2021/07/12 更新

写真a

ササキ トオル
佐々木 徹
SASAKI Toru
所属
環境生命科学学域 教授
職名
教授
外部リンク

学位

  • 博士 (数理科学) ( 東京大学 )

研究キーワード

  • 生物数学

  • 応用解析学

  • 関数方程式

研究分野

  • 自然科学一般 / 応用数学、統計数学

  • 自然科学一般 / 数学基礎

  • 自然科学一般 / 数理解析学

経歴

  • 岡山大学   環境生命科学研究科   教授

    2021年2月 - 現在

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所属学協会

 

論文

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

    Tsuyoshi Kajiwara, Toru Sasaki, Yoji Otani

    Journal of Applied Mathematics and Computing   59 ( 1-2 )   1 - 30   2019年2月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元: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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  • Asymptotic behaviour of the solutions to a virus dynamics model with diffusion 査読

    Toru Sasaki, Takashi Suzuki

    Discrete and Continuous Dynamical Systems - Series B   23 ( 2 )   525 - 541   2018年3月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元: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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  • LYAPUNOV FUNCTIONALS FOR MULTISTRAIN MODELS WITH INFINITE DELAY 査読

    Yoji Otani, Tsuyoshi Kajiwara, Toru Sasaki

    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B   22 ( 2 )   507 - 536   2017年3月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元: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 査読

    Yoji Otani, Tsuyoshi Kajiwara, Toru Sasaki

    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B   20 ( 9 )   3093 - 3114   2015年11月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元: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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  • CONSTRUCTION OF LYAPUNOV FUNCTIONS FOR SOME MODELS OF INFECTIOUS DISEASES IN VIVO: FROM SIMPLE MODELS TO COMPLEX MODELS 査読

    Tsuyoshi Kajiwara, Toru Sasaki, Yasuhiro Takeuchi

    MATHEMATICAL BIOSCIENCES AND ENGINEERING   12 ( 1 )   117 - 133   2015年2月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元: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 査読

    Tsuyoshi Kajiwara, Toru Sasaki, Yasuhiro Takeuchi

    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS   13 ( 4 )   1802 - 1826   2012年8月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元: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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  • Impact of intracellular delay, immune activation delay and nonlinear incidence on viral dynamics 査読

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

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

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元: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 査読

    Toru Inoue, Tsuyoshi Kajiwara, Toru Sasaki

    Journal of Biological Dynamics   4 ( 3 )   282 - 295   2010年5月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    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 査読

    Tsuyoshi Kajiwara, Toru Sasaki

    Journal of Biological Dynamics   4 ( 3 )   258 - 269   2010年5月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    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 査読

    Toru Sasaki, Kensuke Okada, Tsuyoshi Kajiwara, Takahisa Miyatake

    Journal of Biological Dynamics   4 ( 3 )   270 - 281   2010年5月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    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 査読

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

    JOURNAL OF THEORETICAL BIOLOGY   246 ( 4 )   646 - 659   2007年6月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元: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

    Toru Sasaki, Tsuyoshi Kajiwara

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

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    記述言語:英語   掲載種別:研究論文(国際会議プロシーディングス)   出版者・発行元: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 査読

    S Miyata, T Sasaki

    MATHEMATICAL BIOSCIENCES   201 ( 1-2 )   184 - 194   2006年5月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元: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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  • Stability analysis of pathogen-immune interaction dynamics 査読

    A Murase, T Sasaki, T Kajiwara

    JOURNAL OF MATHEMATICAL BIOLOGY   51 ( 3 )   247 - 267   2005年9月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元: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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  • A note on the stability analysis of pathogen-immune interaction dynamics

    T Kajiwara, T Sasaki

    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B   4 ( 3 )   615 - 622   2004年8月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元: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

    Toru Sasaki

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

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    記述言語:英語   掲載種別:研究論文(国際会議プロシーディングス)   出版者・発行元: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 査読

    佐々木 徹

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

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

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  • INTERACTION OF 2 NONLINEAR-WAVES AT THE BOUNDARY 査読

    T SASAKI

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   63 ( 10 )   375 - 378   1987年12月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:JAPAN ACAD  

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