Title

GLOBAL STABILITY OF INFECTIOUS DISEASE MODELS USING LYAPUNOV FUNCTIONS

Authors

Authors

Z. S. Shuai;P. van den Driessche

Comments

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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

Language

English

First Page

1513

Last Page

1532

WOS Identifier

WOS:000323887600009

ISSN

0036-1399

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