Global stability for the system of ordinary differential equations with time delays and its applications to medicine

2013 Fiscal Year Final Research Report

• Project/Area Number: 22540122
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Aoyama Gakuin University (2012-2013); Shizuoka University (2010-2011)
• Principal Investigator: YASUHIRO Takeuchi 青山学院大学, 理工学部, 教授 (20126783)
• Co-Investigator(Renkei-kenkyūsha): OHTSUKI Kohichi 京都産業大学, 先端科学技術研究所, 教授 (00032293) ; KAJIWARA Tsuyoshi 岡山大学, 環境科学研究科, 教授 (50169447) ; KOYANAGI Yoshio 京都大学, ウイルス研究所, 准教授 (80215417) ; SASAKI Tohru 岡山大学, 環境科学研究科, 准教授 (20260664)
• Project Period (FY): 2010-04-01 – 2014-03-31
• Keywords: 数理医学モデル / 時間遅れ / 大域的安定性

Research Abstract

It has been constructed a general basic mathematical model for the propagation of epidemics. Further time delay (describing incubation period, time for immune system to be activated) is introduced into the basic model and considered its effect on the global dynamics of the model. Especially, the mathematical structure of the model ensuring the global asymptotic stability under the effect of time delay is obtained.
The research for four years shows how to construct Lyapunov function (functional) to ensure the global stability of the basic mathematical model.

Research Products

• [Journal Article] Permanence and Stability of the Model for Slave-Maker Ants (2014)
  • Author(s): Kyouiti Sugiura, Yasuhiro Takeuchi
  • Journal Title: Far East Journal of Applied Mathematics Volume: (accepted)
  • Peer Reviewed
• [Journal Article] Apoptosis in Virus Infection Dynamics Models (2014)
  • Author(s): Ruili Fan, Yueping Dong, Gang Huang and Yasuhiro Takeuchi
  • Journal Title: Journal of Biological Dynamics Volume: Vol.8, No.1 Pages: 20-41
  • Peer Reviewed
• [Journal Article] A mathematical model helper T cells in a tumor immune system (2014)
  • Author(s): Yueping Dong, Rinko Miyazaki and Yasuhiro Takeuchi
  • Journal Title: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS SERIES B Volume: Volume 19, Number 1 Pages: 55-72
  • Peer Reviewed
• [Journal Article] Impulsive Control of Multiple Lotka-Volterra Systems (2013)
  • Author(s): Lingzhen Dong and Y. Takeuchi
  • Journal Title: Nonlinear Analysis, RWA. Volume: 14 Pages: 1144-1154
  • Peer Reviewed
• [Journal Article] Qualitative and Bifurcation analysis on an SIR model with a saturated treatment function (2012)
  • Author(s): J. Wang, S. Liu, B. Zheng, Y. Takeuchi
  • Journal Title: Mathematical and Computer Modelling Volume: 55 Pages: 710-722
  • Peer Reviewed
• [Journal Article] Global Stability for Epidemic Model With Constant Latency and Infectious Periods (2012)
  • Author(s): G. Huang, E. Beretta and Y. Takeuchi
  • Journal Title: Mathematical Biosciences and Engineering Volume: 9, 2 Pages: 297-312
  • Peer Reviewed
• [Journal Article] Construction of Lyapunov functionals for delay differential equations in virology and epidemiology (2012)
  • Author(s): T. Kajiwara, T. Sasaki and Y. Takeuchi
  • Journal Title: Nonlinear Analysis Series B : Real World Applications Volume: 13 Pages: 1802-1826
  • Peer Reviewed
• [Journal Article] Lyapunov Functions and Global Stability for Age-Structured HIV Infection Model (2012)
  • Author(s): G. Huang, X. Liu, Y. Takeuchi
  • Journal Title: SIAM Journal on Applied Mathematics Volume: 72, 1 Pages: 25-38
  • Peer Reviewed
• [Journal Article] HIV evolution and progression of the infection to AIDS (2012)
  • Author(s): G. Huang, Y. Takeuchi, Andrei Korobeinikov
  • Journal Title: Journal of Theoretical Biology Volume: 307 Pages: 149-159
  • Peer Reviewed
• [Journal Article] Stability Conditions for a Class of Delay Differential Equations in Single Species Dynamics (2012)
  • Author(s): G. Huang, Y. Takeuchi, R. Miyazaki
  • Journal Title: Discrete and Continuous Dynamical Systems Series B Volume: 17, 7 Pages: 2451-2464
  • Peer Reviewed
• [Journal Article] Threshold Dynamics in a Periodic SVEIR Epidemic Model (2011)
  • Author(s): J. Wang, S. Liu and Y. Takeuchi
  • Journal Title: Int. J. of Biomathematics Volume: 4, 4 Pages: 493-509
  • Peer Reviewed
• [Journal Article] Dynamics of an SIQS epidemic model with transport-related infection and exit-entry screenings (2011)
  • Author(s): X. Liu, X. Chen, Y. Takeuchi
  • Journal Title: Journal of Theoretical Biology Volume: 285, 1 Pages: 25-35
  • Peer Reviewed
• [Journal Article] Impact of Intracellular Delay, Immune Activation Delay and Nonlinear Incidence on Viral Dynamics (2011)
  • Author(s): G. Huang, H. Yokoi, Y. Takeuchi, T. Kajiwara, T. Sasaki
  • Journal Title: Japan J. of Industrial and Applied Math. Volume: 28, 3 Pages: 383-411
  • Peer Reviewed
• [Journal Article] SVEIR epidemiological model with varying infectivity and distributed delays (2011)
  • Author(s): J. Wang, G. Huang, Y. Takeuchi and S. Liu
  • Journal Title: Mathematical Biosciences and Engineering Volume: 8, 3 Pages: 875-888
  • Peer Reviewed
• [Journal Article] Global Analysis on Delay Epidemiological Dynamic Models with Nonlinear Incidence (2011)
  • Author(s): G. Huang, Y. Takeuchi
  • Journal Title: J. Math. Biol. Volume: 63, 1 Pages: 125-139
  • Peer Reviewed
• [Journal Article] Global Analysis for Delay Virus Dynamics Model with Beddington-DeAngelis Functional Response (2011)
  • Author(s): G. Huang, W. Ma, Y. Takeuchi
  • Journal Title: Applied Mathematics Letters Volume: 24/7 Pages: 1199-1203
  • Peer Reviewed
• [Journal Article] Global Stability for Delay SIR and SEIR Epidemic Models with Nonlinear Incidence Rate (2010)
  • Author(s): G. Huang, Y. Takeuchi, W. Ma and D. Wei
  • Journal Title: Bulletin of Mathematical Biology Volume: 72, 5 Pages: 1192-1207
  • Peer Reviewed
• [Journal Article] Lyapunov Functionals for Delay Differential Equations Model of Viral Infections (2010)
  • Author(s): G. Huang, Y. Takeuchi, W. Ma
  • Journal Title: SIAM Journal on Applied Mathematics Volume: 70, 7 Pages: 2693-2708
  • Peer Reviewed
• [Journal Article] Infection Threshold for an Epidemic Model in Site and Bond Percolation Worlds (2010)
  • Author(s): Y. Sakisaka, J. Yoshimura, Y. Takeuchi, K. Sugiura and K. Tainaka
  • Journal Title: J. Phys. Soc. Jpn Volume: 79 (2) Pages: 023002-1-023002-4
  • Peer Reviewed
• [Journal Article] Adaptive evolution of anti-predator effort promotes the diversity of prey species
  • Author(s): J. Zu and Y. Takeuchi
  • Journal Title: BioSystems Volume: (in press)
  • Peer Reviewed
• [Journal Article] Global asymptotic stability for HIV-1 dynamics with two distributed delays
  • Author(s): J. Wang, G. Huang, Y. Takeuchi
  • Journal Title: Mathematical Medicine and Biology-A JOURNAL OF THE IMA Volume: (in press)
  • Peer Reviewed
• [Journal Article] A multi-group SVEIR epidemic models with distributed delays and vaccination
  • Author(s): J. Wang, Y. Takeuchi and S. Liu
  • Journal Title: International Journal of Biomathematics Volume: Vol.5, No.3
  • DOI: 10.1142/S1793524512600017
  • Peer Reviewed
• [Presentation] Construction of Lyapunov functions of models for infectious diseases in vivo : from simple models to complex models (2014)
  • Author(s): Yasuhiro Takeuchi
  • Organizer: International workshop on biomathematical modelling and its dynamical analyis
  • Place of Presentation: Heilongjiang University, Harbin
  • Year and Date: 20140111-13
• [Presentation] Impact of Intracellular Delay, Immune Activation Delay and Nonlinear Incidence on Viral Dynamics (2013)
  • Author(s): Yasuhiro Takeuchi
  • Organizer: 数理生物学におけるホットトピックスに関する2013年国立数理科学研究所ワークショップ, 2013年韓国数理生物学会
  • Place of Presentation: 韓国、大田3
  • Year and Date: 20130602-05, 20130821-23
• [Presentation] Impact of Intracellular Delay, Immune Activation Delay and Nonlinear Incidence on Viral Dynamics (2013)
  • Author(s): Yasuhiro Takeuchi
  • Organizer: 第19回差分方程式と応用に関する国際会議
  • Place of Presentation: オマーン、マスカット
  • Year and Date: 20130527-31
• [Presentation] The effect of Intracellular Delay, Immune Activation Delay and Nonlinear Incidence on Viral Dynamics (2012)
  • Author(s): Yasuhiro Takeuchi
  • Organizer: WORKSHOP ON DYNAMIC MODELS IN MEDICAL AND BIOLOGICAL SCIENCES
  • Place of Presentation: USTB
  • Year and Date: 20120110-11
• [Presentation] The effect of Intracellular Delay, Immune Activation Delay and Nonlinear Incidence on Viral Dynamics (2011)
  • Author(s): Yasuhiro Takeuchi
  • Organizer: Modeling and Analysis in the Life Sciences : A ReaDiLab Conference in Tokyo
  • Year and Date: 20111128-30
• [Presentation] The effect of Intracellular Delay, Immune Activation Delay and Nonlinear Incidence on Viral Dynamics (2011)
  • Author(s): Yasuhiro Takeuchi
  • Organizer: International Conference on Analytic Mathematics and its Applications
  • Place of Presentation: Xinyang Normal University, Xinyang, Henan, China
  • Year and Date: 20110808-12
• [Presentation] Impact of Intracellular Delay, Immune Activation Delay and Nonlinear Incidence on Viral Dynamics (2011)
  • Author(s): Yasuhiro Takeuchi
  • Organizer: The 5th Geoffrey J. Butler Memorial Conference on Differential Equations and Population Biology
  • Place of Presentation: University of Alberta, Edmonton
  • Year and Date: 20110725-30
• [Presentation] The effect of intracellular delay, immune activation delay and nonlinear incidence on viral dynamics (2011)
  • Author(s): Yasuhiro Takeuchi
  • Organizer: Mathematical Ecology Workshop: A satellite symposium for the Symposium of Asian Biodiversity Symposium for the 100 yeas anniversary of Kyushu University
  • Place of Presentation: Large meeting room, Faculty of Sciences, Kyushu University (Hakozaki campus)
  • Year and Date: 2011-11-20
• [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ー中国国際会議, 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: Nanjing Normal University, Nanjing, China. 29, 静岡
  • Year and Date: 20101215-18, 20100722
• [Presentation] Paradox of vaccination (2010)
  • Author(s): Yasuhiro Takeuchi
  • Organizer: The Third China-Japan Colloquium of Mathematical Biology (CJCMB3)
  • Place of Presentation: Beijing
  • Year and Date: 20101018-21
• [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
  • Place of Presentation: Beijing Normal University
  • Year and Date: 2010-10-22
• [Book] 「理論生物学の基礎」,第1章生物の個体数変動論(竹内担当) (2012)
  • Author(s): 関村利朗,山村則男編
  • Total Pages: 1-43
  • Publisher: 海游舎