The Volterra–Lyapunov matrix theory for global stability analysis of alcohol-related health risks model

Abstract

This paper studies the global stability analysis of a modified framework proposed by Mayengo et al. on alcohol-related health risks model. We first present the global stability analysis of risk-free equilibrium (RFE). Later, the global stability of the risk endemic equilibrium is studied. This goal was achieved by appropriate utilization of the symmetrical properties in the structure of Volterra–Lyapunov matrices. The analysis and results presented in this paper make building blocks towards a comprehensive study and deeper understanding of the fundamental mechanism in alcohol-related health risks and similar models. The numerical examples are simulated to validate the theoretical model results presented.