Theory of global asymptotic stability on the basic reproduction number of epidemic mathematical models

• Project/Area Number: 24540219
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Global analysis
• Research Institution: Waseda University
• Principal Investigator: MUROYA YOSHIAKI 早稲田大学, 理工学術院, 名誉教授 (90063718)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000); Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: 関数方程式の大域理論 / 数理モデル / 感染症モデル / 大域漸近安定性 / Lyapunov 関数法 / 関数方定式の大域理論

Outline of Final Research Achievements

We have established much contribution to the theory of global asymptotic stability on multi-group SIRS epidemic models, SIS epidemic models with patch structure, HIV virus disease models and related Lotka-Volterra systems, which are contained new analytical techniques on permanence and the existence of the endemic equilibrium of model by applying the recent results on the global stability by the basic reproduction number of epidemic model.

Research Products

• [Journal Article] A Lotka-Volterra system with patch structure (related to a multi-group SI epidemic model), (2015)
  • Author(s): [1] Y. Muroya
  • Journal Title: DCDS-Series-S as CJS 2013 Proceedings Volume: 印刷中
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Global stability for a delayed multi-group SIRS epidemic model with cure rate and incomplete recovery rate (2015)
  • Author(s): [2] Y. Muroya and T. Kuniya
  • Journal Title: Intern. J. Biomath. Volume: 印刷中 Issue: 04 Pages: 1550048-1550048
  • DOI: 10.1142/s1793524515500485
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] On global stability of an HIV pathogenesis model with cure rate (2015)
  • Author(s): Yoichi Enatsu
  • Journal Title: Mathematical Methods in the Applied Sciences Volume: 印刷中 Issue: 17 Pages: 4001-4018
  • DOI: 10.1002/mma.3334
  • Description: 掲載確定
  • Peer Reviewed
• [Journal Article] Stability of epidemic models with waning immunity (2015)
  • Author(s): [4] Y. Nakata, Y. Enatsu, H. Inaba, T. Kuniya, Y. Muroya and Y. Takeuchi
  • Journal Title: SUT Journal of Mathematics Volume: 50 Pages: 205-245
  • NAID: 120006397889
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] A delayed multi-group SIS epidemic model with nonlinear incidence rates and patch structure (2015)
  • Author(s): [5] Y. Muroya, T. Kuniya and J. Wang
  • Journal Title: J. Math. Anal. Appl. Volume: 425 Issue: 1 Pages: 415-439
  • DOI: 10.1016/j.jmaa.2014.12.019
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Global attractivity and extinction for Lotka-Volterra systems with infinite delay and feedback controls (2015)
  • Author(s): T. Faria, Y. Muroya
  • Journal Title: Proceedings of the Royal Society of Edinburgh: Section A Volume: 印刷中
  • Peer Reviewed
• [Journal Article] Global stability of nonresident computer virus models (2015)
  • Author(s): Y. Muroya, T. Kuniya
  • Journal Title: Math. Methods Appl. Sciences Volume: 印刷中
  • Peer Reviewed
• [Journal Article] Threshold dynamics of an SIR epidemic model with a hybrid of multi-group and patch structures (2014)
  • Author(s): [6] T. Kuniya, Y. Muroya and Y. Enatsu
  • Journal Title: Math. Bios. Eng. Volume: 11 Issue: 6 Pages: 1375-1393
  • DOI: 10.3934/mbe.2014.11.1375
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Further stability analysis of a multi-group SIRS epidemic model with varying total population sizes (2014)
  • Author(s): [7] Y. Muroya and T. Kuniya
  • Journal Title: Appl. Math. Letters Volume: 38 Pages: 73-78
  • DOI: 10.1016/j.aml.2014.07.005
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Global stability of a delayed nonlinear Lotka-Volterra system with feed-back controls and patch structure (2014)
  • Author(s): [1] Y. Muroya
  • Journal Title: Appl. Math. Comput. Volume: 印刷中 Pages: 60-73
  • DOI: 10.1016/j.amc.2014.04.036
  • Peer Reviewed
• [Journal Article] Global stability of a multi-group SIS epidemic model concerning population migration (2014)
  • Author(s): [2] T. Kuniya, Y. Muroya
  • Journal Title: Discrete and Continuous Dynamical Systems-Series B Volume: 19 Issue: 4 Pages: 1105-1118
  • DOI: 10.3934/dcdsb.2014.19.1105
  • Peer Reviewed
• [Journal Article] On global stability of a nonresident computer virus model (2014)
  • Author(s): Y. Muroya. H. Li, T. Kuniya
  • Journal Title: Acta Math. Scientia Volume: 印刷中
  • Peer Reviewed
• [Journal Article] Complete global analysis of an SIRS epidemic model with graded cure rate and incomplete recovery rate (2014)
  • Author(s): Y. Muroya, H. Li, T. Kuniya
  • Journal Title: J. Math. Anal. Appl. Volume: 410 Issue: 2 Pages: 719-732
  • DOI: 10.1016/j.jmaa.2013.08.024
  • Peer Reviewed
• [Journal Article] Global stability of a delayed HTLV-I infection model with a class of nonlinear incidence rate and CTLs immune respons. (2013)
  • Author(s): [1] Y. Muroya, Y. Enatsu, H. Li
  • Journal Title: Appl. Math. Comput. Volume: _______ Issue: 21 Pages: 10559-10573
  • DOI: 10.1016/j.amc.2013.03.081
  • Peer Reviewed
• [Journal Article] Global stability of a delayed SIRS computer virus propagation model (2013)
  • Author(s): Yoichi Enatsu
  • Journal Title: International Journal of Computer Mathematics Volume: (掲載碓定) Issue: 3 Pages: 347-367
  • DOI: 10.1080/00207160.2013.790534
  • Peer Reviewed
• [Journal Article] A simple discrete-time analogue preserving the global stability of a continuous-time SIRS epidemic model (2013)
  • Author(s): Yoichi Enatsu, Yoshiaki Muroya
  • Journal Title: International Journal of Biomathematics Volume: 6 Issue: 02 Pages: 1350001-1350001
  • DOI: 10.1142/s1793524513500010
  • Peer Reviewed
• [Journal Article] Global stability for a class of multi-group SIR epidemic models with patches throuth migration and cross patch infection. (2013)
  • Author(s): [4] Y. Muroya, Y. Enatsu, T. Kuniya
  • Journal Title: Acta Math. Scientia Volume: 33 Pages: 341-361
  • Peer Reviewed
• [Journal Article] Global stability for a multi-group SIRS epidemic model with varying population sizes (2013)
  • Author(s): KUNIYA, Toshikazu
  • Journal Title: Nonlinear Analysis: Real World Applications Volume: 14 Issue: 3 Pages: 1693-1704
  • DOI: 10.1016/j.nonrwa.2012.11.005
  • Peer Reviewed
• [Journal Article] A note on the global stability of an SEIR epidemic model with constant latency time and infectious period (2013)
  • Author(s): Yoshiaki Muroya, Yoichi Enatsu, Huaixing Li
  • Journal Title: Discrete and Continuous Dynamical Systems B Volume: 18 Issue: 1 Pages: 173-183
  • DOI: 10.3934/dcdsb.2013.18.173
  • Peer Reviewed
• [Journal Article] A discrete-time analogue preserving the global stability of a continuous SEIS epidemic model. (2012)
  • Author(s): [5] Y. Muroya, Y. Enatsu
  • Journal Title: J. Differ. Equ. Appl. Volume: _______ Issue: 9 Pages: 1463-1482
  • DOI: 10.1080/10236198.2012.757602
  • Peer Reviewed
• [Journal Article] Complete global dynamics of a delyed viral infection model with lytic and non lytic effectors. (2012)
  • Author(s): [8] Y. Nakata, Y. Enatsu, Y. Muroya
  • Journal Title: Sociedad Esoanola de mathematica Applicada (SeMA) Journal Volume: 60 Pages: 27-50
  • Peer Reviewed
• [Presentation] Global stability of SIRS epidemic models and related models (2015)
  • Author(s): Yoshiaki Muroya, Toshikazu Kuniya and Yoichi Enatsu
  • Organizer: Seminar, Department of Mathematics
  • Place of Presentation: University of Pannonia, Veszprem, Hungary
  • Year and Date: 2015-02-02
  • Invited
• [Presentation] Global stability of SIRS epidemic models and related models (2015)
  • Author(s): Yoshiaki Muroya , Toshikazu Kuniya and Yoich Enatsu
  • Organizer: Seminar of EPIDELAY, Boliyai institute
  • Place of Presentation: University of Szeged, Hungary
  • Year and Date: 2015-01-22
  • Invited
• [Presentation] Global stability of multi-group SIRS epidemic models (2014)
  • Author(s): 室谷義昭(早稲田大学基幹理工学部数学科)、國谷紀良(神戸大学院システム情報学研究科)
  • Organizer: ２７年度合同応用数学研究会
  • Place of Presentation: 龍谷大学瀬田キャンパス
  • Year and Date: 2014-12-18
• [Presentation] Lyapunov function techniques to analyze the global stability of some epidemic (2013)
  • Author(s): Y. Muroya, joint work with Y. Enatsu, K. Kuniya
  • Organizer: Centro de Mathematica e Applicacoes Fundamentais (CMAF)
  • Place of Presentation: CMAF リスボン大学・ポルトガル
  • Invited
• [Presentation] Global stability of epidemic models (感染症モデルの大域安定性）. (2012)
  • Author(s): 室谷義昭
  • Organizer: 第３７回応用数学研究会
  • Place of Presentation: 福岡教育大学・数学教室
• [Presentation] SIRS 感染症モデルの大域安定性 (2012)
  • Author(s): 室谷義昭
  • Organizer: 第41 回数値解析シンポジウム
  • Place of Presentation: 伊香保温泉よろこびの宿 しん喜
• [Presentation] On global stability of SIRS epidemic models with nonlinear incidence rates and delays. (2012)
  • Author(s): Y. Muroya joint work with Y. Enatsu
  • Organizer: 2012 1st China-Japan-Korea International Conference on Mathematical Biology)
  • Place of Presentation: Busan, Korea
• [Presentation] Influence of feedback controls to Lotka-Volterra systems with patch structure.
  • Author(s): 室谷義昭
  • Organizer: 第 10 回「生物数学の理論とその応用」
  • Place of Presentation: 京都大学数理解析研究所 420 号室
• [Presentation] On global dynamics of Lotka-Volterra systems and SIR epidemic models
  • Author(s): 室谷義昭
  • Organizer: 第２回岐阜数理科学研究会
  • Place of Presentation: 飛騨高山まちの博物館研修室
  • Invited
• [Presentation] Global stability of Lotka-Volterra systems with infinite delays and feedback controls
  • Author(s): Yoshiaki Muroya
  • Organizer: Czech-Japanese Seminar in Applied Mathematics 2013 (CJS2013)
  • Place of Presentation: 明治大学中野キャンパス
• [Presentation] Delayed Lotka-Volterra systems with feedback controls and Multi-group epidemic models
  • Author(s): 室谷義昭
  • Organizer: 第38 回応用数学研究集会
  • Place of Presentation: 福岡教育大学自然科学教棟 数学講義・演習室
• [Presentation] 遅延微分方程式に支配される個体群動態モデルの解の漸近挙動とその応用
  • Author(s): 江夏洋一、室谷義昭
  • Organizer: 情報数理セミナー[2013/06/07(金), 東邦大学]
  • Place of Presentation: 東邦大学
  • Invited