| Project/Area Number |
25887011
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Mathematical analysis
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| Research Institution | Kobe University (2014)
The University of Tokyo (2013) |
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Principal Investigator |
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| Project Period (FY) |
2013-08-30 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 感染症 / モデル化 / 関数方程式論 / 解析・評価 / 基本再生産数 / リャプノフ関数 / 年齢構造 / 拡散 / 感染症モデル / 空間構造 / 微分方程式 / 積分方程式 / 力学系 / リャプノフ安定性 |
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| Outline of Final Research Achievements |
We constructed various nonlinear systems of differential equations as mathematical models for various biological phenomena including the spread of epidemics in society and performed their qualitative analysis. In particular, we focused on the structured population models including the nonlinear systems of reaction-diffusion equations which can take into account both effects of the age-structure and spatial spread of populations. For these models, we derived the basic reproduction number Ro and the corresponding threshold conditions and clarified the relation between them and the mathematical properties such as the existence and stability of each equilibrium. Through these analysis, we applied and extended the theory of related Lyapunov functions to various models.
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