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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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: 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: http://dx.doi.org/10.1090/S0002-9939-08-09341-6
PII: S 0002-9939(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.