2011 Fiscal Year Final Research Report
Accurateness and stability of delayed integral and differential equations and their discrete versions.
| Project/Area Number |
21540230
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Waseda University |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2011
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| Keywords | 関数方程式の大域理論 / 数理モデル / 感染症モデル / 大域漸近安定性 / Lyapunov関数法 |
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| Research Abstract |
Applying the Lyapunov function techniques in MacCluskey(2010) which solve the open question on the global stability for delayed SIR epidemic models, we obtain results on sufficient condition of global stability, first by perturbation techniques, and second by extending the Lyapunov function techniques of MacCluskey which are corresponding to small loss rate of immunity recovery individuals. On the other hand, by modified monotone iterative techniques in Xu and Ma(2010), we improve results on the global stability for large loss rate of immunity recovery individuals.
This monotone iterative techniques is a different techniques than that of Lyapunov function and we may hope to their applications to other models.
Moreover, we find some natural extensions on global stability of continuous epidemic models to discrete models derived by the backward Euler method, by which we solve the open problem how to find the discrete version of the continuous model which keeps the global stability property.
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[Presentation]2010
Author(s)
Y. Muroya, Y. Enatsu, Y. Nakata
Organizer
The 3-th China-Japan Colloquium of Mathematical Biology
Place of Presentation
北京(中国)
Year and Date
2010-10-19
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