Dynamics and Stability in a Mathematical Model of Poverty and Alcohol Consumption

Abstract

This paper develops and analyzes a mathematical model describing the dynamic interaction between poverty and alcohol consumption within a population. Both deterministic and stochastic formulations are considered to capture variability in individual and collective behavior. The model incorporates assumptions about how individuals’ economic conditions and alcohol dependency influence each other over time. Equilibrium points are derived and their stability properties are investigated analytically. Numerical simulations illustrate the system’s dynamics under varying parameters and intervention strategies. The results provide insight into the mechanisms linking social behavior and economic status, contributing to the understanding of poverty persistence and recovery within a mathematical social science framework.