Mathematical modeling, analysis and optimal control of an alcohol drinking model with liver complication

Abstract

We want to develop our model [2]. So, this study discusses the influence of awareness programs and treatment on drinking behavior of the drinker’s classes through mathematical models. There are five categories of population in this model, namely: potential drinkers, moderate drinkers, heavy drinkers, heavy drinkers with liver complications, recovered and quitters of drinking. The model is analyzed using stability theory of nonlinear differential equations. Based on analysis result, the model has two equilibrium points: drinking-free equilibrium point and drinking present equilibrium point. These equilibrium points are locally and globally asymptotically stable under certain conditions. We also study the sensitivity analysis of the model parameters to know the parameters that have a high impact on the reproduction number R0. Moreover, the controls used are awareness programs and treatment. The purpose theses optimal controls as to minimize the heavy drinkers with and without complications as well as the control costs. Pontryagin’s principle is then implemented to solve optimal control problems. Finally, numerical simulations are carried out to determine the effectiveness of the controls used.