Transmission Dynamic of HIV/AIDS with Exposed and Death compartments. The model is governed by a system of four ordinary differential equations namely: Susceptible (S), Exposed (E), Infected () I and Removal or Death (𝑅). An analysis was performed on the model to determine the disease-free equilibrium, endemic equilibrium, reproduction number, local stability, and global stability. The results of the analysis indicate that the disease-free equilibrium equation is locally asymptotically stable if the reproduction number is less than one, and unstable if the reproduction number is greater than one. The system has achieved the condition of being globally asymptotically. We have conducted numerical simulations of the model, and the results show that the susceptible population if they maintain their safe sex life will be removed from the population without being infected with the disease. Exposed at the beginning was very high but due to awareness and the danger of HIV/ AIDS people started to maintain a safe sex life which resulted in a total decline of the disease. Still, they cannot return to their origin because of no cure for the disease. The infected continue moving higher due to unsafe sex life and decline a little because of the safe sex life and precaution. The removal or death gave us almost a straight line because if all the infected people can die the disease will go to extinction.