Numerical treatment of stochastic and deterministic alcohol drinker dynamics with Euler–Maruyama method

Abstract

Alcohol abuse is a substantial cause of various health and societal issues, as well as a significant factor in global disease. Once alcohol is consumed in the gastrointestinal tract, it undergoes metabolism in the liver and lungs. In this investigation, the nonlinear deterministic and stochastic differential frameworks are analyzed numerically to predict the dynamic evolution of the virus in the drinker alcohol model. The framework for apprehending drinking patterns is categorized into three distinct groups: the susceptible population, risk drinkers, and moderate drinkers. The approximate solution for each population group is determined by exhaustively creating scenarios that vary the probability ratio of infection in susceptible individuals who do not consume alcohol, the increasing rate of alcohol consumption, the rate at which individuals transition from acute to chronic drinking categories, the rate at which new non-drinking consumers are attracted, the death rate of the population, the ratio affecting the rate of sociability in heavy drinkers, and the overall population rate. The Euler–Maruyama approach for the stochastic framework and the Adams method for the deterministic framework are utilized, respectively, to determine the solutions of the alcohol drinker model. This study compares deterministic and stochastic frameworks to underscore their distinct characteristics and efficiency, achieved through comprehensive simulations and in-depth analysis of the numerical outcomes.