A fractional order age-structured model to study the effect of social awareness on alcohol consumption

Abstract Alcohol misuse is a widespread societal issue that transcends class boundaries and significantly influencing various facets of life. Accordingly, we have developed a nonlinear mathematical model to explore alcohol consumption, incorporating the novel fractional-order derivative in the Caputo sense to determine the impact of memory effects on drinking behavior. The model examines the influence of adult drinking habits on the youth generation’s drinking habits as well as the role of social and media-driven awareness in shaping this phenomenon. The study has calculated the basic reproduction numbers for both youth and adult populations, which serve as measures of the contagiousness of alcohol consumption. The study has determined an alcohol-free equilibrium point that is locally stable when both reproduction numbers are below one. However, if either reproduction number exceeds one, an additional alcohol-persistence equilibrium point emerges, indicating the potential for a backward bifurcation in the model. Numerical findings suggest that increasing the memory effect by decreasing the value of α can significantly reduce the number of drinkers. Additionally, it is observed that if adult potential drinkers abstain from alcohol and create an alcohol-free environment for the youth, the drinking population can be substantially diminished. Therefore, a combined effort from both the youth and adult populations is essential to prevent binge drinking and reduce the overall drinking population.