A graph-theoretic approach to the method of global Lyapunov functions
By Hongbin Guo, Michael Y. Li, Zhisheng Shuai. 2008
327 citations recorded by the source corpus.
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.
Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/f7b91f04795c4fc1449587d9c900a3ec6d39d79a
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In Genetics
In Modeling and Simulation
In Public Health, Environmental and Occupational Health
Citations in the corpus
- Global-stability problem for coupled systems of differential equations on networks (2010, background): “For detailed discussions of the model and interpretations of parameters, we refer the reader to [15,34].”
- Extinction and recurrence of multi-group SEIR epidemic (2013, background): “([21]) pointed out there is a unique endemic equilibrium P ∗ = (S∗ 1 , · · · , S∗ n, E∗ 1 , · · · , E∗ n, I∗ 1 , · · · , I∗ n) in Eq.”
- Global Stability of Infectious Disease Models Using Lyapunov Functions (2013, unknown): “This method has been applied successfully to establish the global stability of the EE for several complex disease models; see, for example, [11, 12, 26].”