Mathematical epidemic models for the rapidly growing infection of HTLV-I

• Project/Area Number: 24540137
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Osaka Prefecture University
• Principal Investigator: TABATA Minoru 大阪府立大学, 工学(系)研究科(研究院), 教授 (70207215)
• Co-Investigator(Kenkyū-buntansha): ESHIMA Nobuoki 大分大学, 医学部, 教授 (20203630)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000); Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 数理疫学モデル / ヒト成人T細胞白血病 / 人口集中 / 人口動態 / master方程式 / 非線形Fokker-Planck方程式 / DSKモデル / replicator 方程式 / 進化ゲーム / Core-periphery model / integral equations / master equation / replicator equation

Outline of Final Research Achievements

We consider a spatially continuous evolutionary game whose payoffs are defined as the density of real wages that is determined by the continuous Dixit-Stiglitz-Krugman model in an urban setting. By this evolutionary game we can clarify the mathematical property of population concentration phenomena. This evolutionary game is expressed by the initial value problem for the replicator equation whose growth rate contains an operator which acts on an unknown function that denotes the density of workers. We prove that this initial value problem has a unique global solution that converges to Dirac delta function. By this result we can clarify the diffusion of HTLV-I caused by the migration of workers motivated by disparity in real wages.

Research Products

• [Journal Article] Existence, uniqueness, and computation of short-run and long-run equilibria of the Dixi-Stiglitz-Krugman model in an urban setting (2014)
  • Author(s): M. Tabata, N. Eshima, and Y. Sakai
  • Journal Title: Applied Mathematics and Computation Volume: 234 Pages: 339-355
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] An extension of Krugman's core-periphery model to the case of a continuous domain: Existence and uniqueness of solutions of a system of nonlinear integral equations in spatial economics (2013)
  • Author(s): Minoru Tabata, Nobuoki Eshima, Yuusuke Sakai, and Ichiro Takagi
  • Journal Title: Nonlinear Analysis Series B: Real World Applications, Elsevier Science Volume: 14 Pages: 1-18
  • DOI: 10.1016/j.nonrwa.2013.04.001
  • Peer Reviewed
• [Book] A Mathematical-Modeling Approach to Urbanization Caused by Migration, in ''Urbanization: Global Trends, Role of Climate Change and Effects on Biodiversity'' (2014)
  • Author(s): M. Tabata, N. Eshima, and I. Takagi
  • Total Pages: 250
  • Publisher: Nova Science Publishers, Inc.
• [Book] A Stochastic Agent-Based Approach to Interregional Migration in Quantitative Sociodynamics, "Mathematical Modelling in Social Sciences and Engineering" (2014)
  • Author(s): M. Tabata, N. Eshima, Keiko Kanenoo, and I. Takagi
  • Total Pages: 200
  • Publisher: Nova Science Publishers, Inc.
• [Book] A Stochastic Agent-Based Approach to Interregional Migration in Quantitative Sociodynamics, "Mathematical Modelling in Social Sciences and Engineering" (2014)
  • Author(s): Minoru Tabata, Nobuoki Eshima, Keiko Kanenoo, and Ichiro Takagi
  • Total Pages: 10
  • Publisher: Nova Science Publishers, Inc.
• [Book] A Mathematical-Modeling Approach to Urbanization Caused by Migration, in ''Urbanization: Global Trends, Role of Climate Change and Effects on Biodiversity'' (2014)
  • Author(s): Minoru Tabata, Nobuoki Eshima, and Ichiro Takagi
  • Total Pages: 10
  • Publisher: Nova Science Publishers, Inc.