Journal
SIAM JOURNAL ON APPLIED MATHEMATICS
Volume 73, Issue 4, Pages 1513-1532Publisher
SIAM PUBLICATIONS
DOI: 10.1137/120876642
Keywords
disease model; global stability; Lyapunov function; graph-theoretic method
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Funding
- Natural Science and Engineering Research Council of Canada (NSERC)
- Mprime project Transmission Dynamics and Spatial Spread of Infectious Diseases: Modelling, Prediction and Control
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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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