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GLOBAL STABILITY OF INFECTIOUS DISEASE MODELS USING LYAPUNOV FUNCTIONS
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Journal Article
GLOBAL STABILITY OF INFECTIOUS DISEASE MODELS USING LYAPUNOV FUNCTIONS
2013
Overview
Two systematic methods are presented to guide the construction of Lyapunov functions for general infectious disease models and are thus applicable to establish their global dynamics. Specifically, a matrix-theoretic method using the Perron eigenvector is applied to prove the global stability of the disease-free equilibrium, while a graph-theoretic method based on Kirchhoff's matrix tree theorem and two new combinatorial identities are used to prove the global stability of the endemic equilibrium. Several disease models in the literature and two new cholera models are used to demonstrate the applications of these methods.
Publisher
Society for Industrial and Applied Mathematics
