Global stability for the system of ordinary differential equations with time delays and its applications to medicine
| Project/Area Number |
22540122
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Aoyama Gakuin University (2012-2013)
Shizuoka University (2010-2011) |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
OHTSUKI Kohichi 京都産業大学, 先端科学技術研究所, 教授 (00032293)
KAJIWARA Tsuyoshi 岡山大学, 環境科学研究科, 教授 (50169447)
KOYANAGI Yoshio 京都大学, ウイルス研究所, 准教授 (80215417)
SASAKI Tohru 岡山大学, 環境科学研究科, 准教授 (20260664)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 数理医学モデル / 時間遅れ / 大域的安定性 / 数理モデル / 応用数学 / 解析学 / 関数方程式論 / 生態学 / 安定性 |
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| Research Abstract |
It has been constructed a general basic mathematical model for the propagation of epidemics. Further time delay (describing incubation period, time for immune system to be activated) is introduced into the basic model and considered its effect on the global dynamics of the model. Especially, the mathematical structure of the model ensuring the global asymptotic stability under the effect of time delay is obtained.
The research for four years shows how to construct Lyapunov function (functional) to ensure the global stability of the basic mathematical model.
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Report
(5 results)
Research Products
(73 results)
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[Presentation] Paradox of vaccination2010
Author(s)
Yasuhiro Takeuchi
Organizer
気候変動と感染症ダイナミクスに関するカナダー中国国際会議, 平成22年全国大学保健管理協会東海北陸地方部会研究集会
Place of Presentation
Nanjing Normal University, Nanjing, China. 29, 静岡
Related Report
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[Presentation] Paradox of vaccination2010
Author(s)
Yasuhiro Takeuchi
Organizer
International Workshop on Mathematics for Biology
Place of Presentation
Posco International Center, POSTECH, Korea
Related Report
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