Застосування функцій Ляпунова для дослідження стійкості в епідеміологічних компартментних системах

Abstract

Mathematical modeling of infectious diseases relies heavily on compartmental models and nonlinear differential equations. This paper considers using Lyapunov’s functions for the stability analysis of such systems. By examining various structures, including multi-strain models with drug resistance and amplification effects, the study demonstrates how to prove global asymptotic stability for disease-free and endemic equilibria. The work categorizes different Lyapunov function types and explores their application to modern challenges. These mathematical frameworks provide essential tools for predicting long-term system behavior in public health