GLOBAL STABILITY OF INFECTIOUS DISEASE MODELS USING LYAPUNOV FUNCTIONS

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...

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Bibliographic Details
Published inSIAM journal on applied mathematics Vol. 73; no. 4; pp. 1513 - 1532
Main Authors SHUAI, ZHISHENG, VAN DEN DRIESSCHE, P.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2013
Subjects
Applied mathematics
Cholera
Combinatorial analysis
Disease transmission
Dynamical systems
Eigenvectors
Equilibrium
Graph theory
Infectious diseases
Lyapunov functions
Mathematical models
Methods
Pathogens
Stability
Waterborne diseases
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Summary: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.
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ISSN:0036-1399
1095-712X
DOI:10.1137/120876642