Modeling tobacco smoking effect on HIV antiretroviral therapy

Abstract

In this paper, we formulate a mathematical model to study how tobacco smoking affects antiretroviral therapy. The model is based on the fact that smoking induces metabolism of ARVs and HIV patient addiction to smoking affects adherence to drugs. Equilibrium states and effective reproduction number $R_{ef}$ are computed. Conditions for equilibria stability are derived. The model shows that in the absence of tobacco smoking and HIV, disease free equilibrium is stable when $R_{ef}<1$ and in the presence of tobacco smoking and HIV, endemic equilibrium is stable when $R_{ef}>1$. The analysis shows that tobacco smoking decreases the efficacy of antiretroviral therapy and this effect is critical when smoking induces metabolism of antiretroviral drugs by $30\%$ to $70\%$. Even if a HIV infected smoker remains adherent to therapy, still the effect of tobacco smoking on drugs' efficacy is inevitable. For management of HIV epidemic and its therapy, abstinence from smoking by HIV patients is recommended.