JaLCDOI 10.18926/fest/48237
タイトル(別表記) Basic Reproductive Ratio for Epdiemic Models (Review)
フルテキストURL fest_017_001_006.pdf
著者 住田 正憲| 梶原 毅|
抄録 We review some fundamental results on the basic reproductive ratio of models in epidemiology following several documents. We present the general denition of the basic reproductive ratio and the threshold theorem of for the stability of the disease free equilibrium. All results for non-negative matrices and non singular M-matrices which we need in the denition of the basic reproductive ratio and the proof of the threshold theorem are also presented. All parts of the review are self-contained, and all parts of the proof are given explicitly.
キーワード Basic reproductive ratio epidemic model Non negative matrix M-matrix
出版物タイトル 岡山大学環境理工学部研究報告
発行日 2012-03
17巻
1号
開始ページ 1
終了ページ 6
ISSN 2185-3347
言語 Japanese
論文のバージョン publisher
NAID 120004025482
JaLCDOI 10.18926/fest/11426
タイトル(別表記) Hydrodynamic and structural simulation by a particle approach
フルテキストURL 011_019_026.pdf
著者 守田 利昌| 梶原 毅|
抄録 This paper is a research report concerning the hydrodynamic simulation and the structural simulation by a particle approach. The proposal particle method model is introduced in this report, and the calculation example by the calculation code which uses the proposal model is shown. The high possibility of the particle method is shown by calculation examples which is difficult to solve by FDM and FEM. It is shown by caliculation examples of both the hydrodynamic and the structure analysis problems that the proposal model enables us to treat the fluid and the structure in a unified way.
キーワード Particle Simulation Hydrodynamic analysis Structural analysis
出版物タイトル 岡山大学環境理工学部研究報告
発行日 2006-03-15
11巻
1号
開始ページ 19
終了ページ 26
ISSN 1341-9099
言語 Japanese
論文のバージョン publisher
NAID 120002313653
JaLCDOI 10.18926/fest/11483
タイトル(別表記) On Persistence in Dynamical Systems (Review)
フルテキストURL 010_013_021.pdf
著者 佐々木 徹| 梶原 毅|
抄録 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.
キーワード persistence ordinary differential equation dynamical system
出版物タイトル 岡山大学環境理工学部研究報告
発行日 2005-02-28
10巻
1号
開始ページ 13
終了ページ 21
ISSN 1341-9099
言語 Japanese
論文のバージョン publisher
NAID 120002313932
JaLCDOI 10.18926/fest/11481
フルテキストURL 010_009_011.pdf
著者 梶原 毅| 佐々木 徹|
抄録 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.
キーワード Permanence dynamical system pathogen
出版物タイトル 岡山大学環境理工学部研究報告
発行日 2005-02-28
10巻
1号
開始ページ 9
終了ページ 11
ISSN 1341-9099
言語 English
論文のバージョン publisher
NAID 120002313596
JaLCDOI 10.18926/fest/11455
フルテキストURL 009_045_051.pdf
著者 Iuchi Takuma| 梶原 毅|
抄録 Qualitative analysis for the model of HIV infection in vivo presented by Perelson and Nelson are developed. The local stability analysis is done for the interior equilibrium, and it is shown that, for some paramter value, the interior equilibrium can be unstable and a Hopf bifurcation can occur. It is shown that the boundary equilibrium is globally asymptotically stable. Last, it is shown that this system is permanent.
キーワード HIV Mathematical model Stability Liapunov function
出版物タイトル 岡山大学環境理工学部研究報告
発行日 2004-02-27
9巻
1号
開始ページ 45
終了ページ 51
ISSN 1341-9099
言語 English
論文のバージョン publisher
NAID 120002313809
JaLCDOI 10.18926/fest/11495
タイトル(別表記) A note on the effect of quadratic term on final pattern in Turing model
フルテキストURL 008_019_022.pdf
著者 山内 憲一| 梶原 毅|
抄録 The effect of the quadratic term on the final pattern in Turing model is disscussed numerically. Turing models are non linear reaction diffusion equations. Linear analysis for wave length is very useful to find evolving waves. But when a quadratic term appear in the equation, an initial wave can disappears and changes drastically to a spot which is independent of linear analysis.
キーワード Turing instability Reaction Diffusion equation Quadratic term
出版物タイトル 岡山大学環境理工学部研究報告
発行日 2003-03
8巻
1号
開始ページ 19
終了ページ 22
ISSN 1341-9099
言語 Japanese
論文のバージョン publisher
NAID 120002313586
JaLCDOI 10.18926/fest/11515
タイトル(別表記) Stability analysis of mathematical models of infectious disease
フルテキストURL 007_017_021.pdf
著者 村瀬 晶子| 佐々木 徹| 梶原 毅|
抄録 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.
キーワード mathematical model infectious disease dynamics in vivo stability analysis symbolic calculation
出版物タイトル 岡山大学環境理工学部研究報告
発行日 2002-03-22
7巻
1号
開始ページ 17
終了ページ 21
ISSN 1341-9099
言語 Japanese
論文のバージョン publisher
NAID 120002313783
JaLCDOI 10.18926/fest/11524
タイトル(別表記) Speeds of travelling wave solutions in a mathematical model of some infectious disease in predator-prey system
フルテキストURL 006_017_023.pdf
著者 梶原 毅| 沖田 知毅|
抄録 In this paper we construct a simple mathematical model for infectious disease in a pradator-prey system, and study the speeds of travelling wave solutions of this model. We present a method of estimation of speeds and make a numerical study about this matter.
キーワード Travelling wave Infectious disease
出版物タイトル 岡山大学環境理工学部研究報告
発行日 2001-02-28
6巻
1号
開始ページ 17
終了ページ 23
ISSN 1341-9099
言語 Japanese
論文のバージョン publisher
NAID 120002313731
JaLCDOI 10.18926/fest/11557
タイトル(別表記) Mathematical analysis of virus infectious diseases by ordinary differential equations
フルテキストURL 005_023_030.pdf
著者 佐々木 徹| 梶原 毅|
抄録 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.
キーワード Virus Mathematica models HIV HCV HBV
出版物タイトル 岡山大学環境理工学部研究報告
発行日 2000-02-29
5巻
1号
開始ページ 23
終了ページ 30
ISSN 1341-9099
言語 Japanese
論文のバージョン publisher
NAID 120002313498
JaLCDOI 10.18926/fest/11553
タイトル(別表記) Mathematical analysis of pathogenesis of viral hepatitis.
フルテキストURL 005_007_011.pdf
著者 佐々木 徹| 梶原 毅|
抄録 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.
キーワード hepatitis mathematical model mutation
出版物タイトル 岡山大学環境理工学部研究報告
発行日 2000-02-29
5巻
1号
開始ページ 7
終了ページ 11
ISSN 1341-9099
言語 Japanese
論文のバージョン publisher
NAID 120002313400
JaLCDOI 10.18926/fest/19724
フルテキストURL 004_077_080.pdf
著者 梶原 毅|
抄録 In this paper, we contruct Hilbert C* -bimodules for continuous graphs whose vertexes are countable 1-dimensiona tori, and show some uniquness property of the C* -representatiion of these bimodules.
キーワード Hilbert bimodule C* -algebras continous graph
出版物タイトル 岡山大学環境理工学部研究報告
発行日 1999-02-26
4巻
1号
開始ページ 77
終了ページ 80
ISSN 1341-9099
言語 English
論文のバージョン publisher
NAID 120002309008
JaLCDOI 10.18926/fest/11560
フルテキストURL 003_031_036.pdf
著者 佐々木 徹| 梶原 毅| 石川 洋文|
抄録 We have computed the phase of spreading contaminations in Kojima Lake by using the upwind-type finite element method. We have treated the two cases: the pollutant flows from the Sasagase river and from the Kurashiki River. We see that the upwind-type finite element method is effective in both cases, when the diffusion constant is quite small.
キーワード Upwind-type Finite element method Kojima Lake
出版物タイトル 岡山大学環境理工学部研究報告
発行日 1998-01-14
3巻
1号
開始ページ 31
終了ページ 36
ISSN 1341-9099
言語 English
論文のバージョン publisher
NAID 120002313715
JaLCDOI 10.18926/fest/11558
フルテキストURL 003_025_029.pdf
著者 梶原 毅|
抄録 In this paper, we define coaction crossed product of Hilbert C*-bimodule by finite groups. We show that resulting bimodule is of finite type, and compute indices of them. We present a Takesaki-Takai duality theorem which is some non-commutative generalization of abelian groups case in [KW2].
キーワード Hilbert bimodule Coaction Crossed product
出版物タイトル 岡山大学環境理工学部研究報告
発行日 1998-01-14
3巻
1号
開始ページ 25
終了ページ 29
ISSN 1341-9099
言語 English
論文のバージョン publisher
NAID 120002313716
JaLCDOI 10.18926/fest/11608
フルテキストURL 001_043_046.pdf
著者 梶原 毅|
抄録 This paper contains some remarks supplementary to the previous paper [KW] concerning Hilbert C*-bimodules given from bundle constructions and a example given by this construction concerning the product type action on C*-algebras.
キーワード Hilbert bimodule bundle tensor product
出版物タイトル 岡山大学環境理工学部研究報告
発行日 1996-03
1巻
1号
開始ページ 43
終了ページ 46
ISSN 1341-9099
言語 English
論文のバージョン publisher
NAID 120002313825
JaLCDOI 10.18926/fest/11610
フルテキストURL 001_047_053.pdf
著者 佐々木 徹| 石川 洋文| 梶原 毅| 渡辺 雅二|
抄録 We treat the problem of water pollution by the method of a mathematical model. We illustrate the method of analysis with Kojima Lake. We analyze in-flow and out-flow of the lake, compute numerical solutions of the governing equations of the water flow and the pollutant. The simulation leads to the conclusion concerning the figure of Kojima Lake.
キーワード Kojima lake Water analysis Finite element method
出版物タイトル 岡山大学環境理工学部研究報告
発行日 1996-03
1巻
1号
開始ページ 47
終了ページ 53
ISSN 1341-9099
言語 English
論文のバージョン publisher
NAID 120002313787