Faculty Information

（Last updated : 2024-09-27 16:36:17）

NAKATA Yukihiko
Department Aoyama Gakuin University Department of Mathematical Sciences, College of Science and Engineering

Position Associate Professor

■ Specialization and related fields

Mathematical analysis, Basic mathematics (Key Word：Delay differential equations, Dynamical systems, Mathematical biology)

■ Academic background

1.	Waseda University Graduated
2.	Waseda University
3.	Waseda University〔Master Course〕 Completed
4.	Waseda University
5.	Waseda University〔Doctorial Course〕 Completed
6.	Waseda University
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■ Business career

1.	2010/06～2012/05	Basque Center for Applied Methematics
2.	2012/06～2014/03	University of Szeged, Bolyai Institute
3.	2020/04～2021/03	Aoyama Gakuin University College of Science and Engineering Department of Physics and Mathematics Associate Professor
4.	2021/04～	Aoyama Gakuin University College of Science and Engineering Department of Mathematical Sciences Associate Professor

■ Book and thesis

1.	Article	A note on blow-up solutions for a scalar differential equation with a discrete delay Japan Journal of Industrial and Applied Mathematics 39(3),pp.959-971 (Collaboration) 2022
2.	Article	Correction to: A note on blow-up solutions for a scalar differential equation with a discrete delay Japan Journal of Industrial and Applied Mathematics 39(3),pp.1109-1109 (Collaboration) 2022
3.	Article	Estimating the comprehensive overview of Oncorhynchus masou virus disease outbreak in Rainbow trout using mortality data: Coupling data on experimental infection and field observation by mathematical modeling Aquaculture 554,pp.738165 (Collaboration) 2022
4.	Article	Delay-induced blow-up in a planar oscillation model Japan Journal of Industrial and Applied Mathematics 38(3),pp.1037-1061 (Collaboration) 2021
5.	Article	Note on the uniqueness of an endemic equilibrium of an epidemic model with boosting of immunity Journal of Biological Systems 29(02),pp.291-302 (Collaboration) 2021
6.	Article	An explicit periodic solution of a delay differential equation Journal of Dynamics and Differential Equations 32(1),pp.163-179 (Single) 2020
7.	Article	Pharmacological interventions for preventing clotting of extracorporeal circuits during continuous renal replacement therapy Cochrane Database of Systematic Reviews (12),pp.CD012467 (Collaboration) 2020
8.	Article	The age distribution of mortality from novel coronavirus disease (COVID-19) suggests no large difference of susceptibility by age Scientific Reports 10(1),pp.16642 (Collaboration) 2020
9.	Article	Dialysate temperature reduction for intradialytic hypotension for people with chronic kidney disease requiring haemodialysis (Collaboration) 2019
10.	Article	Epidemic dynamics with a time-varying susceptibility due to repeated infections Journal of Biological Dynamics 13(1),pp.567-585 (Collaboration) 2019
11.	Article	Stability analysis of a state-dependent delay differential equation for cell maturation: analytical and numerical methods Journal of Mathematical Biology 79(1),pp.281-328 (Collaboration) 2019
12.	Article	The change of susceptibility following infection can induce failure to predict outbreak potential by $\mathcal{R}_{0}$ Mathematical Biosciences and Engineering 16(2),pp.813-830 (Collaboration) 2019
13.	Article	Delay-induced blow-up in an oscillation model (Succession and Innovation of Studies on ODEs in Real Domains) pp.18-24 (Collaboration) 2018
14.	Article	Dynamics of an ultra-discrete SIR epidemic model with time delay Mathematical Biosciences and Engineering 15,pp.653-666 (Collaboration) 2018
15.	Article	Global stability of an SIS epidemic model with a finite infectious period Differential Integral Equations 31,pp.161-172 (Collaboration) 2018
16.	Article	Third‐line systemic chemotherapy for small cell lung cancer Cochrane Database of Systematic Reviews (Collaboration) 2018
17.	Article	Unbounded and blow-up solutions for a delay logistic equation with positive feedback Communications on Pure & Applied Analysis 17(6),pp.2845-2854 (Collaboration) 2018
18.	Article	Convergence of a logistic type ultra-discrete model 2017,pp.7893049 (Collaboration) 2017
19.	Article	Ultrasonography for confirmation of gastric tube placement Cochrane Database of Systematic Review (Collaboration) 2017
20.	Article	Note on stability conditions for structured population dynamics models Electronic Journal of Qualitative Theory of Differential Equations 78,pp.1-14 (Single) 2016
21.	Article	Note on stability of an SIRS epidemic model 数理解析研究所講究録 1994,pp.6-11 (Single) 2016
22.	Article	On the characteristic equation $\lambda =\alpha _{1}+(\alpha _{2}+\alpha _{3}\lambda )e^{-\lambda }$ and its use in the context of a cell population model Journal of Mathematical Biology 72(4),pp.877-908 (Collaboration) 2016
23.	Article	Delay equation formulation for an epidemic model with waning immunity: an application to mycoplasma pneumoniae IFAC-PapersOnLine 48(18),pp.132-135 (Collaboration) 2015
24.	Article	Global analysis for spread of infectious diseases via transportation networks Journal of Mathematical Biology 70,pp.1411-1456 (Collaboration) 2015
25.	Article	Global dynamics of a delay differential system of a two-patch SIS-model with transport-related infections Mathematica Bohemica 140(2),pp.171-193 (Collaboration) 2015
26.	Article	The determinant of periodicity in Mycoplasma pneumoniae incidence: an insight from mathematical modelling Scientific Reports 5(1),pp.14473 (Collaboration) 2015
27.	Article	Transmission dynamics and final epidemic size of Ebola Virus Disease outbreaks with varying interventions PLOS ONE 10(7),pp.e0131398 (Collaboration) 2015
28.	Article	Visualisation of stability regions for logistic difference equations with multiple delays 数理解析研究所講究録 (1937),pp.32-41 (Collaboration) 2015
29.	Article	Malaria dynamics with long incubation period in hosts 68(9),pp.915-930 (Collaboration) 2014
30.	Article	Stability analysis of a renewal equation for cell population dynamics with quiescence SIAM Journal on Applied Mathematics 74(4),pp.1266-1297 (Collaboration) 2014
31.	Article	Stability and bifurcation analysis of epidemic models with saturated incidence rates: An application to a nonmonotone incidence rate Mathematical Biosciences and Engineering 11(4),pp.785-805 (Collaboration) 2014
32.	Article	Stability of epidemic models with waning immunity SUT Journal of Mathematics 50(2),pp.205-245 (Collaboration) 2014
33.	Article	Global dynamics of two-compartment models for cell production systems with regulatory mechanisms Mathematical Biosciences 245(2),pp.258-268 (Collaboration) 2013
34.	Article	Complete global dynamics of a delayed viral infection model with lytic and nonlytic effectors SeMA Journal 60(1),pp.27-50 (Collaboration) 2012
35.	Article	Global dynamics of a delayed SIRS epidemic model with a wide class of nonlinear incidence rates Journal of Applied Mathematics and Computing 39,pp.15-34 (Collaboration) 2012
36.	Article	Global dynamics of difference equations for SIR epidemic models with a class of nonlinear incidence rates Journal of Difference Equations and Applications 18(7),pp.1163-1181 (Collaboration) 2012
37.	Article	Global stability for a discrete epidemic model for disease with immunity and latency spreading in a heterogeneous host population Nonlinear Analysis: Real World Applications 13(1),pp.258-274 (Collaboration) 2012
38.	Article	Global stability for a discrete SIS epidemic model with immigration of infectives Journal of Difference Equations and Applications 18(11),pp.1913-1924 (Collaboration) 2012
39.	Article	Global stability of SIRS epidemic models with a class of nonlinear incidence rates and distributed delays Acta Mathematica Scientia 32(3),pp.851-865 (Collaboration) 2012
40.	Article	Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model Nonlinear Analysis: Real World Applications 13(5),pp.2120-2133 (Collaboration) 2012
41.	Article	On a generalization of the global attractivity for a periodically forced Pielou's equation 18(3),pp.375-396 (Collaboration) 2012
42.	Article	Permanence and extinction for a nonautonomous SEIRS epidemic model Applied Mathematics and Computation 218(18),pp.9321-9331 (Collaboration) 2012
43.	Article	Stability analysis of delayed SIR epidemic models with a class of nonlinear incidence rates Applied Mathematics and Computation 218(9),pp.5327-5336 (Collaboration) 2012
44.	Article	Stability analysis of multi-compartment models for cell production systems Journal of Biological Dynamics 6(sup1),pp.2-18 (Collaboration) 2012
45.	Article	Two types of condition for the global stability of delayed sis epidemic models with nonlinear birth rate and disease induced death rate International Journal of Biomathematics 05(01),pp.1250009 (Collaboration) 2012
46.	Article	Global dynamics of a cell mediated immunity in viral infection models with distributed delays Journal of Mathematical Analysis and Applications 375(1),pp.14-27 (Collaboration) 2011
47.	Article	Global dynamics of a viral infection model with a latent period and Beddington–DeAngelis response Nonlinear Analysis: Theory, Methods & Applications 74(9),pp.2929-2940 (Single) 2011
48.	Article	Global stability of a delayed SIRS epidemic model with a non-monotonic incidence rate Journal of Mathematical Analysis and Applications 377(1),pp.1-14 (Collaboration) 2011
49.	Article	Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays Discrete & Continuous Dynamical Systems - B 15(1),pp.61-74 (Collaboration) 2011
50.	Article	Monotone iterative techniques to SIRS epidemic models with nonlinear incidence rates and distributed delays Nonlinear Analysis: Real World Applications 12(4),pp.1897-1910 (Collaboration) 2011
51.	Article	On the global stability of a delayed epidemic model with transport-related infection Nonlinear Analysis: Real World Applications 12(6),pp.3028-3034 (Single) 2011
52.	Article	Permanence and global stability of a class of discrete epidemic models Nonlinear Analysis: Real World Applications 12(4),pp.2105-2117 (Collaboration) 2011
53.	Article	An affirmative answer to “Gopalsamy and Liu’s conjecture” on population models with multiple piecewise constant arguments International Journal of Qualitative Theory of Differential Equations and Applications 4(1),pp.1-20 (Collaboration) 2010
54.	Article	Global asymptotic stability beyond 3/2 type stability for a logistic equation with piecewise constant arguments Nonlinear Analysis: Theory, Methods & Applications 73(10),pp.3179-3194 (Single) 2010
55.	Article	Global dynamics of a class of SEIRS epidemic models in a periodic environment Journal of Mathematical Analysis and Applications 363(1),pp.230-237 (Collaboration) 2010
56.	Article	Global stability for a class of discrete SIR epidemic models Mathematical Biosciences and Engineering 7(2),pp.347-361 (Collaboration) 2010
57.	Article	Global stability of nonautonomous logistic equations with a piecewise constant delay 11(3),pp.2115-2126 (Collaboration) 2010
58.	Article	Permanence for nonautonomous Lotka–Volterra cooperative systems with delays Nonlinear Analysis: Real World Applications 11(1),pp.528-534 (Collaboration) 2010
59.	Article	Contractivity for nonautonomous logistic equation with piecewise constant delays 1124(1),pp.254-263 (Collaboration) 2009
60.	Article	Permanence for the Lotka–Volterra cooperative system with several delays International Journal of Biomathematics 02(03),pp.267-285 (Single) 2009
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■ Lecturer and lecture

2016/09/08

Delay equations for epidemic models

■ Academic conference presentation

1.	2024/06	Blow-up to $\infty$ or convergence to $0$ for a delay differential equation (Equadiff 2024)
2.	2023/08	An epidemic model for reinfection dynamics with heterogeneous susceptibility (ICIAM 2023 (10th International Congress on Industrial and Applied Mathematics), Mathematics of Epidemics: modelling, data analysis, and control)
3.	2023/08	An epidemic model for reinfection dynamics with heterogeneous susceptibility (The 4th International Conference on Dynamics of Differential Equations, in Memory of Jack K. Hale, Fields Institute)
4.	2023/06	Extinction of mosquito population with sterile mosquito release (The 8th CIJK Conference Mathematical analysis of population dynamics, Sono Belle Jeju)
5.	2023/06	Period-two solutions for a class of distributed delay differential equations (12th Colloquium on the Qualitative Theory of Differential Equations)
6.	2021/08/30	On a blow-up phenomenon in scalar delay differential equations (BioMATEmatics An International Conference on Biomathematics and Biostatistics)
7.	2021/07	Periodic solution of a class of distributed delay differential equations (Encontro Nacional da SPM 2021)
8.	2021/01	On a blow-up phenomenon in scalar delay differential equations (Czech-Japanese Seminar in Applied Mathematics 2021)
9.	2019/07	Period two solutions of distributed delay differential equations (Equadiff 2019)
10.	2019/06	Period two solutions of distributed delay differential equations (11th Colloquium on the Qualitative Theory of Differential Equations)
11.	2019/05	Stability analysis of an epidemic model with boosting of immunity (The Fifth International Conference on Computational and Mathematical Population Dynamics (CMPD5))
12.	2018/11	Period two solutions of a class of a delay differential equations (RIMS 研究集会「常微分方程式の定性的理論および数理モデル研究への応用」)
13.	2018/07	Periodic solutions of a delay differential equation (12th AIMS International Conference, Special Session ‘Delay Equations in Population Dynamics’)
14.	2017/11	Infection and reinfection dynamics in a heterogeneous susceptible population (RIMS Workshop ‘Theory of Biomathematics and its Applications XIV - Modelling and Analysis for Structured Population Dynamics and its Applications’)
15.	2017/05	Delay equations for epidemic models with waning immunity (SIAM Conference on Applications of Dynamical Systems)
16.	2016/11	Delay equations for epidmic models: instability due to waning immunity (RIMS共同研究「常微分方程式の定性的理論とその周辺」)
17.	2016/11	感染症流行モデルのための遅延方程式：免疫低下による不安定性
18.	2016/10	Epidemic models with waning immunity (70th Anniversary Conference of the Korean Mathematical Society)
19.	2016/07	複数の時間遅れをもつロジスティック方程式の安定性解析
20.	2015/08	Delay equation formulation for an epidemic model with waning immunity: an application to mycoplasma pneumoniae (4th IFAC Conference on Analysis and Control of Chaotic Systems)
21.	2015/07	On a transcendental equation from an endemic model (10th Colloquium on the Qualitative Theory of Differential Equations, Bolyai Institute)
22.	2015/05	Dynamics of a reinfection epidemic model and an application to a childhood disease (Short Thematic Program on Delay Differential Equations)
23.	2014/02	Age-structured epidemic model with infection during transportation (Szeged Dynamics Days)
24.	2013/07	On the logistic equation with two discrete delays (International Conference on Delay Differential and Difference Equations and Applications)
25.	2013/05	Global analysis for spread of an infectious disease via human transportation (Encounters Between Discrete and Continuous Mathematics, Workshop on Dynamical Networks, Numerical Analysis and Ergodic Theor)
26.	2012/07	Compactness property for structured population models by Delay Equations (6th European Congress of Mathematics)
27.	2012/06	Global analysis for spread of an infectious disease via human transportation (BJMT Applied Mathematics Conference 2012)
28.	2011/12	An age structured model describing transitions between quiescent and proliferating cell populations (3rd Swedish Meeting on Mathematics in Biology)
29.	2011/11	Global dynamics of two compartment models for cell production systems with regulatory mechanisms (Interdisciplinary Conference, Modeling in Life Sciences 2011)
30.	2011/06	Analysis of a characteristic equation for a Delay Equation from cell population dynamics (8th European Conference on Mathematical and Theoretical Biology: Annual Meeting of The Society for Mathematical Biology)
31.	2010/10	Stability analysis of multi-compartment models for cell production systems (The 3rd China-Japan Colloquium of Mathematical Biology)
32.	2009/09	Global asymptotic stability beyond 3/2 type stability for a logistic equation with piecewise constant arguments (Workshop on Delay Differential Equations: from theory to applications)
33.	2008/09	Contractivity and global asymptotic stability for nonautonomous Lotka-Volterra ystems with piecewise constant arguments (Mathematical Models in Engineering, Biology and Medicine. International Conference on Boundary Value Problems)
34.	2008/08	Permanence for nonautonomous Lotka-Volterra cooperative systems with several deviating arguments (The 2nd China-Japan Mathematical Colloquim)
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