2018 Fiscal Year Final Research Report
Mathematical Analysis on Stability and Unstable Phenomena of Immune Models
| Project/Area Number |
26400211
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Aoyama Gakuin University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2019-03-31
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| Keywords | 数理モデル / ウィルス免疫系 / 数理生物学 / 時間遅れ |
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| Outline of Final Research Achievements |
The purpose of the research is to make clear the relationship between the structure and function of virus infection versus immune response of human. Particular we focus on the unstable phenomena of the immune dynamics. First, we construct a general mathematical models ofimmune systems describing virus infection process and activating process of our immune systems. Further, we introduce the time delays into the model to express the time duration for the infected cell to produce the virus particles and for the immune systems to be activated. We consider the effects of the these time delays on the dynamics of the mathematical models. Especially we investigate the effect of the time delays on the global stability of the model and unstable dynamics.
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| Free Research Field |
数理生物学
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| Academic Significance and Societal Importance of the Research Achievements |
デング熱感染におけるＴ細胞の適応免疫細胞としての役割を考慮した数理モデルを構築し，デング熱ウイルスとの闘いにおけ るＴ細胞の役割を解析 した．またＴ細胞を活性化させる免疫療法の効果を議論した．また富栄養化のパラドクスとして知られている有名な個体群生態学におけ る数理モデルに対して， 捕食者の成長段階を考慮（捕食者の成長に対する時間遅れ）した数理モデルに拡張し，ダイナミクスを考察した．この時間遅れによっ て，富栄養化のパラドクス が消滅することを証明した.
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