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Mathematical theory of structured population dynamics and its applications to mathematical models for infectious diseases

Research Project

Project/Area Number 19540116
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionThe University of Tokyo

Principal Investigator

INABA Hisashi  The University of Tokyo, 大学院・数理科学研究科, 准教授 (80282531)

Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Keywords感染症 / 人口 / 数理モデル / 基本再生産数 / 微分方程式 / 感染症数理モデル / タイプ別再生産数 / 次世代作用素 / 弱エルゴード性 / 繁殖価 / 状態別再生産数 / 閾値条件 / 安定人口
Research Abstract

We formulated structured population dynamics models for infectious diseases to analyse their mathematical structures, and developed key ideas in mathematical epidemiology as the basic reproduction number and its derivatives. In particular, we have shown the estimation methods of the basic reproduction number and relations between the basic reproduction number and the host population growth based on an age-structured infectious disease dynamics model in a stable population. Moreover, we developed the state-reproduction number theory, by which we cleared the eradication condition by case isolation of symptomatic infecteds. Subsequently, we have shown a new approach to formulate the basic reproduction number and the intrinsic growth rate of infecteds in a heterogeneous environment.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (47 results)

All 2011 2010 2009 2008 2007 Other

All Journal Article (20 results) (of which Peer Reviewed: 12 results) Presentation (20 results) Book (3 results) Remarks (4 results)

  • [Journal Article] The net reproduction rate and the type-reproduction number in multiregional demography2010

    • Author(s)
      H. Inaba
    • Journal Title

      Vienna Yearbook of Population Research 2009

      Pages: 197-215

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] The net reproduction rate and the type-reproduction number in multiregional demography2010

    • Author(s)
      H.Inaba
    • Journal Title

      Vienna Yearbook of Population Research 2009 197-215

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Two critical issues in quantitative modeling of communicable diseases : Inference of unobservables and dependent happening2009

    • Author(s)
      H. Nishiura, M. Kakehashi, H. Inaba
    • Journal Title

      Mathematical and Statistical Estimation Approaches in Epidemiology(G. Chowell, J. M. Hyman, L. M. A. Bettencourt and C. Castillo-Chavez (eds.))(Springer)

      Pages: 53-87

    • Related Report
      2009 Final Research Report
  • [Journal Article] Two critical issues in quantitative modeling of communicable diseases : Inference of unobservables and dependent happening2009

    • Author(s)
      H.Nishiura, M.Kakehashi, H.Inaba
    • Journal Title

      Mathematical and Statistical Estimation Approaches in Epidemiology、Springer 53-87

    • Related Report
      2009 Annual Research Report
  • [Journal Article] 人口問題2008

    • Author(s)
      稲葉寿
    • Journal Title

      現代社会と科学技術(東島清・大貫惇睦編)(大阪大学出版会)

      Pages: 1-36

    • Related Report
      2009 Final Research Report
  • [Journal Article] 微分方程式と感染症数理疫学2008

    • Author(s)
      稲葉寿
    • Journal Title

      数理科学 No. 538

      Pages: 19-25

    • Related Report
      2009 Final Research Report
  • [Journal Article] The basic reproduction number of an infectious disease in a stable population : The impact of population growth rate on the eradication threshold2008

    • Author(s)
      H. Inaba, H. Nishiura
    • Journal Title

      Mathematical Modelling of Natural Phenomena Vol. 3, No. 7

      Pages: 194-228

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] The state-reproduction number for a multistate class age structured epidemic system and its application to the asymptomatic transmission model2008

    • Author(s)
      H. Inaba, H. Nishiura
    • Journal Title

      Math.Biosci. 216

      Pages: 77-89

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] The basic reproduction number of an infectious disease in a stable population: The impact of population growth rate on the eradication threshold2008

    • Author(s)
      H. Inaba and H. Nishiura
    • Journal Title

      Mathematical Modelling of Natural Phenomena 3(7)

      Pages: 194-228

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The state-reproduction number for a multistate class age structured epidemic system and its application to the asymptomatic transmission model2008

    • Author(s)
      H. Inaba and H. Nishiura
    • Journal Title

      Mathematical Biosciences 216

      Pages: 77-89

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 微分方程式と感染症数理疫学2008

    • Author(s)
      稲葉寿
    • Journal Title

      数理科学 538

      Pages: 19-25

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Age-structured homogeneous epidemic systems with application to the MSEIR epidemic model2007

    • Author(s)
      H. Inaba
    • Journal Title

      J.Math.Biol. 54

      Pages: 101-146

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Homogeneous epidemic systems in the stable population,「経済の数理解析」2007

    • Author(s)
      H. Inaba
    • Journal Title

      数理解析研究所講究録(京都大学数理解析研究所) 1557

      Pages: 28-44

    • Related Report
      2009 Final Research Report
  • [Journal Article] Discussion : Emergence of the concept of the basic reproduction number from mathematical demography2007

    • Author(s)
      H. Nishiura, H. Inaba
    • Journal Title

      J.Theor.Biol 244

      Pages: 357-364

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Effects of age shift on the tempo and quantum of non-repeatable events2007

    • Author(s)
      H. Inaba
    • Journal Title

      Math. Popul. Studies 14(3)

      Pages: 131-168

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] 数理生物学とは何か2007

    • Author(s)
      稲葉寿
    • Journal Title

      数学イノベーション(文部科学省科学技術政策研究所編著)(工業調査会)

      Pages: 131-148

    • Related Report
      2009 Final Research Report
  • [Journal Article] Discussion: Emergence of the concept of the basic reproduction number from mathematical demography2007

    • Author(s)
      Hiroshi Nishiura and Hisashi Inaba
    • Journal Title

      Journal of Theoretical Biology 244

      Pages: 357-364

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Age-structured homogeneous epidemic systems with application to the MSEIR epidemic model2007

    • Author(s)
      Hisashi Inaba
    • Journal Title

      Journal of Mathematical Biology 54

      Pages: 101-146

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Homogeneous epidemic systems in the stable population2007

    • Author(s)
      Hisashi Inaba
    • Journal Title

      「経済の数理解析」京都大学数理解析研究所講究録 1557

      Pages: 28-44

    • Related Report
      2007 Annual Research Report
  • [Journal Article] Effects of age shift on the tempo and quantum of non-repeatable events2007

    • Author(s)
      Hisashi Inaba
    • Journal Title

      Mathjematical Population Studies 14(3)

      Pages: 131-168

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [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2011

    • 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
      2011-02-20
    • Related Report
      2009 Final Research Report
  • [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
    • Year and Date
      2010-02-20
    • Related Report
      2009 Annual Research Report
  • [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~-分野の垣根を越えて-
    • 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
    • Related Report
      2009 Final Research Report
  • [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~-分野の垣根を越えて-
    • Place of Presentation
      明治大学生田校舎
    • Year and Date
      2010-02-18
    • Related Report
      2009 Annual Research Report
  • [Presentation] 連続状態変数に基づく感染症のタイプ別再生産数2009

    • Author(s)
      稲葉寿
    • Organizer
      RIMS研究集会「第6回生物数学の理論とその応用」
    • Place of Presentation
      龍谷大学セミナーハウス「ともいき荘」
    • Year and Date
      2009-11-10
    • Related Report
      2009 Annual Research Report
  • [Presentation] 感染症の数理, 日本アクチュアリー会 平成20年度第7回例会 研究集会「医療とアクチュアリー」2009

    • Author(s)
      稲葉寿
    • Organizer
      こまばエミナース
    • Year and Date
      2009-03-18
    • Related Report
      2009 Final Research Report
  • [Presentation] 感染症の状態別再生産数とその応用2009

    • Author(s)
      稲葉寿・西浦博
    • Organizer
      鳥インフルエンザを中心とする感染症の数理-モデリングと解析-
    • Place of Presentation
      京都産業大学工学部9号館
    • Related Report
      2009 Final Research Report
  • [Presentation] 多状態人口学における純再生産率と状態別再生産数2009

    • Author(s)
      稲葉寿
    • Organizer
      日本人口学会第61回大会
    • Place of Presentation
      関西大学千里山キャンパス
    • Related Report
      2009 Annual Research Report 2009 Final Research Report
  • [Presentation] 連続状態変数に基づく感染症のタイプ別再生産数, RIMS研究集会「第6回生物数学の理論とその応用」2009

    • Author(s)
      稲葉寿
    • Organizer
      龍谷大学セミナーハウス「ともいき荘」
    • Related Report
      2009 Final Research Report
  • [Presentation] 現代人口学の射程-小子高齢化からエイズまで-2008

    • Author(s)
      稲葉寿
    • Organizer
      平成20年度日本アクチュアリー会年次大会特別講演
    • Place of Presentation
      経団連会館
    • Year and Date
      2008-11-10
    • Related Report
      2009 Final Research Report
  • [Presentation] 感染症の数理モデル, 食の安全研究センター主催セミナー「感染症と数理科学」2008

    • Author(s)
      稲葉寿
    • Organizer
      東京大学農学部7号館A棟
    • Year and Date
      2008-09-30
    • Related Report
      2009 Final Research Report
  • [Presentation] The basic reproduction number of an infectiuous disease in astable population: The impact of population growth rate on the eradication threshold2008

    • Author(s)
      H. Inaba
    • Organizer
      The Second Cina-Japan Colloquium of Mathe matical Biology
    • Place of Presentation
      岡山大学
    • Year and Date
      2008-08-04
    • Related Report
      2008 Annual Research Report
  • [Presentation] 感染症数理モデルにおける基本再生産数と閾値原理, ワークショップ「生命現象における先端数理」2008

    • Author(s)
      稲葉寿
    • Organizer
      岡山大学総合研究棟
    • Year and Date
      2008-01-15
    • Related Report
      2009 Final Research Report
  • [Presentation] 感染症数理モデルにおける基本再生産数と閾値原理2008

    • Author(s)
      稲葉寿
    • Organizer
      ワークショップ「生命現象における先端数理」
    • Place of Presentation
      岡山大学総合研究棟
    • Year and Date
      2008-01-15
    • Related Report
      2007 Annual Research Report
  • [Presentation] The basic reproduction number of an infectiuous disease in a stable population : The impact of population growth rate on the eradication threshold2008

    • Author(s)
      H. Inaba, H. Nishiura
    • Organizer
      The Second Cina-Japan Colloquium of Mathematical Biology, Okayama University, Okayama
    • Related Report
      2009 Final Research Report
  • [Presentation] Population dynamics of infectious diseases : Threshold principle and prevention policy, Japan-Slovenia Symposium on Nonlinear Science2008

    • Author(s)
      H. Inaba
    • Organizer
      Graduate School of Mathematical Sciences, The University of Tokyo
    • Related Report
      2009 Final Research Report
  • [Presentation] 安定人口における感染症流行 : 基本再生産数の推定と人口成長率の影響2008

    • Author(s)
      稲葉寿
    • Organizer
      第8回盛岡応用数学小研究会
    • Place of Presentation
      岩手大学人文社会科学部1号館
    • Related Report
      2009 Final Research Report
  • [Presentation] 数理人口学の過去・現在・未来, 2007年度第2回東日本地域部会「人口学の現在と未来」2007

    • Author(s)
      稲葉寿
    • Organizer
      東京大学医学系研究科教育研究棟
    • Year and Date
      2007-12-22
    • Related Report
      2009 Final Research Report
  • [Presentation] 数理人口学の過去・現在・未来2007

    • Author(s)
      稲葉寿
    • Organizer
      2007年度第2回東日本地域部会「人口学の現在と未来」
    • Place of Presentation
      東京大学医学系研究科
    • Year and Date
      2007-12-22
    • Related Report
      2007 Annual Research Report
  • [Presentation] 感染症におけるタイプ別再生産数とその未発症感染モデルへの応用2007

    • Author(s)
      稲葉寿
    • Organizer
      京都大学数理解析研究所共同研究集会「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
    • Related Report
      2009 Final Research Report 2007 Annual Research Report
  • [Book] 感染症の数理モデル2008

    • Author(s)
      稲葉寿(編著)
    • Total Pages
      311
    • Publisher
      培風館
    • Related Report
      2008 Annual Research Report
  • [Book] 現代人口学の射程2007

    • Author(s)
      稲葉寿(編著)
    • Publisher
      ミネルヴァ書房
    • Related Report
      2009 Final Research Report 2007 Annual Research Report
  • [Book] 感染症の数理モデル2007

    • Author(s)
      稲葉寿(編著)
    • Publisher
      培風館
    • Related Report
      2009 Final Research Report
  • [Remarks] ホームページ等

    • URL

      http://www.ms.u-tokyo.ac.jp/~inaba/index.html

    • Related Report
      2009 Final Research Report
  • [Remarks]

    • URL

      http://www.ms.u-tokyo.ac.jp/~inaba/index.html

    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://www.ms.u-tokyo.ac.Jp/~inaba/index.html

    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://www.ms.u-tokyo.ac.jp/~inaba/index.html

    • Related Report
      2007 Annual Research Report

URL: 

Published: 2007-04-01   Modified: 2016-04-21  

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