Abbreviated Journal Title
SIAM J. Appl. Math.
Keywords
disease model; global stability; Lyapunov function; graph-theoretic; method; EPIDEMIC MODELS; DYNAMICS; TRANSMISSION; CHOLERA; COMPUTATION; NETWORKS; Mathematics, Applied
Abstract
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.
Journal Title
Siam Journal on Applied Mathematics
Volume
73
Issue/Number
4
Publication Date
1-1-2013
Document Type
Article
DOI Link
Language
English
First Page
1513
Last Page
1532
WOS Identifier
ISSN
0036-1399
Recommended Citation
Shuai, Zhisheng and Driessche, P. Van Den, "Global Stability of Infectious Disease Models Using Lyapunov Functions" (2013). Faculty Bibliography 2010s. 4700.
https://stars.library.ucf.edu/facultybib2010/4700
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