2014 Fiscal Year Final Research Report
Analysis of nonlinear reaction-diffusion systems for spatial spread of age-structured biological populations
| 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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| 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 |
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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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| Free Research Field |
応用数学・数理疫学・数理生物学
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