A Modified SEIR Model for Poverty Dynamics: Analysis and Stability

Abstract

This study presents a modified SEIR model to analyze poverty dynamics in a population. The total population is divided into four compartments: financially stable, economically vulnerable, poor, and recovered individuals. Poverty transmission occurs through interaction between stable and poor populations, while relapse of recovered individuals is incorporated via economic shocks. The model includes demographic recruitment and natural exit rates, making it realistic for long-term population studies. Analytical techniques such as positivity of solutions, invariant region, existence and uniqueness, disease-free equilibrium, and stability analysis are applied. The basic reproduction number  is derived to measure the potential for poverty persistence. Numerical simulations illustrate the impact of varying transmission, progression, and recovery rates on poverty prevalence. Local stability of the disease-free equilibrium is established via eigenvalue analysis and upper-triangular reduction. Global stability is proved using a Lyapunov function. The findings provide insight into policy interventions to reduce economic vulnerability.