期刊
SIAM JOURNAL ON APPLIED MATHEMATICS
卷 73, 期 4, 页码 1513-1532出版社
SIAM PUBLICATIONS
DOI: 10.1137/120876642
关键词
disease model; global stability; Lyapunov function; graph-theoretic method
资金
- Natural Science and Engineering Research Council of Canada (NSERC)
- Mprime project Transmission Dynamics and Spatial Spread of Infectious Diseases: Modelling, Prediction and Control
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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