MATHEMATICAL MODELING OF ALCOHOLISM INCORPORATING MEDIA AWARENESS

Abstract

Alcohol addiction is a phenomenon that has attracted the attention of numerous researchers and academics in a variety of professions due to its serious repercussion on all spheres of human life. Alcoholism is a common addiction in adults throughout the globe. To shed light on the causes of this phenomenon and pinpoint efficient preventative and therapeutic measures, a mathematical model that incorporates media awareness and the impact of the exposed class on light and heavy drinkers’ is crucial. The impact of media awareness and treatment on the drinking behavior of various drinker classes is discussed in several mathematical models. Nevertheless, the impact of the exposed class of alcoholics on light and heavy drinkers in the presence of media awareness, has not been addressed. There is correlation between the exposed class and awareness over time, hence it is vital to understand the spread of alcoholism and the need to curb it. The main objective of this study is to formulate and analyze, a mathematical model of alcoholism incorporating media awareness and the influence of the exposed class on light and heavy drinkers. A set of differential equations served as the foundation for the model’s formulation. To perform stability analysis of the model at each equilibrium point, Jacobian matrix method and the next generation matrix approach were employed. This further aided in the computation of the basic reproduction number, R0. By use of MATLAB, numerical simulations on the impact of awareness on alcoholism were performed. Secondary data obtained from NACADA and data from rehabilitation centers in Kenya was used to validate the analytical results of the impact of media awareness on the drinking population. Stability analysis of the model indicated that the Alcohol Free Equilibrium (AFE) point is locally asymptotically stable whenever R0 < 1 and unstable whenever R0 > 1. Additionally, the Alcohol Endemic Point (AEP) exists and is locally asymptotically stable when R0 > 1. Numerical simulations showed that increase in media awareness programs reduces alcohol prevalence in the community. The study concluded that maximum media awareness is an ideal measure in curbing alcohol abuse in the community. The findings of this study will provide useful insight to the government and policy makers in targeting suitable media awareness programs in combating alcoholism.