Mathematical consideration of new modeling for biological population dynamics

• Project/Area Number: 24540129
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Tohoku University
• Principal Investigator: SENO Hiromi 東北大学, 情報科学研究科, 教授 (50221338)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000); Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2012: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 数理生物学 / 数理モデル / モデル化 / 応用数学 / 生態学 / 差分方程式 / 微分方程式 / 個体群動態 / 疫学

Outline of Final Research Achievements

The principal research subject is the mathematical relation of models with nonlinear difference equations and nonlinear differential equations for the theoretical study about the biological popoulation dynamics. In this research project, to be systematically discussed is the rationality of the mathematical structure in such models, that is, its logical relation to the biological structure of targeted phenomenon. It is aimed to provide with a mathematical base to promote some new mathematical modeling, and to analyze the mathematical model newly built by it. Especially for some typical mathematical models in mathematical ecology, this project focused the formulus of functions involved in them and revisited the modeling to find out some new raltionality in them. As a result, some new mathematical models in biological population dynamics were built with the system of difference equations, and considered their mathematical natures.

Research Products

• [Journal Article] メタ個体群モデルに関するモデリングの数理（A mathematical modeling for metapopulation dynamics） (2015)
  • Author(s): 瀬野裕美, 佐藤一憲，齋藤保久
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 1966 Pages: 41-52
• [Journal Article] 複数パッチ環境下における個体群存続に対する閾パッチ数問題（Critical patch number problem for the population persistence in multi-patchy environment） (2015)
  • Author(s): 瀬野裕美
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 1937 Pages: 68-80
• [Journal Article] 過去の履歴による影響を考慮した感染規模年次変動の数理モデル：疫学データへの適用可能性（A mathematical model for the annual variation of incidence size affected by past epidemic experience: Applicability to real data） (2014)
  • Author(s): 瀬野裕美
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 1917 Pages: 129-142
  • Open Access
• [Journal Article] 過去の感染規模が現在の予防水準に及ぼす影響を考慮した感染規模年変動の数理モデル（A simple mathematical model for the annual variation of epidemic outbreak with prevention level affected by past incidence sizes） (2013)
  • Author(s): 瀬野裕美，寺田恵華，井上美香
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 1853 Pages: 141-157
• [Journal Article] 外来捕食者侵入による見かけの競争の効果の変質に関する数理モデル解析（Analaysis of a mathematical model on the modification of apparent competition effect with the invasion of alien predator） (2012)
  • Author(s): 瀬野裕美，恩田 芳
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 1796 Pages: 141-157
• [Journal Article] 離散時間モデルによる感染症伝染ダイナミクスにおける感染個体再生産数（Reproduction numbers of infectives for a time-discrete epidemic population dynamics model） (2012)
  • Author(s): 瀬野裕美
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 1789 Pages: 35-45
• [Journal Article] A mathematical model of population dynamics for Batesian mimicry system (2012)
  • Author(s): H. Seno and T. Kohno
  • Journal Title: Journal of Biological Dynamics Volume: 6 Issue: 2 Pages: 1034-1051
  • DOI: 10.1080/17513758.2012.672659
  • Peer Reviewed
• [Presentation] Mathematical Modeling on Biology (2015)
  • Author(s): Hiromi Seno
  • Organizer: Intensive Workshop: Mathematical Modelling on Biology
  • Place of Presentation: Kyungpook National University, Daegu, Korea
  • Year and Date: 2015-02-22 – 2015-02-25
  • Invited
• [Presentation] 複数パッチ環境下における個体群存続に対する閾パッチ数問題（Critical patch number problem for the population persistence in patchy environment） (2014)
  • Author(s): 瀬野裕美
  • Organizer: 京都大学数理解析研究所共同利用研究集会「第11回生物数学の理論とその応用」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2014-09-17
• [Presentation] A Mathematical Model for Annual Variation of Incidence Size Affected by Past Epidemic Experience (2014)
  • Author(s): Hiromi Seno
  • Organizer: The Joint Annual Meeting of the Japanese Society for Mathematical Biology and the Society for Mathematical Biology
  • Place of Presentation: 大阪国際会議場
  • Year and Date: 2014-07-30
• [Presentation] A Time-Discrete SIRS Model and Total Reproduction Number (2012)
  • Author(s): Hiromi Seno
  • Organizer: BIOCOMP2012 ― Mathematical Modeling and Computational Topics in Biosciences
  • Place of Presentation: Lloyd's Baia Hotel, Vietri sul Mare, Italy
• [Presentation] 過去の感染規模が現在の予防水準に及ぼす影響を考慮した感染規模年変動の数理モデル（A simple mathematical model for the annual variation of epidemic outbreak with prevention level affected by past incidence sizes） (2012)
  • Author(s): 瀬野裕美
  • Organizer: 京都大学数理解析研究所共同利用研究集会 「第9回 生物数学の理論とその応用」
  • Place of Presentation: 京都大学数理解析研究所（京都）
• [Presentation] 子に対する教育投資への親の意識分布の世代間遷移ダイナミクスモデル（Mathematical model on generational transition of parents' attitude in educational investment for child）
  • Author(s): 瀬野裕美
  • Organizer: 日本数理生物学会第23回大会
  • Place of Presentation: 静岡大学（浜松）
• [Presentation] 過去の感染規模が現在の予防水準に及ぼす影響を考慮した感染規模年変動の数理モデル（A simple mathematical model for the annual variation of epidemic outbreak with prevention level affected by past incidence sizes）
  • Author(s): 瀬野裕美
  • Organizer: 日本数学会2013年度秋季総合分科会
  • Place of Presentation: 愛媛大学（松山）
• [Presentation] 過去の感染規模が予防水準に及ぼす影響を考慮した数理モデルと感染規模年次変動データ（A mathematical model for the annual variation of epidemic outbreak with prevention level affected by past incidence size: With perspective on comparison to real data）
  • Author(s): 瀬野裕美
  • Organizer: 京都大学数理解析研究所共同利用研究集会「第10回生物数学の理論とその応用」
  • Place of Presentation: 京都大学数理解析研究所（京都）