A New Approach to the Method of Lyapunov Functionals and Its Applications
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 th...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/276579 |
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| _version_ | 1849307927482990592 |
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| author | Yunguo Jin Shouming Zhong |
| author_facet | Yunguo Jin Shouming Zhong |
| author_sort | Yunguo Jin |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-1db5c6fdb2e5453ba65b79f02039f0b7 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-1db5c6fdb2e5453ba65b79f02039f0b72025-08-20T03:54:37ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/276579276579A New Approach to the Method of Lyapunov Functionals and Its ApplicationsYunguo Jin0Shouming Zhong1School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaWe 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.http://dx.doi.org/10.1155/2013/276579 |
| spellingShingle | Yunguo Jin Shouming Zhong A New Approach to the Method of Lyapunov Functionals and Its Applications Journal of Applied Mathematics |
| title | A New Approach to the Method of Lyapunov Functionals and Its Applications |
| title_full | A New Approach to the Method of Lyapunov Functionals and Its Applications |
| title_fullStr | A New Approach to the Method of Lyapunov Functionals and Its Applications |
| title_full_unstemmed | A New Approach to the Method of Lyapunov Functionals and Its Applications |
| title_short | A New Approach to the Method of Lyapunov Functionals and Its Applications |
| title_sort | new approach to the method of lyapunov functionals and its applications |
| url | http://dx.doi.org/10.1155/2013/276579 |
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