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A graph-theoretic approach to the method of global Lyapunov functions
Proceedings of the American Mathematical Society · 2008 · Vol. 136(08) · pp. 2793–2802
Hongbin Guo✉(University of Alberta)Michael Y. Li(University of Alberta)Zhisheng Shuai(University of Alberta)
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.
Mathematical and Theoretical Epidemiology and Ecology ModelsCOVID-19 epidemiological studiesEvolution and Genetic DynamicsLyapunov functionUniquenessMathematicsLyapunov equationGraphClass (philosophy)Stability (learning theory)Applied mathematicsStability theoryLyapunov redesign
Funding
- University of Alberta
- Killam Trusts
- Natural Sciences and Engineering Research Council of Canada
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328
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