時間遅れを含む微分方程式系の大域的安定性とその医学への応用

2010 Fiscal Year Annual Research Report

• Project/Area Number: 22540122
• Research Institution: Shizuoka University
• Principal Investigator: 竹内 康博 静岡大学, 創造科学技術大学院, 教授 (20126783)
• Keywords: 応用数学 / 解析学 / 関数方程式論 / 生態学 / 時間遅れ / 安定性

Research Abstract

(1) 感染症の伝播を記述する数理モデルにおいて,感染症伝播関数を従来用いられていた関数形を特殊な場合として含む一般的な関数形に拡張して,数理モデルの定性的な性質を解明した.感染症が拡大する条件が伝播関数形によらず基本再生産数で決定されることを明らかにした.このことにより,個々の感染症の伝播形式ではなく,基本再生産数を求めることが感染症防御のために重要であることを明らかにした(Journal of Mathematical Biology).
(2) HIV感染症における時間遅れの影響を検討した.HIVがCD4T細胞中で複製されるまでの時間やの免疫反応が惹起されるための時間遅れを考察した.その結果このような時間遅れを導入してもHIVダイナミクスは基本再生産数で定性的に決定されることを示した.このような性質は一般化された非線形関数を仮定しても成り立つことが示された.(Bulletin of Mathematical Biology, July, (2010) 72,5 : 1192-1207, SIAM Journal on Applied Mathematics. Volume 70, Issue 7, pp.2693-2708 (10 August 2010)).

Research Products

• [Journal Article] A Dynamic Model Describing Heterotrophic Culture of Chlorella and Its Stability Analysis (2011)
  • Author(s): Y.Zhang, W.Ma, H.Yan, Y.Takeuchi
  • Journal Title: Mathematical Biosciences and Engineering Volume: 8 Pages: 1117-1133
  • Peer Reviewed
• [Journal Article] Global Analysis on Delay Epidemiological Dynamic Models with Nonlinear Incidence (2011)
  • Author(s): Gang Huang, Yasuhiro Takeuchi
  • Journal Title: Journal of Mathematical Biology Volume: 63 Pages: 125-139
  • Peer Reviewed
• [Journal Article] Threshold Dynamics in a Periodic SVEIR Epidemic Model (2011)
  • Author(s): J.Wang, S.Liu, Y.Takeuchi
  • Journal Title: International Journal of Biomathematics Volume: 4 Pages: 493-509
  • Peer Reviewed
• [Journal Article] Global Analysis for Delay Virus Dynamics Model with Beddington-DeAnegelis Functional Response (2011)
  • Author(s): Gang Huang, Wanbiao Ma, Yasuhiro Takeuchi
  • Journal Title: Applied Mathematics Letters Volume: 24 Pages: 1199-1203
  • Peer Reviewed
• [Journal Article] Impact of Intracellular Delay, Immune Activation Delay and Nonlinear Incidence on Viral Dynamics (2011)
  • Author(s): Gang Huang, Hiroki Yokoi, Yasuhiro Takeuchi, T.Kajiwara, T.Sasaki
  • Journal Title: Japan Journal of Industrial and Applied Mathematics
  • Peer Reviewed
• [Journal Article] SVEIR epidemiological model with varying infectivity and distributed delay (2011)
  • Author(s): Jinliang Wang, Gang Huang, Yasuhiro Takeuchi, Shengqiang Liu
  • Journal Title: Mathematical Biosciences and Engineering
  • Peer Reviewed
• [Journal Article] Dynamics of the Density Dependent Predator-Prey System with Beddington-DeAngelis Functional Response (2011)
  • Author(s): Haiyin Li, Yasuhiro Takeuchi
  • Journal Title: Journal of Applied Mathematics and Applications Volume: 374 Pages: 644-654
  • Peer Reviewed
• [Journal Article] Adaptive evolution of foraging-related traits in a predator-prey community (2011)
  • Author(s): Jian Zu, Masayasu Mimura, Yasuhiro Takeuchi
  • Journal Title: Journal of Theoretical Biology Volume: 268 Pages: 14-29
  • Peer Reviewed
• [Journal Article] Infection Threshold for an Epidemic Model in Site and Bond Percolation Worlds (2010)
  • Author(s): Yukio Sakisaka, Jin Yoshimura, Yasuhiro Takeuchi, Koji Sugiura, Kei-ichi Tainaka
  • Journal Title: J.Phys.Soc.Jpn Volume: 79 Pages: 023002-1-023002-4
  • Peer Reviewed
• [Journal Article] Global Stability for Delay SIR and SEIR Epidemic Models with Nonlinear Incidence Rate (2010)
  • Author(s): Gang Huang, Y.Takeuchi, Wanbiao Ma, Daijun Wei
  • Journal Title: Bulletin of Mathematical Biology Volume: 72 Pages: 1192-1207
  • Peer Reviewed
• [Journal Article] Lyapunov Functionals for Delay Differential Equations Model of Viral Infections (2010)
  • Author(s): Gang Huang, Yasuhiro Takeuchi, Wanbiao Ma
  • Journal Title: SIAM Journal on Applied Mathematics Volume: 70 Pages: 2693-2708
  • Peer Reviewed
• [Presentation] Paradox of vaccination (2010)
  • Author(s): Yasuhiro Takeuchi
  • Organizer: International Workshop on Mathematics for Biology
  • Place of Presentation: Posco International Center, POSTECH, Korea
  • Year and Date: 20100712-13
• [Presentation] Paradox of vaccination (2010)
  • Author(s): Yasuhiro Takeuchi
  • Organizer: 湖北民俗学院
  • Place of Presentation: 中国,湖北民俗学院
  • Year and Date: 2010-12-20
• [Presentation] Paradox of vaccination (2010)
  • Author(s): Yasuhiro Takeuchi
  • Organizer: 気候変動と感染症ダイナミクスに関するカナダ-中国国際会議
  • Place of Presentation: 中国,南京師範大学
  • Year and Date: 2010-12-17
• [Presentation] Paradox of vaccination (2010)
  • Author(s): Yasuhiro Takeuchi
  • Organizer: 青山数理セミナー,25 October, 2010
  • Place of Presentation: 神奈川県,青山学院大学理工学部
  • Year and Date: 2010-10-25
• [Presentation] Paradox of vaccination (2010)
  • Author(s): Yasuhiro Takeuchi
  • Organizer: The Third China-Japan Colloquium of Mathematical Biology (CJCMB3)
  • Place of Presentation: Beijing, Sea North Green Garden
  • Year and Date: 2010-10-18
• [Presentation] 数理モデルによる感染症危機管理への提言 (2010)
  • Author(s): 竹内康博
  • Organizer: 平成22年全国大学保健管理協会東海北陸地方部会研究集会
  • Place of Presentation: 静岡,B-nest静岡市産学交流センター
  • Year and Date: 2010-07-22