Analysis of the stability of a mathematical model for measles

Abstract

The worldwide measles crisis has escalated into a significant public health issue due to its lethal nature, generating widespread anxiety. Our study presents a dynamic mathematical model constructed using comprehensive mortality data from the World Health Organization and actual data on measles outbreak propagation. By utilizing the Routh-Hurwitz criteria and formulating Lyapunov functions, we demonstrated both local and global stability for scenarios with and without the presence of the disease. Furthermore, we conducted a sensitivity analysis on the model’s parameters to assess their impact on the basic reproduction number, R0. Our theoretical results were substantiated through numerical simulations performed with MATLAB.