Updated on 2024/12/24

写真a

 
SASAKI Toru
 
Organization
Faculty of Environmental, Life, Natural Science and Technology Professor
Position
Professor
External link

Degree

  • 博士 (数理科学) ( 東京大学 )

Research Interests

  • Biomathematics

  • Applied Analysis

  • Functional Equations

Research Areas

  • Natural Science / Applied mathematics and statistics

  • Natural Science / Basic mathematics

  • Natural Science / Mathematical analysis

Education

  • The University of Tokyo   大学院数理科学研究科  

    1992.4 - 1993.3

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    Notes： 博士課程

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  • The University of Tokyo   大学院理学系研究科  

    1986.4 - 1988.3

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    Notes： 修士課程

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  • The University of Tokyo   理学部   数学科

    1981.4 - 1986.3

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Research History

  • Okayama University   学術研究院環境生命自然科学学域   Professor

    2024.10

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  • Okayama University   Professor

    2023.4

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  • Okayama University   環境生命科学研究科   Professor

    2020.10 - 2023.3

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  • Okayama University   The Graduate School of Environmental and Life Science   Associate Professor

    2012.4 - 2020.9

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  • Okayama University   大学院環境学研究科   Associate Professor

    2007.4 - 2012.3

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  • Okayama University   大学院環境学研究科   Lecturer

    2005.4 - 2007.3

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  • Okayama University   Faculty of Environmental Science and Technology Department of Environmental and Mathematical Sciences   Lecturer

    1994.10 - 2005.3

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  • Okayama University   教養部   Lecturer

    1993.10 - 1994.9

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Professional Memberships

  • THE MATHEMATICAL SOCIETY OF JAPAN

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  • THE JAPAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS

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  • THE JAPANESE SOCIETY FOR MATHEMATICAL BIOLOGY

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  • THE ECOLOGICAL SOCIETY OF JAPAN

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Committee Memberships

  • 日本数理生物学会   会計監事  

    2017.1 - 2018.12   

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    Committee type：Academic society

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  • 日本数理生物学会   運営委員  

    2015.1 - 2016.12   

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    Committee type：Academic society

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  • 日本数理生物学会   幹事長  

    2015.1 - 2016.12   

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    Committee type：Academic society

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  • 日中韓数理生物コロキウム   第5回日中韓数理生物コロキウム実行委員  

    2015.1   

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    Committee type：Other

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  • RIMS 共同研究   第10回生物数学の理論と応用 研究代表者  

    2013.1 - 2013.12   

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    Committee type：Other

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  • 新しい研究の芽を育む会   選考委員  

    2012.4 - 2014.3   

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  • 日本数理生物学会   年会 大会副委員長  

    2012.1 - 2012.12   

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    Committee type：Academic society

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  • 日本数理生物学会   研究奨励賞選考委員  

    2011.10 - 2014.10   

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    Committee type：Academic society

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  • 日本数理生物学会   大久保賞選考委員  

    2011.10 - 2014.9   

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    Committee type：Academic society

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  • 日本数理生物学会   研究奨励賞選考委員  

    2010.1 - 2010.12   

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    Committee type：Academic society

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  • 第2回日中数理生物コロキウム   Local Co-Chair  

    2008.1 - 2008.12   

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    Committee type：Other

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  • 日本数理生物学会   学会サーバー運営委員  

    2007.1 - 2008.12   

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    Committee type：Academic society

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  • 日本数理生物学会   学会サーバー運営委員会 委員長  

    2005.1 - 2006.12   

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    Committee type：Academic society

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  • 日本数理生物学会   幹事  

    2005.1 - 2006.12   

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    Committee type：Academic society

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Papers

  • Asymptotic behaviour of the solutions to a virus dynamics model with diffusion Reviewed

    Toru Sasaki, Takashi Suzuki

    Discrete and Continuous Dynamical Systems - Series B   23 ( 2 )   525 - 541   2018.3

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Institute of Mathematical Sciences  

    Asymptotic behaviour of the solutions to a basic virus dynamics model is discussed. We consider the population of uninfected cells, infected cells, and virus particles. Diffusion effect is incorporated there. First, the Lyapunov function effective to the spatially homogeneous part (ODE model without diffusion) admits the L1 boundedness of the orbit. Then the precompactness of this orbit in the space of continuous functions is derived by the semigroup estimates. Consequently, from the invariant principle, if the basic reproductive number R0 is less than or equal to 1, each orbit converges to the disease free spatially homogeneous equilibrium, and if R0 &gt
    1, each orbit converges to the infected spatially homogeneous equilibrium, which means that the simple diffusion does not affect the asymptotic behaviour of the solutions.

    DOI： 10.3934/dcdsb.2017206

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  • CONSTRUCTION OF LYAPUNOV FUNCTIONS FOR SOME MODELS OF INFECTIOUS DISEASES IN VIVO: FROM SIMPLE MODELS TO COMPLEX MODELS Reviewed

    Tsuyoshi Kajiwara, Toru Sasaki, Yasuhiro Takeuchi

    MATHEMATICAL BIOSCIENCES AND ENGINEERING   12 ( 1 )   117 - 133   2015.2

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER INST MATHEMATICAL SCIENCES  

    We present a constructive method for Lyapunov functions for ordinary differential equation models of infectious diseases in vivo. We consider models derived from the Nowak-Bangham models. We construct Lyapunov functions for complex models using those of simpler models. Especially, we construct Lyapunov functions for models with an immune variable from those for models without an immune variable, a Lyapunov functions of a model with absorption effect from that for a model without absorption effect. We make the construction clear for Lyapunov functions proposed previously, and present new results with our method.

    DOI： 10.3934/mbe.2015.12.117

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  • Construction of Lyapunov functionals for delay differential equations in virology and epidemiology Reviewed

    Tsuyoshi Kajiwara, Toru Sasaki, Yasuhiro Takeuchi

    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS   13 ( 4 )   1802 - 1826   2012.8

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：PERGAMON-ELSEVIER SCIENCE LTD  

    In the present paper, we present a method for constructing a Lyapunov functional for some delay differential equations in virology and epidemiology. Here some delays are incorporated to the original ordinary differential equations, for which a Lyapunov function is already obtained. We present simple and clear explanation of our method using some models whose Lyapunov functionals are already obtained. Moreover, we present several new results for constructing Lyapunov functionals using our method. (C) 2011 Elsevier Ltd. All rights reserved.

    DOI： 10.1016/j.nonrwa.2011.12.011

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  • Stability analysis of pathogen-immune interaction dynamics Reviewed

    A Murase, T Sasaki, T Kajiwara

    JOURNAL OF MATHEMATICAL BIOLOGY   51 ( 3 )   247 - 267   2005.9

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER  

    The paper considers models of dynamics of infectious disease in vivo from the standpoint of the mathematical analysis of stability. The models describe the interaction of the target cells, the pathogens, and the humoral immune response. The paper mainly focuses on the interior equilibrium, whose components are all positive. If the model ignores the absorption of the pathogens due to infection, the interior equilibrium is always asymptotically stable. On the other hand, if the model does consider it, the interior equilibrium can be unstable and a simple Hopf bifurcation can occur. A sufficient condition that the interior equilibrium is asymptotically stable is obtained. The condition explains that the interior equilibrium is asymptotically stable when experimental parameter values are used for the model. Moreover, the paper considers the models in which uninfected cells are involved in the immune response to pathogens, and are removed by the immune complexes. The effect of the involvement strongly affects the stability of the interior equilibria. The results are shown with the aid of symbolic calculation software.

    DOI： 10.1007/s00285-005-0321-y

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  • Effects That Cause the Instability of the Positive Equilibrium for Simple Pathogen Dynamics Models Reviewed

    Toru Sasaki, Tsuyoshi Kajiwara, Yoji Otani, Yuki Ishimaru

    Funkcialaj Ekvacioj   67 ( 3 )   327 - 339   2024.12

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Division of Functional Equations, The Mathematical Society of Japan (JST)  

    DOI： 10.1619/fesi.67.327

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  • Global stability of an age-structured infection model in vivo with two compartments and two routes Reviewed

    Tsuyoshi Kajiwara, Toru Sasaki, Yoji Otani

    Mathematical Biosciences and Engineering   19 ( 11 )   11047 - 11070   2022

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    Publishing type：Research paper (scientific journal)   Publisher：American Institute of Mathematical Sciences (AIMS)  

    <p lang="fr">&lt;abstract&gt;&lt;p&gt;In this paper, for an infection age model with two routes, virus-to-cell and cell-to-cell, and with two compartments, we show that the basic reproduction ratio $ R_0 $ gives the threshold of the stability. If $ R_0 &amp;gt; 1 $, the interior equilibrium is unique and globally stable, and if $ R_0 \le 1 $, the disease free equilibrium is globally stable. Some stability results are obtained in previous research, but, for example, a complete proof of the global stability of the disease equilibrium was not shown. We give the proof for all the cases, and show that we can use a type reproduction number for this model.&lt;/p&gt;&lt;/abstract&gt;</p>

    DOI： 10.3934/mbe.2022515

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  • Global stability for an age-structured multistrain virus dynamics model with humoral immunity Reviewed

    Tsuyoshi Kajiwara, Toru Sasaki, Yoji Otani

    Journal of Applied Mathematics and Computing   62 ( 1-2 )   239 - 279   2020.2

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

    DOI： 10.1007/s12190-019-01283-w

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    Other Link： http://link.springer.com/article/10.1007/s12190-019-01283-w/fulltext.html

  • Global stability of an age-structured model for pathogen–immune interaction Reviewed

    Tsuyoshi Kajiwara, Toru Sasaki, Yoji Otani

    Journal of Applied Mathematics and Computing   59 ( 1-2 )   1 - 30   2019.2

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Verlag  

    In this paper, we present an age-structured mathematical model for infectious disease in vivo with infection age of cells. The model contains an immune variable and the effect of absorption of pathogens into uninfected cells. We construct Lyapunov functionals for the model and prove that the time derivative of the functionals are nonpositive. Using this, we prove the global stability results for the model. Especially, we present the full mathematical detail of the proof of the global stability.

    DOI： 10.1007/s12190-018-1194-8

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  • LYAPUNOV FUNCTIONALS FOR MULTISTRAIN MODELS WITH INFINITE DELAY Reviewed

    Yoji Otani, Tsuyoshi Kajiwara, Toru Sasaki

    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B   22 ( 2 )   507 - 536   2017.3

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER INST MATHEMATICAL SCIENCES-AIMS  

    We construct Lyapunov functionals for delay differential equation models of infectious diseases in vivo to analyze the stability of the equilibria. The Lyapunov functionals contain the terms that integrate over all previous states. An appropriate evaluation of the logarithm functions in those terms guarantees the existence of the integrals. We apply the rigorous analysis for the one-strain models to multistrain models by using mathematical induction.

    DOI： 10.3934/dcdsb.2017025

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  • LYAPUNOV FUNCTIONALS FOR VIRUS-IMMUNE MODELS WITH INFINITE DELAY Reviewed

    Yoji Otani, Tsuyoshi Kajiwara, Toru Sasaki

    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B   20 ( 9 )   3093 - 3114   2015.11

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER INST MATHEMATICAL SCIENCES-AIMS  

    We present a systematic method to construct Lyapunov functionals of delay differential equation models of infectious diseases in vivo. For generality we construct Lyapunov functionals of models with infinitely distributed delay. We begin with simpler models without delay and construct Lyapunov functionals for the complex models progressively. We construct those functionals using our result obtained previously instead of constructing each functional independently. Additionally we discuss some problems that arise from the mathematical requirements caused by the infinitely distributed delay.

    DOI： 10.3934/dcdsb.2015.20.3093

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  • Impact of intracellular delay, immune activation delay and nonlinear incidence on viral dynamics Reviewed

    Gang Huang, Hiroki Yokoi, Yasuhiro Takeuchi, Tsuyoshi Kajiwara, Toru Sasaki

    JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS   28 ( 3 )   383 - 411   2011

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：KINOKUNIYA CO LTD  

    This paper investigates a class of viral infection models with a nonlinear infection rate and two discrete delays, one of which represents an intracellular latent period for the contacted target cell with virus to begin producing virions, the other of which represents the time needed in cytotoxic T cells (CTLs) response before immune becomes effective after a novel pathogen invades. Since immune system is a complex network of cells and signals that have evolved to respond to the presence of pathogens, we further assume two situations for immune activation delay. When both delays are ignored, the global stability for the ordinary differential equations model are established. While both delays are included, the positivity and boundedness of all solutions of the delay differential equations model are proved. Utilizing Lyapunov functionals and LaSalle invariance principle, the global dynamical properties are also studied. In particular, stability switch is shown to occur as immune delay increasing by bifurcation theory. Our results exhibit that the intracellular delay does not affect the stability of equilibria. However, the immune activation delay is able to destabilize the interior equilibrium and brings periodic solutions. Numerical simulations are performed to verify the theoretical results and display the different impacts of two type delays in two cases. Those analysis give us some useful suggestions on new drugs to fight against viral infection such that it is effective for the drugs to prolong the latent period, and/or to reduce the activation delay of CTLs immune response and/or to inhibit infection.

    DOI： 10.1007/s13160-011-0045-x

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  • Global stability of models of humoral immunity against multiple viral strains Reviewed

    Toru Inoue, Tsuyoshi Kajiwara, Toru Sasaki

    Journal of Biological Dynamics   4 ( 3 )   282 - 295   2010.5

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    Language：English   Publishing type：Research paper (scientific journal)  

    We analyse, from a mathematical point of view, the global stability of equilibria for models describing the interaction between infectious agents and humoral immunity. We consider the models that contain the variables of pathogens explicitly. The first model considers the situation where only a single strain exists. For the single strain model, the disease steady state is globally asymptotically stable if the basic reproductive ratio is greater than one. The other models consider the situations where multiple strains exist. For the multi-strain models, the disease steady state is globally asymptotically stable. In the model that does not explicitly contain an immune variable, only one strain with the maximum basic reproductive ratio can survive at the steady state. However, in our models explicitly involving the immune system, multiple strains coexist at the steady state. © 2010 Taylor &amp
    Francis.

    DOI： 10.1080/17513750903180275

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  • Global stability of pathogen-immune dynamics with absorption Reviewed

    Tsuyoshi Kajiwara, Toru Sasaki

    Journal of Biological Dynamics   4 ( 3 )   258 - 269   2010.5

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    Language：English   Publishing type：Research paper (scientific journal)  

    In this paper, we consider the global stability of the models which incorporate humoural immunity or cellmediated immunity.We consider the effect of loss of a pathogen, which is called the absorption effect when it infects an uninfected cells.We construct Lyapunov functions for these models under some conditions of parameters, and prove the global stability of the interior equilibria. It is impossible to remove the condition of parameters for the model incorporating humoural immunity. © 2010 Taylor &amp
    Francis.

    DOI： 10.1080/17513750903051989

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  • On the optimal duration of memory of losing a conflict - a mathematical model approach Reviewed

    Toru Sasaki, Kensuke Okada, Tsuyoshi Kajiwara, Takahisa Miyatake

    Journal of Biological Dynamics   4 ( 3 )   270 - 281   2010.5

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    Language：English   Publishing type：Research paper (scientific journal)  

    In male broad-horned flour beetles, Gnatocerus cornutus, losers of conflicts avoid fighting at subsequent encounters. The loser effect lasts for 4 days. It is considered that the memory of losing remains for 4 days. The duration of the memory is expected to affect the fitness, and the duration, 4 days, is expected to be optimal.We consider the fitness of a mutant in an homogeneous population to obtain the optimal duration. Here we carry out simulations using an individual-based model. The results suggest that the trade-off of getting mating chances and avoiding damage can cause the optimal duration of the memory, and that the decay in time of the female population is an important factor. © 2010 Taylor &amp
    Francis.

    DOI： 10.1080/17513750903161036

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  • Dynamical properties of autoimmune disease models: Tolerance, flare-up, dormancy Reviewed

    Shingo Iwami, Yasuhiro Takeuchi, Yoshiharu Miura, Toru Sasaki, Tsuyoshi Kajiwara

    JOURNAL OF THEORETICAL BIOLOGY   246 ( 4 )   646 - 659   2007.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD  

    The mechanisms of autoimmune disease have remained puzzling for a long time. Here we construct a simple mathematical model for autoimmune disease based on the personal immune response function and the target cell growth function. We show that these two functions are sufficient to capture the essence of autoimmune disease and can explain characteristic symptom phases such as tolerance, repeated flare-ups and dormancy. Our results strongly suggest that a more complete understanding of these two functions will underlie the development of an effective therapy for autoimmune disease. (C) 2007 Elsevier Ltd. All rights reserved.

    DOI： 10.1016/j.jtbi.2007.01.020

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  • Global Dynamics of B Cells and Anti-Idiotipic B Cells and its Application to Autoimmunity Reviewed

    Toru Sasaki, Tsuyoshi Kajiwara

    Japan Journal of Industrial and Applied Mathematics   24 ( 1 )   105 - 118   2007

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    Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Springer Tokyo  

    Global behavior of B models is discussed. When the source term for new B cells equals zero, the system has a conservation quantity. It implies the structurally unstability. It suggests that lack of the source of new B cells may unstabilize the immune system. When the B model incorporates autoimmunity, it loses symmetry. The asymmetry suggests the transition from a tolerant state to autoimmune state is more likely than the inverse transition. Effect of dose of antigen is also considered.

    DOI： 10.1007/BF03167510

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  • Asymptotic analysis of a chemotactic model of bacteria colonies Reviewed

    S Miyata, T Sasaki

    MATHEMATICAL BIOSCIENCES   201 ( 1-2 )   184 - 194   2006.5

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE INC  

    An estimate of the distance between spots generated by a bacterial colony model is obtained. The model describes the morphogenesis of a spot pattern in colonies of chemotactic strains of Escherichia coli. Asymptotic methods for other cell-chemotaxis models, which have been successfully used by previous researchers, can be applied also to this model. However the calculations and the result is more complicated for this model. The result is verified by comparing it with the results by numerical computations of solutions of the model. (c) 2005 Elsevier Inc. All rights reserved.

    DOI： 10.1016/j.mbs.2005.12.007

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  • A note on the stability analysis of pathogen-immune interaction dynamics Reviewed

    T Kajiwara, T Sasaki

    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B   4 ( 3 )   615 - 622   2004.8

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER INST MATHEMATICAL SCIENCES  

    The stability analysis of the interior equilibria, whose components are all positive, of non linear ordinary differential equation models describing in vivo dynamics of infectious diseases are complicated in general. Liu, "Non-linear oscillation in models of immune responses to persistent viruses, Theor. Popul. Biol. 52(1997), 224-230" and Murase, Sasaki and Kajiwara, "Stability analysis of pathogen-immune interaction dynamics (submitted)" proved the stability of the interior equilibria of such models using symbolic calculation software on computers. In this paper, proofs without using symbolic calculation software of the stability theorems given by Liu and Murase et al. are presented. Simple algebraic manipulations, properties of determinants, and their derivatives are used. The details of the calculation given by symbolic calculation software can be seen clearly.

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  • The effect of local prevention in an SIS model with diffusion Reviewed

    Toru Sasaki

    Discrete and Continuous Dynamical Systems - Series B   4 ( 3 )   739 - 746   2004

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    Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Southwest Missouri State University  

    The effect of spatially partial prevention of infectious disease is considered as an application of population models in inhomogeneous environments. The area is divided into two ractangles, and the local contact rate between infectives and susceptibles is sufficiently reduced in one rectangle. The dynamics of the infection considered here is that described by an SIS model with diffusion. Then the problem can be reduced to a Fisher type equation, which has been fully studied by many authors, under some conditions. The steady states of the linearized equation are considered, and a Nagylaki type result for predicting whether the infection will become extinct over time or not is obtained. This result leads to some necessary conditions for the extinction of the infection.

    DOI： 10.3934/dcdsb.2004.4.739

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  • Propagation of ultradifferentiability for the solutions of semi-linear hyperbolic equations in one space dimension Reviewed

    Toru Sasaki

    Journal of the Faculty of Science, the Universtity of Tokyo   40 ( 2 )   529 - 547   1993

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  • INTERACTION OF 2 NONLINEAR-WAVES AT THE BOUNDARY Reviewed

    T SASAKI

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   63 ( 10 )   375 - 378   1987.12

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：JAPAN ACAD  

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Books

  • 数理モデリング入門 : ファイブ・ステップ法

    Meerschaert, Mark M., 佐藤, 一憲, 梶原, 毅, 佐々木, 徹, 竹内, 康博, 宮崎, 倫子, 守田, 智（ Role： Joint translator）

    共立出版  2015.1  （ ISBN:9784320111004 ）

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    Total pages：xiv, 382p   Language：Japanese

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  • 偏微分方程式

    John, Fritz, 佐々木, 徹, 示野, 信一, 橋本, 義武（ Role： Joint translator）

    丸善出版  2012.3  （ ISBN:9784621065600 ）

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    Total pages：ix, 321p   Language：Japanese

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  • 生物数学入門 : 差分方程式・微分方程式の基礎からのアプローチ

    Allen, Linda J. S., 竹内, 康博, 佐藤, 一憲, 守田, 智, 宮崎, 倫子（ Role： Joint translator）

    共立出版  2011.10  （ ISBN:9784320057159 ）

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    Total pages：xiv, 440p   Language：Japanese

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  • 「数」の数理生物学

    日本数理生物学会, 瀬野, 裕美（ Role： Contributor）

    共立出版  2008.9  （ ISBN:9784320056756 ）

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    Total pages：viii, 224p   Language：Japanese

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  • 感染症の数理モデル

    稲葉, 寿, 西浦, 博, 梶原, 毅, 佐々木, 徹, 竹内, 康博, 細野, 雄三, 増田, 直紀, 今野, 紀雄, 梯, 正之, 加茂, 将史, 佐々木, 顕（ Role： Contributor）

    培風館  2008.7  （ ISBN:9784563011376 ）

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    Total pages：x, 311p   Language：Japanese

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  • 進化のダイナミクス : 生命の謎を解き明かす方程式

    Nowak, M. A. (Martin A.), 竹内, 康博, 佐藤, 一憲, 巌佐, 庸, 中岡, 慎治（ Role： Joint translator）

    共立出版  2008.2  （ ISBN:9784320056657 ）

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    Total pages：xii, 333p   Language：Japanese

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  • 生物集団の数学 : 人口学・生態学・疫学へのアプローチ

    Thieme, Horst R., 齋藤, 保久（ Role： Joint translator）

    日本評論社  2006  （ ISBN:4535784183 ）

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    Total pages：2冊   Language：Japanese

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MISC

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Presentations

  • Stability analysis of a simple cell-pathogen-immune system

    Toru Sasaki

    2023.9.6 

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    Event date： 2023.9.4 - 2023.9.6

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • ウイルスダイナミクス基本モデルの安定性解析

    佐々木徹, 梶原毅, 應谷洋二, 石丸優希

    第16回生物数学の理論とその応用  2020.1.30 

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    Event date： 2020.1.27 - 2020.1.31

    Language：Japanese   Presentation type：Oral presentation (general)  

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  • クマの食べ残しの競争系への効果について

    佐々木徹, 坪田一輝

    数理生物学会年会  2021.9.13 

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    Language：Japanese   Presentation type：Oral presentation (general)  

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Research Projects

  • Analysis of functional equations describing dynamics of infectious disease

    Grant number：17K05365  2017.04 - 2023.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    佐々木 徹

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    Grant amount：\3510000 （ Direct expense: \2700000 、 Indirect expense：\810000 ）

    ウイルスダイナミクス・数理モデルにおいて安定な平衡点を不安定化させうる要素として，(1) 時間遅れ (感染からウイルス放出までのタイムラグ), (2) 吸収効果 (感染時にウイルスが細胞内に吸収され、その後新しい細胞に感染しなくなる効果), (3)免疫変数の採用 (免疫の強さを未知変数として取り入れる), の三つに焦点をあてる研究を, 前年度に引き続き行なった. 上記 3 つの効果の他に, 未知変数として感染細胞密度を取り入れる事も平衡点を不安定化させうる (Murase, Kajiwara, Sasaki 2005). これは, 細胞が感染した後感染細胞に変化し, その感染細胞がウイルスを放出するという意味では時間遅れと考えられる. しかし, 今まで検討したのは, いわゆる離散時間遅れと呼ばれる場合で, 感染細胞経由による時間遅れとは意味が異なる. これに関して, 時間遅れがガンマ分布に従う場合の考察を行なった.
    <BR>
    ウイルスダイナミクス・数理モデルにおいて, 2 つの感染経路と 2 つのコンパーメント, 齢構造を考慮した微分方程式系の解析を進めた. 前年度に得た平衡点の安定性に関する結果を進めるとともに, 時間大域解の存在と一意性について詳細に検討したり，解の正値性に関しては先行研究を調査し研究を進めた. また, 先行研究の基礎再生産数に関する議論に対して, タイプ別再生産数の概念を利用してその意味に関する検討を進めた. 更にパーシステンスなどについて詳細に解析を行ない, 研究を進めた. これらの結果を詳細に検討し, まとめる作業を行ない, 論文の作成に着手した.

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  • The analysis of mathematical models describing dynamics of infection

    Grant number：22540135  2010.04 - 2015.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    SASAKI Toru, KAJIWARA Tsuyoshi

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    Grant amount：\3900000 （ Direct expense: \3000000 、 Indirect expense：\900000 ）

    We investigated the behaviour of solutions of mathematical models describing the reproduction of pathogen in vivo and describing the spread of infectious disease. Our main results concern construction of Lyapunov functions. Once a Lyapunov function is obtained, we can know the behaviour of the solution since the solution moves to the direction in which the value of the function decreases. Unfortunately, general methods of constructing a Lyapunov function are unknown, and applications of Lyapunov functions are restricted to some models. In our studies, we used a method to construct a Lyapunov function by using a known Lyapunov function for another model.

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  • Qualitative theory of differential equations describing dynamics of infectious disease

    Grant number：18540122  2006 - 2009

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    SASAKI Toru, KAJIWARA Tsuyoshi

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    Grant amount：\2750000 （ Direct expense: \2300000 、 Indirect expense：\450000 ）

    We obtained some results on qualitative properties of differential equation models describing the dynamics of infectious agents in a host. Here we dealt with the interaction among viruses, target cells, infected cells, and immunity. We showed for some models that the interior equilibrium, which corresponds to the infected state, is, under some conditions, globally asymptotically stable. In this connection, we considered some mathematical models of immunity, and established some properties of systems of differential equations describing autoimmunity.

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

    Grant number：22540122  2010.04 - 2014.03

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    YASUHIRO Takeuchi, OHTSUKI Kohichi, KAJIWARA Tsuyoshi, KOYANAGI Yoshio, SASAKI Tohru

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    Grant amount：\4030000 （ Direct expense: \3100000 、 Indirect expense：\930000 ）

    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.

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  • 非線型双曲型偏微分方程式の解の特異性の伝播の研究

    Grant number：06740120  1994

    日本学術振興会  科学研究費助成事業  奨励研究(A)

    佐々木 徹

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    Grant amount：\900000 （ Direct expense: \900000 ）

    1.空間次元1の場合の一般の非線型2階双曲型方程式の解の超可微分性が,その線型化方程式の特性曲線に沿って伝播するかどうかを考察した.これは,半線型方程式に帰着させるとよい.この半線型方程式については,既に超可微分性の伝播について研究してあるので,いかにこの方程式に帰着させるかが問題である.H.LewyやK.Friedrichsの方法を研究した.
    2.空間1次元の半線型双曲型方程式系および3階以上の方程式の超可微分関数のカテゴリーにおける研究を、J.RauchやM.Reedが無限回微分可能関数のカテゴリーにおいて行なった超局所解析を参考に行なった.
    3.変則的な特異性が生ずる条件を,空間次元が1の場合を中心に行なっている.空間次元が1の時には2階の単独方程式では変則的な特異性が現われないので,ここでは方程式系を考察している.まず,J.RauchとM.Reedによって得られた例を中心に検討した.J.RauchとM.Reedの例は,線型の非斉次方程式に帰着して考察しているものである.さらに非線型項のフーリェ変換を精密に考察している.
    4.J.F.Colombeauの一般関数を用いて解の特異性の伝播を考察している.まず,一般関数のクラスや同値関係の定義を整理し,理論を展開し易くするよう試みている.ここでは,パラディストリビューションの理論や超準解析を参考にしつつ,超局所解析の理論などにのりやすいクラスや同値関係を考察している.

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