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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
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/20535481
Page Count: 10
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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.
Proceedings of the American Mathematical Society © 2008 American Mathematical Society