A model of HIV/AIDS transmission dynamics with treatment: The case of the DRC
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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 $R_0$ 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 $R_0 < 1$ and the endemic equilibrium (EE) is locally asymptotically stable if $R_0 > 1$. We also proved by means of the Lyapunov method that the disease-free equilibrium is globally asymptotically stable if $R_0 < 1$. 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).
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