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On Mathematical Structure of Time-Discrete Model for Epidemic Population Dynamics

Research Project

Project/Area Number 21540130
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 InstitutionHiroshima University

Principal Investigator

SENO Hiromi  広島大学, 大学院・理学研究科, 准教授 (50221338)

Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords数理生物学 / 数理モデル / モデル化 / 差分方程式 / 感染症 / 生態学 / 応用数学 / 公衆衛生学
Research Abstract

We proposed and mathematically analyzed some new time-discrete models with non-linear difference equations, which are derived by a mathematical modeling applied the stochastic process, in comparison to some basic time-continuous models of epidemic population dynamics with ordinary differential equations, which have been applied for many other subjects in population dynamics. Further for our new models, we can define the expected reproduction number of infectives in a natural manner, and we obtained some fundamental issues about its mathematical nature.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (40 results)

All 2012 2011 2010 2009 Other

All Journal Article (13 results) (of which Peer Reviewed: 4 results) Presentation (25 results) Book (1 results) Remarks (1 results)

  • [Journal Article] A mathematical model of population dynamics for Batesian mimicry system2012

    • Author(s)
      Seno, H. and Kohno, T.
    • Journal Title

      J. Biol. Dyn[ in press]

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A mathematical model of population dynamics for Batesian mimicry system2012

    • Author(s)
      Hiromi Seno, Takahiro Kohno
    • Journal Title

      Journal of Biological Dynamics

      Volume: (掲載決定)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 離散型Kermack. McKendrick SIRモデルの特性(Some remarks on the nature of discrete Kermack. McKendrick SIR model)2011

    • Author(s)
      瀬野裕美
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1757 Pages: 37-43

    • Related Report
      2011 Final Research Report
  • [Journal Article] 離散型と連続型のSIRSモデルのDynamical Consistency(On dynamical consistency between time-discrete and time-continuous SIRS models)2011

    • Author(s)
      瀬野裕美
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1751 Pages: 63-74

    • Related Report
      2011 Final Research Report
  • [Journal Article] 離散型Kermack-McKendrick SIRモデルの特性2011

    • Author(s)
      瀬野裕美
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1757 Pages: 37-43

    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
  • [Journal Article] 離散型と連続型のSIRSモデルのDynamical Consistency2011

    • Author(s)
      瀬野裕美
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1751 Pages: 63-74

    • Related Report
      2011 Annual Research Report
  • [Journal Article] A mathematical model of population dynamics with predator' s behavioral change induced by prey' s Batesian mimicry2010

    • Author(s)
      Seno, H. and Kohno, T.
    • Journal Title

      被食者のベイツ型擬態に誘発される捕食者の行動変化を導入した個体群動態モデル

      Volume: 1704 Pages: 85-94

    • Related Report
      2011 Final Research Report
  • [Journal Article] Native intra-and inter-specific reactions may cause the paradox of pest control with harvesting2010

    • Author(s)
      Seno, H.
    • Journal Title

      J. Biol. Dyn.

      Volume: 4(3) Pages: 235-247

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Amathematical model of population dynamics with predator's behavioral change induced by prey's Batesian mimicry.2010

    • Author(s)
      Hiromi Seno
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1704 Pages: 85-94

    • Related Report
      2010 Annual Research Report
  • [Journal Article]2010

    • Author(s)
      瀬野裕美, ほか
    • Journal Title

      『行動・進化』の数理生物学(共立出版株式会社)

      Pages: 49-92

    • Related Report
      2009 Annual Research Report
  • [Journal Article] 感染症個体群動態に関する時間離散モデルについての考察2009

    • Author(s)
      瀬野裕美
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1663 Pages: 20-29

    • Related Report
      2011 Final Research Report
  • [Journal Article] Native intra-and inter-specific reactions may cause the paradox of pest control with harvesting2009

    • Author(s)
      瀬野裕美
    • Journal Title

      Journal of Biological Dynamics (in press)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 感染症個体群動態に関する時間離散モデルについての考察2009

    • Author(s)
      瀬野裕美
    • Journal Title

      京都大学数理解析研究所講究録 1663

      Pages: 20-29

    • Related Report
      2009 Annual Research Report
  • [Presentation] 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(Analysis of A Mathematical Model on The Modification of Apparent Competition Effect with The Invasion of Alien Predator),京都大学数理解析研究所共同利用研究集会2011

    • Author(s)
      恩田芳, 瀬野裕美
    • Organizer
      第8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)
    • Year and Date
      2011-11-18
    • Related Report
      2011 Final Research Report
  • [Presentation] 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2011

    • 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8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
    • Year and Date
      2011-11-18
    • Related Report
      2011 Annual Research Report
  • [Presentation] 感染症伝染ダイナミクスの離散時間モデル,盛岡応用数学小研究集会2011

    • Author(s)
      瀬野裕美
    • Organizer
      盛岡応用数学小研究集会(第11回)
    • Place of Presentation
      岩手大学(盛岡)
    • Year and Date
      2011-11-12
    • Related Report
      2011 Final Research Report
  • [Presentation] 感染症伝染ダイナミクスの離散時間モデル2011

    • Author(s)
      瀬野裕美
    • Organizer
      第11回盛岡応用数学小研究集会
    • Place of Presentation
      岩手大学,盛岡(招待講演)
    • Year and Date
      2011-11-12
    • Related Report
      2011 Annual Research Report
  • [Presentation] 複数のブルードから構成される被食者を伴う離散型個体群動態モデル(A Discrete Population Dynamics Model with Some Different Broodsof Prey)2011

    • Author(s)
      志波[松本]翔, 瀬野裕美
    • Organizer
      日本数理生物学会第21回大会
    • Place of Presentation
      明治大学駿河台キャンパス(東京)
    • Year and Date
      2011-09-13
    • Related Report
      2011 Final Research Report
  • [Presentation] 複数のブルードから構成される被食者を伴う離散型個体群動態モデル(A Discrete Population Dynamics Model with Some Different Broods of Prey)2011

    • Author(s)
      瀬野裕美
    • Organizer
      日本数理生物学会第21回大会
    • Place of Presentation
      明治大学駿河台キャンパス,東京
    • Year and Date
      2011-09-13
    • Related Report
      2011 Annual Research Report
  • [Presentation] A Simple Mathematical Model for The Annual Variation of Epidemic Outbreak with Prevention Level Affected by Incidence Size in The Last Season2011

    • Author(s)
      Hiromi Seno
    • Organizer
      8th European Conference on Mathematical and Theoretical Biology, and Annual Meeting of The Society for Mathematical Biology-ECMTB 2011
    • Place of Presentation
      The Jagiellonian University, Krakow, Poland
    • Year and Date
      2011-06-30
    • Related Report
      2011 Annual Research Report
  • [Presentation] A Simple Mathematical Model for The Annual Variation of Epidemic Outbreak with Prevention Level Affected by Incidence Size in The Last Season, 8th European Conference on Mathematical and Theoretical Biology, and Annual Meeting of The Society for Mathematical Biology-ECMTB 20112011

    • Author(s)
      H. Seno and A. Terada
    • Organizer
      The Jagiellonian University, Krakow, Poland
    • Place of Presentation
      The Jagiellonian University, Krakow, Poland
    • Related Report
      2011 Final Research Report
  • [Presentation] 離散型と連続型のSIRモデルのDynamical Consistency(On Dynamical Consistency between Time-Continuous and Time-Discrete SIR Models),京都大学数理解析研究所共同利用研究集会2010

    • Author(s)
      瀬野裕美
    • Organizer
      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(京都)
    • Year and Date
      2010-11-18
    • Related Report
      2011 Final Research Report
  • [Presentation] 離散型と運続型のSIRモデルのDynamical Consistency (On Dynamical Consistency between Time-Continuous and Time-Discrete SIR Models).2010

    • 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,京都
    • Year and Date
      2010-11-18
    • Related Report
      2010 Annual Research Report
  • [Presentation] A Mathematical Model of Population Dynamics with Predator's Behaviora-Change Induced by Prey's Batesian Mimicry.2010

    • Author(s)
      Hiromi Seno
    • Organizer
      The Third China-Japan Colloquium of Mathematical Biology
    • Place of Presentation
      北京,中国(招待講演)
    • Year and Date
      2010-10-19
    • Related Report
      2010 Annual Research Report
  • [Presentation] 2株系Kermack. McKendrick型SIRモデルにおけるワクチン2種の最適配分問題(Optimal Allocation Problem of Strain-Specific Vaccines for a Two Strain Kermack. McKendrick SIR Model)2010

    • Author(s)
      国貞宗久, 瀬野裕美
    • Organizer
      日本数理生物学会第20回大会
    • Place of Presentation
      北海道大学学術交流会館(札幌)
    • Year and Date
      2010-09-13
    • Related Report
      2011 Final Research Report
  • [Presentation] 複数回交尾戦略の適応性に関する数理的考察(A Mathematical Consideration on The Optimality of Multiple Mating Strategy)2010

    • Author(s)
      瀬野裕美, 井上宏樹
    • Organizer
      日本数理生物学会第20回大会
    • Place of Presentation
      北海道大学学術交流会館(札幌)
    • Year and Date
      2010-09-13
    • Related Report
      2011 Final Research Report
  • [Presentation] 複数回交尾戦略の適応性に関する数理的考察(A Mathematical Consideration on The Optimality of Multiple Mating Strategy).2010

    • Author(s)
      瀬野裕美
    • Organizer
      日本数理生物学会第20回大会
    • Place of Presentation
      北海道大学学術交流会館,札幌
    • Year and Date
      2010-09-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] A Mathematical Model for A Group Wave Emergence with Waving Behavior of Ocypodid Crab Ilyoplax pusillus.2010

    • Author(s)
      Hiromi Seno
    • Organizer
      Conference on Computational and Mathematical Population Dynamics-CMPD3
    • Place of Presentation
      University Victor Segalen Bordeaux 2, Bordeaux, France
    • Year and Date
      2010-06-02
    • Related Report
      2010 Annual Research Report
  • [Presentation] A Mathematical Model of Population Dynamics with Predator's Behavioral Change Induced by Prey's Batesian Mimicry.2010

    • Author(s)
      Hiromi Seno
    • Organizer
      Conference on Computational and Mathematical Population Dynamics-CMPD3
    • Place of Presentation
      University Victor Segalen Bordeaux 2, Bordeaux, France
    • Year and Date
      2010-06-01
    • Related Report
      2010 Annual Research Report
  • [Presentation] Royama の理論を応用した時間離散型捕食者-被食者系の数理モデリング2010

    • Author(s)
      瀬野裕美
    • Organizer
      日本生態学会第57回大会(ESJ57)自由集会W02「第1原理から理解する個体群動態モデル」
    • Place of Presentation
      東京大学駒場キャンパス, 東京
    • Year and Date
      2010-03-15
    • Related Report
      2009 Annual Research Report
  • [Presentation] A Mathematical Model of Population Dynamics with Predator' s Behavioral Change Induced by Prey' s Batesian Mimicry2010

    • Author(s)
      H. Seno and T. Kohno
    • Organizer
      The Third China-Japan Colloquium of Mathematical Biology
    • Place of Presentation
      北京
    • Related Report
      2011 Final Research Report
  • [Presentation] A MathematicalModel for A Group Wave Emergence withWaving Behavior of Ocypodid Crab Ilyoplaxpusillus2010

    • Author(s)
      H. Seno and K. Tsutamura
    • Organizer
      Conference on Computational and Mathematical Population Dynamics-
    • Place of Presentation
      University Victor Segalen Bordeaux2, Bordeaux, France
    • Related Report
      2011 Final Research Report
  • [Presentation] A Mathematical Model of Population Dynamics with Predator' s Behavioral Change Induced by Prey' s Batesian Mimicry2010

    • Author(s)
      H. Seno and T. Kohno
    • Organizer
      Conference on Computational and Mathematical Population Dynamics-CMPD3
    • Place of Presentation
      University Victor Segalen Bordeaux 2, Bordeaux, France
    • Related Report
      2011 Final Research Report
  • [Presentation] Royamaの理論を応用した時間離散型捕食者.被食者系の数理モデリング2010

    • Author(s)
      瀬野裕美
    • Organizer
      日本生態学会第57回大会(ESJ57)
    • Place of Presentation
      東京大学(東京)
    • Related Report
      2011 Final Research Report
  • [Presentation] ベイッ型擬態種による捕食行動の変化を導入した個体群動熊モデル (A Mathematical Model of Population Dynamics with A Predator's Behavioral Change by the Batesian Mimic Prey)2009

    • 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」, 京都
    • Year and Date
      2009-11-11
    • Related Report
      2009 Annual Research Report
  • [Presentation] A Mathematical Model Analysis for An Artificial Recovery of Environment Degraded by Population Dynamics (個体群による自己環境劣化に対する環境改善効果についての数理モデル解析)2009

    • Author(s)
      瀬野裕美
    • Organizer
      日本数理生物学会第19回大会
    • Place of Presentation
      東京大学数理科学研究科, 東京
    • Year and Date
      2009-09-10
    • Related Report
      2009 Annual Research Report
  • [Presentation] A Time-Discrete Model for the Epidemic Population Dynamics2009

    • Author(s)
      瀬野裕美
    • Organizer
      An International Conference and LMS Workshop : Mathematical Models of Collective Dynamics in Biology and Evolution-MDBE'09
    • Place of Presentation
      University of Leicester, UK
    • Year and Date
      2009-05-12
    • Related Report
      2009 Annual Research Report
  • [Presentation] A Time-Discrete Model for the Epidemic Population Dynamics, An International Conference and LMS Workshop2009

    • Author(s)
      H. Seno
    • Organizer
      Mathematical Models of Collective Dynamics in Biology and Evolution-MDBE' 09
    • Place of Presentation
      University ofLeicester, UK
    • Related Report
      2011 Final Research Report
  • [Book] 『行動・進化』の数理生物学」『第4章動的計画法による最適行動連鎖』2010

    • Author(s)
      瀬野裕美
    • Total Pages
      224
    • Publisher
      共立出版
    • Related Report
      2011 Final Research Report
  • [Remarks]

    • URL

      http://www.math.sci.hiroshima-u.ac.jp/~seno/

    • Related Report
      2011 Final Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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