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2013 A New Approach to the Method of Lyapunov Functionals and Its Applications
Yunguo Jin, Shouming Zhong
J. Appl. Math. 2013: 1-12 (2013). DOI: 10.1155/2013/276579


We show some results which can replace the graph theory used to construct global Lyapunov functions in some coupled systems of differential equations. We present an example of an epidemic model with stage structure and latency spreading in a heterogeneous host population and obtain a more general threshold for the extinction and persistence of a disease. Using some results obtained by mathematical induction and suitable Lyapunov functionals, we prove the global stability of the endemic equilibrium. For some coupled systems of differential equations, by a similar approach to the discussion of the epidemic model, the conditions of threshold property or global stability can be established without the assumption that the relative matrix is irreducible.


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Yunguo Jin. Shouming Zhong. "A New Approach to the Method of Lyapunov Functionals and Its Applications." J. Appl. Math. 2013 1 - 12, 2013.


Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 06950594
MathSciNet: MR3138977
Digital Object Identifier: 10.1155/2013/276579

Rights: Copyright © 2013 Hindawi


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