Local and Global Stability in Epidemiology using Lyapunov Function
This project discusses the significance of Lyapunov functions in assessing the stability of equilibria. Lyapunov functions serve as the foundation for various analytical methods in dynamical systems, including frequency criteria and comparisons with other systems. While the theory of Lyapunov functions is a robust analytical tool, identifying an appropriate Lyapunov function can often pose significant scientific challenges. Additionally, the project covers the Dulac Criterion and La Salle’s Principle, modifications of Lyapunov functions, which assist in determining the stability of solutions in epidemic models.