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Numerical simulation of agent-based model describing human migration

Research Project

Project/Area Number 15560053
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Engineering fundamentals
Research InstitutionOsaka Prefecture University (2005)
Kobe University (2003-2004)

Principal Investigator

TABATA Minoru  Osaka Prefecture University, Graduate School of Engineering, Department of Mathematical Sciences, Professor, 工学研究科, 教授 (70207215)

Project Period (FY) 2003 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 2005: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2004: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2003: ¥500,000 (Direct Cost: ¥500,000)
Keywordshuman migration / numerical simulation / agent / mathematical model / mathematical economic geography / mathematical sociology / master equation / nonlinear integro-partial differential equation / エージェント・ベースド・モデル / スケーリング・リミット / クラマース-モイヤル展開 / 人口移動理論 / フォッカープランク方程式 / 非線形放物型偏微分方程式 / 感染モデル / HTLV-I / ポピュレーション・ダイナミクス / 離散モデル / 自己言及性 / 比較定理
Research Abstract

HTLV-I is a retrovirus that causes ATL. The transmission routes of HTLV-I are (i) from infected mothers to their new born babies, (ii) from infected males (husbands) to females (their wives) by long-term sexual intercourse, and (iii) from infected females (wives) to males (their husbands). In the first paper of the references we consider the population dynamics of HTLV-I infection in a discrete-time mathematical model incorporating an age structure. The necessary and sufficient condition for the extinction of HTLV-I is derived from the model. In order to quantitatively describe interregional migration, in the second paper of the references, we construct two stochastic agent-based models that consist of a large number of agents relocating to obtain higher utility in a discrete bounded domain. In one model we assume that the utility is defined as an increasing affine function of the density of agents. In the other model we assume that the utility is equal to a concave quadratic function of the density of agents. We obtain estimates for the behavior of the models when the number of agents and the time variable tend to infinity. In the third paper of the references we mathematically prove that if the effort required in moving is large, then the models are close to each other in the following sense : the mixed problem with the periodic boundary condition for the master equation has a unique solution that is very close to a solution of that for the Fokker-Planck equation, where the effort is a sociodynamic quantity that represents a cost incurred in moving.

Report

(4 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • Research Products

    (11 results)

All 2006 2004 2003 Other

All Journal Article (9 results) Publications (2 results)

  • [Journal Article] A geometrical similarity between migration of human population and diffusion of biological particles2006

    • Author(s)
      M.Tabata, N.Eshima, I.Takagi
    • Journal Title

      Nonlinear Analysis, Real World Applications, Elsevier Science, Amsterdam. 掲載号未定(掲載決定)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] The behavior of stochastic agent-based models when the number of agents and the time variable tend to infinity2004

    • Author(s)
      M.Tabata, N.Eshima
    • Journal Title

      Applied Mathematics and Computation, Elsevier Science, Amsterdam, 152-1

      Pages: 47-70

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The Fokker-Planck equation and the master equation in the theory of migration2004

    • Author(s)
      M.Tabata, N.Eshima
    • Journal Title

      IMA Journal of Applied Mathematics, Oxford University Press 69

      Pages: 585-603

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The behavior of stochastic agent-based models when the number of agents and the time variable tend to infinity2004

    • Author(s)
      M.Tabata, N.Eshima
    • Journal Title

      Applied Mathematics and Computation (Elsevier Science, Amsterdam) Vol.152, No.1

      Pages: 47-70

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The Fokker-Planck equation and the master equation in the theory of migration2004

    • Author(s)
      M.Tabata, N.Eshima
    • Journal Title

      IMA Journal of Applied Mathematics (Oxford University Press) Vol.69

      Pages: 585-603

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The behavior of stochastic agent-based models when the number of agent and the time variable tend to infinity2004

    • Author(s)
      Minoru Tabata
    • Journal Title

      Applied Mathematics and Computation 第152巻・第1号

      Pages: 47-70

    • Related Report
      2004 Annual Research Report
  • [Journal Article] The Fokker-Planck equation and the master equation in the theory of migration2004

    • Author(s)
      Minoru Tabata
    • Journal Title

      IMA Journal of Applied Mathematics 第69号

      Pages: 585-603

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Population dynamics of HTLV-I infection : A discrete-time mathematical epidemic model approach2003

    • Author(s)
      N.Eshima, M.Tabata, T.Okada, S.Karukaya
    • Journal Title

      Mathematical Medicine and BioIogy : A Journal of the IMA, Oxford University Press 20-1

      Pages: 29-45

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Population dynamics of HTLV-I infection : A discrete-time mathematical epidemic model approach2003

    • Author(s)
      N.Eshima, M.Tabata, T.Okada, S.Karukaya
    • Journal Title

      Mathematical Medicine and Biology : A Journal of the IMA (Oxford University Press) Vol.20, Issue 1

      Pages: 29-45

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Publications] M.Tabata: "A self-referential Agent-based model that consists of a large number of agents moving stochastically in a discrete bounded domain"Applied Mathematics And Computation (Elsevier Science). 第143巻・第2号. 443-483 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] N.Eshima: "Population dynamics of HTLV-I infection : A discrete-time mathematical epidemic model approach"IMA Journal Mathematical Medicine and Biology (Oxford University press). 第20巻・第1号. 29-45 (2003)

    • Related Report
      2003 Annual Research Report

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Published: 2003-04-01   Modified: 2016-04-21  

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