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Mathematical studies for the reaction-diffusion models of the biological invasion and propagation phenomena

Research Project

Project/Area Number 18540144
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 InstitutionKyoto Sangyo University

Principal Investigator

HOSONO Yuzo  Kyoto Sangyo University, 理学部, 教授 (50008877)

Co-Investigator(Kenkyū-buntansha) TSUJII Yoshiki  京都産業大学, 理学部, 教授 (90065871)
Project Period (FY) 2006 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥3,990,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywords応用数学 / 数理生物学 / 数理モデル / 反応拡散系 / 進行波解 / 伝播速度 / 感染症モデル / 餌食と捕食者モデル / 特異摂動法 / 相空間解析 / 非線形感染率 / 線形予測
Research Abstract

The major result obtained in this research consists of two ingredients : (1) for the reaction-diffusion model of the infectious diseases, we analyze how the propagation speed of the infectious diseases depends on the parameters appearing in the model system and give the analytical estimate on the speed, (2) for the reaction-diffusion predator-prey model, we show the new features of the profile and the speed of the waves of the predator invading into the region occupied by the prey.

Report

(6 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report   Self-evaluation Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (33 results)

All 2009 2008 2007 2006

All Journal Article (24 results) (of which Peer Reviewed: 15 results) Presentation (6 results) Book (3 results)

  • [Journal Article] 侵入問題に現れる進行波解について2009

    • Author(s)
      細野雄三
    • Journal Title

      京都大学数理解析研究所講究録 1663

      Pages: 65-71

    • Related Report
      2009 Final Research Report
  • [Journal Article] Quantile hedging and minimizing the expected shortfall for bond options2009

    • Author(s)
      Y. Tsujii
    • Journal Title

      京都産業大学論集, 自然科学系列 第38号

      Pages: 17-27

    • NAID

      110007094427

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] 侵入問題に現れる進行波解について2009

    • Author(s)
      細野雄三
    • Journal Title

      京都大学数理解析研究所考究録 1663

      Pages: 65-71

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Quantile hedging and minimizing the expected shortfall for bond options2009

    • Author(s)
      Y.Tsujii
    • Journal Title

      京都産業大学論集 38

      Pages: 17-27

    • NAID

      110007094427

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Integral of Fine computable functions and Walsh Fourier series2008

    • Author(s)
      T. Mori, Y. Tsujii, M. Yasugi
    • Journal Title

      Electronic Notes of Theoretical Computer Science Vol.202

      Pages: 279-293

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Effective Fine-convergence of Walsh-Fourier series2008

    • Author(s)
      T. Mori
    • Journal Title

      Mathematical Logic Quarterly 54

      Pages: 519-534

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Integral of Fine computable functions and Walsh Fourier series2008

    • Author(s)
      T. Mori
    • Journal Title

      Electronic Notes of Theoretical Computer Science 202

      Pages: 279-293

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 感染症の伝播を視る2008

    • Author(s)
      細野 雄三
    • Journal Title

      数理科学 No.535

      Pages: 34-38

    • Related Report
      2007 Annual Research Report
  • [Journal Article] The propagation speeds of traveling fronts for higher order autocatalytic reaction-diffusion systems2007

    • Author(s)
      Y. Hosono
    • Journal Title

      Japan J. Indust. Appl. Math. Vol.24,No.1

      Pages: 79-104

    • NAID

      10020152715

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] 感染症の伝播を記述する決定論的モデルによる空間的な伝播速度の評価2007

    • Author(s)
      細野雄三
    • Journal Title

      京都産業大学論集, 自然科学系列 第36号

      Pages: 1-19

    • NAID

      110006284661

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Phase plane analysis of travelling waves for higher order autocatalytic reaction-diffusion systems2007

    • Author(s)
      Y. Hosono
    • Journal Title

      Discrete Contin. Dyn. Syst. Ser. B Vol.8,No.1

      Pages: 115-125

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] The effective sequence of uniformities and its limit: as a methodology in computer analysis2007

    • Author(s)
      M. Yasugi, T. Mori, Y. Tsujii
    • Journal Title

      Annals of the Japan Association for Philosophy of Science Vol.15

      Pages: 99-121

    • NAID

      110007033699

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Phase plane analysis oftravelling waves for higher orderautocatalytic reaction-diffusion systems2007

    • Author(s)
      Y. Hosono
    • Journal Title

      Discrete Contin.Dyn.Syst.Ser.B Vol.8, No.1

      Pages: 115-125

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] 感染症の伝播を記述する決定論的モデルによる空間的な伝播速度の評価2007

    • Author(s)
      細野雄三
    • Journal Title

      京都産業大学論集,自然科学系列 第36号

      Pages: 1-19

    • NAID

      110006284661

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] The propagation speeds oftraveling fronts for higher order autocatalytic reaction-diffusion systems2007

    • Author(s)
      Y. Hosono
    • Journal Title

      Japan J.Indust.Appl.Math. Vol.24, No.1

      Pages: 79-104

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] The propagation speeds of traveling fronts for higher order auto-catalytic reaction-diffusion systems2007

    • Author(s)
      Y. Hosono
    • Journal Title

      Discrete and Continuous Dynamical Systems. Ser. B 8

      Pages: 115-125

    • NAID

      10020152715

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Integral of Fine Computable functions and Walsh Fourie series2007

    • Author(s)
      T. Mori
    • Journal Title

      CCA2007, Informatik Berichte 338-6/2007, FernUniversitat in Hagen 338-6

      Pages: 265-282

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 感染症の伝播を記述する決定論的モデルによる空間的な伝播速度の評価2007

    • Author(s)
      細野雄三
    • Journal Title

      京都産業大学論集、自然科学系列 第36号(印刷中)

    • NAID

      110006284661

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Phase plan analysis of traveling waves for higher order autocatalytic reaction-diffusion systems2007

    • Author(s)
      Y.Hosono
    • Journal Title

      Discrete and Continuous Systems Series B 8・1

      Pages: 115-125

    • Related Report
      2006 Annual Research Report
  • [Journal Article] The propagation speeds of traveling front for higher order autocatalytic reaction-diffusion systems2007

    • Author(s)
      Y.Hosono
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics 24・1(印刷中)

    • NAID

      10020152715

    • Related Report
      2006 Annual Research Report
  • [Journal Article] 伝染病伝播の反応拡散モデルにたいする進行波解2006

    • Author(s)
      細野雄三
    • Journal Title

      京都大学数理解析研究所講究録 1499

      Pages: 7-23

    • Related Report
      2009 Final Research Report 2006 Annual Research Report
  • [Journal Article] Traveling fronts for hig her order autocatalytic reaction-diffus ion systems2006

    • Author(s)
      Y. Hosono
    • Journal Title

      京都大学数理解析研究所講究録 1498

      Pages: 26-35

    • Related Report
      2009 Final Research Report
  • [Journal Article] Seque ntial computability of a function-Effec tive Fine space and limiting recursion-2006

    • Author(s)
      M. Yasugi, Y. Tsujii, T. Mori
    • Journal Title

      Journal of Universal Computer Scienc e Vol.11

      Pages: 2179-2191

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] traveling fronts for higher order autocatalytic reaction-diffusion systems2006

    • Author(s)
      Y.Hosono
    • Journal Title

      京都大学数理解析研究所講究録 1498

      Pages: 26-35

    • Related Report
      2006 Annual Research Report
  • [Presentation] 侵入過程に現れる進行波解について, 研究集会2009

    • Author(s)
      細野雄三, 李聖林, 村田宙俊
    • Organizer
      「第5回生物数学の理論とその応用」(日本数理生物学会後援)
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-01-14
    • Related Report
      2009 Final Research Report
  • [Presentation] 侵入過程に現れる進行波解について,研究集会「第5回生物数学の理論とその応用」2009

    • Author(s)
      細野雄三, 李聖林, 村田宙俊
    • Organizer
      日本数理生物学会後援
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-01-14
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] 侵入問題と進行波解2008

    • Author(s)
      細野雄三
    • Organizer
      第18回日本数理生物学会大会
    • Place of Presentation
      同志社大学
    • Year and Date
      2008-09-18
    • Related Report
      2009 Final Research Report 2008 Annual Research Report 2008 Self-evaluation Report
  • [Presentation] Traveling fronts for the reaction-diffusion epidemic models with nonlinear incidence2008

    • Author(s)
      Y. Hosono
    • Organizer
      The Second China-Japan Colloquium of Mathematical Biology
    • Place of Presentation
      Okayama University
    • Year and Date
      2008-08-06
    • Related Report
      2009 Final Research Report
  • [Presentation] Traveling fronts for the reaction-diffusion epidemic models with nonlinear incidence2008

    • Author(s)
      Y. Hosono
    • Organizer
      The Second China-Japan Colloquium of Mathematicalbiology
    • Place of Presentation
      岡山大学
    • Year and Date
      2008-08-06
    • Related Report
      2008 Annual Research Report
  • [Presentation] Fine-continuous functions and fractals defined by infinite systems of contractions2007

    • Author(s)
      Y. Tsujii
    • Organizer
      International Conference on Infinity in Logic & Computation,
    • Place of Presentation
      University of Cape Town
    • Related Report
      2007 Annual Research Report
  • [Book] 感染症の空間的な伝播を記述する数理モデル2008

    • Author(s)
      稲葉寿編著
    • Publisher
      培風館
    • Related Report
      2009 Final Research Report
  • [Book] 感染症の数理モデル(第5章「感染症の空間的な伝播を記述する数理モデル」)2008

    • Author(s)
      稲葉寿
    • Publisher
      培風館
    • Related Report
      2008 Self-evaluation Report
  • [Book] 感染症の数理モデル2008

    • Author(s)
      稲葉寿編著
    • Publisher
      培風館
    • Related Report
      2008 Annual Research Report

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Published: 2006-04-01   Modified: 2016-04-21  

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