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

Guo, Hongbin; Li, Michael; Shuai, Zhisheng

doi:10.1090/S0002-9939-08-09341-6

A graph-theoretic approach to the method of global Lyapunov functions
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by Hongbin Guo, Michael Y. Li and Zhisheng Shuai

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

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

Published electronically: March 27, 2008

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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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