Mathematical Modeling the Dynamics of HIV/AIDS with Treatment and Vertical Transmission
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Date
2024-08
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Addis Ababa University
Abstract
A non linear Mathematical model is proposed the dynamics of HIV/AIDS with treatment and vertical transmission in order to decrease mother to child transmission. The equilibrium points of the model are found and the stability analyses of the model around those equilibrium points are conducted.
The stability analysis on the model shows that the disease free equilibrium point 𝐸0 is locally asymptotically stable If 𝑅0<1. The positive endemic equilibrium point 𝐸∗ is locally asymptotically stable if 𝑅0>1. This shows that the basic reproduction number of the present model is greater than the one which is obtained from the model modeled without vertical transmission. Vertical transmission contributes positively to the spread of the disease. Numerical simulation of the model is carried out to assess the dynamics of HIV/AIDS infected immigrants and vertical transmission (MTCT) in the spread of HIV/AIDS disease.
The result showed that HIV infective immigrants and vertical transmission (MTCT) significantly affects the spread of the disease. The disease reduces the spread of HIV and also prevents mother to child transmission (PMTCT).It is well accepted that both vertical transmission and immigration contribute positively to the spread of the disease and these two parameters cannot be avoided in practice.
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Keywords
Mathematical Modeling, Dynamics of HIV/AIDS, Treatment, Vertical Transmission