Researches on mathematical structured population dynamics and its applications to mathematical models for infectious diseases

• Project/Area Number: 22540114
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: The University of Tokyo
• Principal Investigator: INABA Hisashi 東京大学, 大学院・数理科学研究科, 准教授 (80282531)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2010: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 構造化個体群ダイナミクス / 感染症数理モデル / 基本再生産数 / タイプ別再生産数 / 汎流行閾値定理 / SIS型感染症流行モデル / 年齢構造 / 周期的環境 / 構造化固体群 / 内的成長率 / 構造化個体群

Research Abstract

We formulate structured population models of biological populations by taking into account individual traits and using differential and integral equations, then we mathematically analyzed qualitative behavior and developed applications to mathematical epidemiology. In particular, we have shown a new definition for the basic reproduction number and the type-reproduction number in time-heterogeneous environments, by which we have given a unified perspective in the theory of basic reproduction number.

Research Products

• [Journal Article] On the definition and the computation of the type-reproduction number T for structured populations in heterogeneous environments (2013)
  • Author(s): H. Inaba
  • Journal Title: J. Math. Biol. Volume: 66 Pages: 1065-1097
• [Journal Article] Endemic thresholdresults for anage-structured SIS epidemic model with periodic parameters, to appear in J. Math. (2013)
  • Author(s): T. Kuniya and H. Inaba
  • Journal Title: Anal. Appls.
• [Journal Article] On the definition and the computation of the type-reproduction number T for structured populations in heterogeneous environments (2013)
  • Author(s): Hisashi Inaba
  • Journal Title: Journal of Mathematical Biology Volume: 66, Nos. 4-5 Issue: 4-5 Pages: 1065-1097
  • DOI: 10.1007/s00285-012-0522-0
  • Peer Reviewed
• [Journal Article] Endemic threshold results for an age-structured SIS epidemic model with periodic parameters (2013)
  • Author(s): KUNIYA, Toshikazu
  • Journal Title: Journal of Mathematical Analysis and Applications Volume: (掲載確定) Issue: 2 Pages: 477-492
  • DOI: 10.1016/j.jmaa.2013.01.044
  • Peer Reviewed
• [Journal Article] The Malthusian parameter and R0 for heterogeneous populations in periodic environments (2012)
  • Author(s): H. Inaba
  • Journal Title: Math. Biosci. Eng. Volume: 9(2) Pages: 313-346
• [Journal Article] On a new perspective of the basic reproduction number in heterogeneous environments (2012)
  • Author(s): H. Inaba
  • Journal Title: J. Math. Biol. Volume: 65(2) Pages: 309-348
• [Journal Article] The Malthusian parameter and RO for heterogeneous populations in periodic environments (2012)
  • Author(s): H.Inaba
  • Journal Title: Mathematical Biosciences and Engineering Volume: 9巻2号 Issue: 2 Pages: 313-346
  • DOI: 10.3934/mbe.2012.9.313
  • Peer Reviewed
• [Journal Article] On a new perspective of the basic reproduction number in heterogeneous environments (2012)
  • Author(s): Hisashi Inaba
  • Journal Title: Journal of Mathematical Biology Volume: 65(2) Issue: 2 Pages: 309-348
  • DOI: 10.1007/s00285-011-0463-z
  • Peer Reviewed
• [Journal Article] Estimation of the incubation period ofinfluenza A (H1N1-2009) among imported cases: Addressing censoring using outbreak data at the origin of importation (2011)
  • Author(s): H. Nishiura and H. Inaba
  • Journal Title: J. Theor. Biol Volume: 272 Pages: 123-130
• [Journal Article] 感染症の制御による癌リスク減少の評価手法 (2011)
  • Author(s): 西浦博・稲葉寿
  • Journal Title: 統計数理 Volume: 第59巻第2号 Pages: 267-286
  • NAID: 120006020401
• [Journal Article] Estimation of the incubation period of influenza A (H1N1-2009) among imported cases : Addressing censoring using outbreak data at the origin of importation (2011)
  • Author(s): H.Nishiura, H.Inaba
  • Journal Title: Journal of Theoretical Biology Volume: 272 Issue: 1 Pages: 123-130
  • DOI: 10.1016/j.jtbi.2010.12.017
  • Peer Reviewed
• [Journal Article] Estimation of the incubation period of influenza A (H1N1-2009) among imported cases: Addressing censoring using outbreak data at the origin of importation (2011)
  • Author(s): H.Nishiura, H.Inaba
  • Journal Title: Journal of Theoretical Biology Volume: 272 Pages: 123-130
  • Peer Reviewed
• [Journal Article] 連続的状態変数に基づ く感染症のタイプ別再生産数とその応用 (2010)
  • Author(s): 稲葉 寿
  • Journal Title: 数理解析研究所講究録 1704第6回生物 数学の理論とその応用 Pages: 22-30
• [Journal Article] ケルマック・マッケンドリック方程式--感染症流行のダイナミ クス (2010)
  • Author(s): 稲葉 寿
  • Journal Title: 数理科学 Volume: 564 Pages: 65-70
• [Journal Article] 連続的状態変数に基づく感染症のタイプ別再生産数とその応用 (2010)
  • Author(s): 稲葉寿
  • Journal Title: 数理解析研究所講究録1704「第6回生物数学の理論とその応用」 Volume: 1704 Pages: 22-30
• [Journal Article] ケルマック・マッケンドリック方程式-感染症流行のダイナミクス (2010)
  • Author(s): 稲葉寿
  • Journal Title: 数理科学 Volume: 564 Pages: 65-70
• [Journal Article] (2010), The net reproduction rate and the type-reproduction number in multiregional demography (2009)
  • Author(s): H. Inaba
  • Journal Title: Vienna Yearbook of Population Research Pages: 197-215
• [Presentation] 基本再生産数理論の最近の発展について (2013)
  • Author(s): 稲葉寿
  • Organizer: FIRST合原最先端数理モデルプロジェクトTWS16:感染症の動態理解と対策に向けた数理的アプローチ
  • Place of Presentation: 東京大学生産技術研究所
  • Year and Date: 2013-01-30
• [Presentation] 前期ケルマック・マッケンドリックモデルにおける汎流行閾値定理について (2012)
  • Author(s): 稲葉寿
  • Organizer: RIMS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
  • Year and Date: 2012-11-13
• [Presentation] 基本再生産数R0の数学--個体群ダイナミクスのキーパラメータを追って-- (2012)
  • Author(s): 稲葉寿
  • Organizer: 日本数学会秋期総合分科会企画特別講演
  • Year and Date: 2012-09-20
• [Presentation] ウィルス感染動態の年齢構造化個体群モデルについて--細胞のHIV感染モデルから-- (2012)
  • Author(s): 稲葉寿
  • Organizer: 第22回日本数理生物学会企画シンポジウム「計算ウィルス学の展開」
  • Place of Presentation: 岡山大学自然科学研究棟
  • Year and Date: 2012-09-10
• [Presentation] A new perspective of the basic reproduction number for structured populations in heterogeneous environments (2012)
  • Author(s): Hisashi Inaba
  • Organizer: Basque Center for Applied Mathematics
  • Year and Date: 2012-04-12
• [Presentation] On the definition and the computation of the type-reproduction number for structured populations in heterogeneous environments (2012)
  • Author(s): Hisashi Inaba
  • Organizer: ReaDiLab workshop
  • Place of Presentation: Orsay University
  • Year and Date: 2012-04-04
• [Presentation] A new perspective of the basic reproduction number for structured populations in heterogeneous environments (2012)
  • Author(s): Hisashi Inaba
  • Organizer: Bordeaux 2 University
  • Year and Date: 2012-03-22
• [Presentation] 感染症数理モデルの基礎 (2011)
  • Author(s): 稲葉寿
  • Organizer: 合原最先端数理モデルプロジェクトG3研究会
  • Year and Date: 2011-10-18
• [Presentation] 変動環境下における基本再生産数--R0の数学と人口学・感染症疫学への応用-- (2011)
  • Author(s): 稲葉寿
  • Organizer: 合原最先端数理モデルプロジェクトG3サブグループ会議
  • Place of Presentation: 東京大学生産技術研究所
  • Year and Date: 2011-05-18
• [Presentation] 変動環境における構造化個体群の基本再生産数 (2011)
  • Author(s): 稲葉寿
  • Organizer: 第21回日本数理生物学会大会
  • Place of Presentation: 明治大学リバティータワー
• [Presentation] The basic reproduction number for infectious diseases in heterogeneous environments (2010)
  • Author(s): H.Inaba
  • Organizer: The 3rd Conference of Computational and Mathe matical Population Dynamics
  • Place of Presentation: Bordeaux, France
  • Year and Date: 2010-06-01
• [Presentation] 変動環境下における感染症の基本再生生産数について (2010)
  • Author(s): 稲葉寿
  • Organizer: 数理と生物・生命科学との融合に向けて--MathESDの実践--
  • Place of Presentation: 岡山大学環境理工学部棟105教室
  • Year and Date: 2010-02-20
• [Presentation] 基本再生産数と閾値原理-感染症数理モデルの基礎- (2010)
  • Author(s): 稲葉寿
  • Organizer: 感染症～実像とモデリング～ー分野の垣根を越えてー
  • Place of Presentation: 明治大学生田校舎第二校舎A館207教室
  • Year and Date: 2010-02-18
• [Presentation] The basic reproduction number for infectious diseases in heterogeneous environments (2010)
  • Author(s): H. Inaba
  • Organizer: The 3rd Conference of Computational and Mathematical Population Dynamics
  • Place of Presentation: Bordeaux, France
• [Presentation] On the definition of the basic reproduction number for infectious diseases in heterogeneous environments (2010)
  • Author(s): H. Inaba
  • Organizer: The 3rd China-Japan Colloquium of Mathematical Biology
  • Place of Presentation: Beijing, China
• [Presentation] 変動環境下における感染症の基本再生産数の定義について (2010)
  • Author(s): 稲葉寿
  • Organizer: RIMS研究集会「第7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
• [Presentation] 基本再生産数R0の数学--個体群ダイナミクスのキーパラメータを追って--
  • Author(s): 稲葉寿
  • Organizer: 日本数学会秋期総合分科会企画特別講演
  • Place of Presentation: 九州大学
  • Invited
• [Presentation] On the definition and the computation of the type-reproduction number for structured populations in heterogeneous environments
  • Author(s): Hisashi Inaba
  • Organizer: ReaDiLab workshop, Orsay University
  • Place of Presentation: オルセー大学
  • Invited
• [Presentation] A new perspective of the basic reproduction number for structured populations in heterogeneous environments
  • Author(s): Hisashi Inaba
  • Organizer: Basque Center for Applied Mathematics
  • Place of Presentation: バスク応用数学センター
  • Invited
• [Remarks]
  • URL: http://www.ms.u-tokyo.ac.jp/~inaba/index.html
• [Remarks]
  • URL: http://www.ms.u-tokyo.ac.jp/~inaba/index.html