Fractional SAQ alcohol model: stability analysis and Türkiye application

Alcohol dependence and alcohol abuse are public health problems. According to the World Health Organization data, approximately two billion people in the world consume alcoholic beverages and approximately 77 million people suffer alcohol use disorder. Epidemiologic studies show that the rate of alcohol dependence varies by region. Fractional derivative models are preferred over integer step models in the control theory of physical, biological, and dynamical systems. Fractional operators are particularly useful in describing the memory and hereditary properties of substances and processes, which are often ignored in integer stepwise derivatives. In this study, we consider a fractional model of alcohol use and analyze its stability. This model consists of three compartments: those who do not use alcohol yet but may use alcohol in the future (S), those who use alcohol (A) and those who quit alcohol for good (Q). The fractional derivative is used in the Caputo sense. Mathematical analysis of the fractional SAQ model for the mathematical model of alcohol use is performed and numerical results are obtained with the help of the Euler method and graphs are drawn.