A graph-theoretic approach to the method of global Lyapunov functions

Authors:
Hongbin Guo, Michael Y. Li and Zhisheng Shuai

Journal:
Proc. Amer. Math. Soc. **136** (2008), 2793-2802

MSC (2000):
Primary 34D23, 92D30

Published electronically:
March 27, 2008

MathSciNet review:
2399043

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Abstract | References | Similar Articles | Additional Information

Abstract: A class of global Lyapunov functions is revisited and used to resolve a long-standing open problem on the uniqueness and global stability of the endemic equilibrium of a class of multi-group models in mathematical epidemiology. We show how the group structure of the models, as manifested in the derivatives of the Lyapunov function, can be completely described using graph theory.

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Additional Information

**Hongbin Guo**

Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada

Address at time of publication:
Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada

Email:
hguo@math.ualberta.ca

**Michael Y. Li**

Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada

Email:
mli@math.ualberta.ca

**Zhisheng Shuai**

Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada

Email:
zshuai@math.ualberta.ca

DOI:
https://doi.org/10.1090/S0002-9939-08-09341-6

Keywords:
Lyapunov functions,
multi-group epidemic models,
global stability,
graph theory.

Received by editor(s):
November 8, 2006

Published electronically:
March 27, 2008

Communicated by:
Carmen C. Chicone

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.