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A Graph-Theoretic Approach to the Method of Global Lyapunov Functions

Hongbin Guo, Michael Y. Li and Zhisheng Shuai
Proceedings of the American Mathematical Society
Vol. 136, No. 8 (Aug., 2008), pp. 2793-2802
Stable URL: http://www.jstor.org/stable/20535481
Page Count: 10
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Graph-Theoretic Approach to the Method of Global Lyapunov Functions
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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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