Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 136, Issue 8, Pages 2793-2802Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/S0002-9939-08-09341-6
Keywords
Lyapunov functions; multi-group epidemic models; global stability; graph theory
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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.
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