A model of HIV or AIDS transmission dynamics with treatment the case of the DRC

Abstract

In this paper, we propose a novel HIV/AIDS epidemic treatment model to reduce the number of HIV cases. We divide infected individuals into four compartments, that is, a compartment of infected individuals who are unaware of their HIV status and do not show any symptoms, a compartment of infected individuals who are aware of their status but do not show any symptoms, infected individuals in the asymptomatic compartment and a treatment compartment that receives infected individuals who are aware of their status, whether they are sick or not. The basic reproduction number R0 for the proposed model is computed using the next generation matrix (NGM). Using a corollary of Gershgorin’s circle theorem, the results show that the disease-free equilibrium (DFE) is locally asymptotically stable (LAS) if R0 < 1 and the endemic equilibrium (EE) is locally asymptotically stable if R0 > 1. We also proved by means of the Lyapunov method that the disease-free equilibrium is globally asymptotically stable if R0 < 1. Finally, numerical simulations of the model are conducted to support the theoretical results and also to investigate the sensitivity of certain parameters using HIV/AIDS data from the Democratic Republic of the Congo (DRC).