掲載種別：研究論文（学術雑誌）   出版者・発行元：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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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 Science and Business Media LLC  

DOI： 10.1007/s12190-019-01283-w

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その他リンク： http://link.springer.com/article/10.1007/s12190-019-01283-w/fulltext.html

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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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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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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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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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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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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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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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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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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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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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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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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記述言語：英語   掲載種別：研究論文（学術雑誌）  

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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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総ページ数：xii, 333p   記述言語：日本語

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総ページ数：2冊   記述言語：日本語

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記述言語：日本語   出版者・発行元：京都大学  

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記述言語：日本語   出版者・発行元：京都大学  

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その他リンク： http://hdl.handle.net/2433/223342

記述言語：日本語   出版者・発行元：京都大学  

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その他リンク： http://hdl.handle.net/2433/172919

記述言語：日本語   出版者・発行元：京都大学  

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その他リンク： http://hdl.handle.net/2433/171131

記述言語：日本語   出版者・発行元：京都大学  

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記述言語：日本語   出版者・発行元：京都大学  

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その他リンク： http://hdl.handle.net/2433/141012

記述言語：日本語   出版者・発行元：京都大学  

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その他リンク： http://hdl.handle.net/2433/141021

記述言語：日本語   出版者・発行元：京都大学  

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その他リンク： http://hdl.handle.net/2433/140993

記述言語：日本語   出版者・発行元：京都大学  

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その他リンク： http://hdl.handle.net/2433/140718

記述言語：日本語   出版者・発行元：京都大学  

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その他リンク： http://hdl.handle.net/2433/81717

記述言語：日本語   出版者・発行元：京都大学  

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その他リンク： http://hdl.handle.net/2433/47404

記述言語：日本語   出版者・発行元：岡山大学環境理工学部  

Some important results on persistence are reviewed. These results concern the behavior of the orbits approaching the boundary. The orbits restrict the flow on the boundary, if one of them approaches more than one invariant set. A typical example is a model for cyclic competition, where the heteroclinic cycle can be the ω-limit set. Thus the persistence can be reduced to some conditions on the boundary flow.

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記述言語：英語   出版者・発行元：岡山大学環境理工学部  

An elementary proof of permanence for a simple mathematical model proposed by Nowak and Bangham. In many papers, permanence property is proved by theorems established by the general theory of dynamical system. In this paper, we present an elementary proof only using differential inequalities and the theory of linear differential equations with constant coefficients.

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記述言語：日本語   出版者・発行元：岡山大学環境理工学部  

Dynamics of infectious disease in vivo is described by coupled differential equations. Stability analysis of the complicated systems is difficult without computer calculation, while stability analysis is, in general, important to investigate qualitative behaviour of models. Liu analyzes stability of systems describing HIV dynamics in vivo with a symbolic calculation software. The same method is used for stability analysis of a mathematical model of malaria.

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記述言語：日本語   出版者・発行元：岡山大学環境理工学部  

Simple mathematical models are considered to explain the pathogenesis of viral hepatitis. Dynamics of populations of liver cells and two virus strains are analyzed qualitatively. This analysis suggests the possibility that the viral mutation causes the hepatitis from the state of carrier.

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記述言語：日本語   出版者・発行元：岡山大学環境理工学部  

Some mathematical models describing interaction of virus and cells in vivo are reviewed. Similar models using systems of ordinary differential equations can be used for the analysis of dynamics of virus and cells for different kinds of virus. Models for human immunodeficiency virus, hepatitis C virus and hepatitis B virus are treated here. Although models are similar, different approximations can reduce the systems to the explicitly solvable forms. The solutions obtained here can be used to estimate biological parameters.

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その他リンク： http://ousar.lib.okayama-u.ac.jp/11557