Aitzhanov Y.2025-06-132025-06-132024Aitzhanov Y / Global stability of dynamical systems and Lyapunov functions / 7M05401 - Department of Mathematics and Natural Sciences / 2024https://repository.sdu.edu.kz/handle/123456789/1761In this study, we explore the global stability of a novel epidemic model that integrates reported and unreported cases, distinguishing between symptomatic and asymptomatic individuals. Using a Lyapunov function, we demonstrate the model’s stability, highlighting the crucial role of asymptomatic cases in shaping disease dynamics and control effectiveness. Furthermore, we perform a novel hybrid parameter estimation method based on genetic algorithms, utilizing COVID19 data from the UK to better understand the distribution of reported and unreported cases in the early phases of an epidemic. In addition, we employ sensitivity analysis to understand the impact of this division on the fundamental reproduction number. Our findings underscore the importance of accounting for both symptomatic and asymptomatic cases in epidemic modeling and control strategies.enLyapunov functionCOVID19SIS modelThesis