Modeling Tobacco Smoking Effect on HIV Antiretrovira Therapy and Stability Analysisl

Jacob Ismail Irunde, Livingstone S. Luboobi, Yaw Nkansah-Gyekye

Abstract


Tobacco smoking effect on ARVs remains a topic under investigation. In this paper, a deterministic model is formulated by considering smoking interference in metabolism of ARVs and its effect on one's adherence to drugs in order to assess stability of equilibrium states and determine how tobacco smoking affects antiretroviral drugs. Equilibrium states and effective reproduction number $R_{eff}$ are computed and stability condition for equilibrium states established. Using linearization method and comparison theorem, analysis shows that disease free equilibrium is globally stable when $R_{eff}<1$ and it is unstable when $R_{eff}>1$. However, due to high smoking impairment effective reproduction number $R_{eff}$ cannot be less than unity and the classical requirement $R_{eff}<1$ for global stability of disease free equilibrium cannot be realized. Therefore tobacco smoking affects stability of disease free equilibrium. By applying logarithmic Lyapunov function, endemic equilibrium is asymptotically stable when $R_{eff}>1$. The analysis shows that, as tobacco smoking interference with metabolism of ARVs increases, HIV infected T-cells and macrophages, and free virus record a corresponding increase and this shows that tobacco smoking decreases the efficacy of ARVs. To improve patient's immune system and manage HIV epidemic and its therapy, integration of smoking cessation programs in HIV care services is recommended.


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