岡山大学環境理工学部Acta Medica Okayama2185-33471712012感染症数理モデルの再生産数(レビュー)16ENMasanoriSumitaTsuyoshiKajiwara10.18926/fest/48237We 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.No potential conflict of interest relevant to this article was reported.岡山大学環境理工学部Acta Medica Okayama1341-90991112006粒子的アプローチによる構造・流体シミュレーション1926ENToshimasaMoritaTsuyoshiKajiwara10.18926/fest/11426This 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.No potential conflict of interest relevant to this article was reported.岡山大学環境理工学部Acta Medica Okayama1341-90991012005力学系のパーシステンスについて（レビュー）1321ENToruSasakiTsuyoshiKajiwara10.18926/fest/11483Some 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.No potential conflict of interest relevant to this article was reported.岡山大学環境理工学部Acta Medica Okayama1341-90991012005A permanence theorem for a mathematical model for dynamics of pathogens and cells in vivo using elementary methods911ENTsuyoshiKajiwaraToruSasaki10.18926/fest/11481An 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.No potential conflict of interest relevant to this article was reported.岡山大学環境理工学部Acta Medica Okayama1341-9099912004The qualitative properties of mathematical models for HIV infection4551ENTsuyoshiKajiwara10.18926/fest/11455Qualitative 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.No potential conflict of interest relevant to this article was reported.岡山大学環境理工学部Acta Medica Okayama1341-9099812003チューリングモデルにおける2次の反応項のパターンに与える影響1922ENKen-ichiYamauchiTsuyoshiKajiwara10.18926/fest/11495The 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.No potential conflict of interest relevant to this article was reported.岡山大学環境理工学部Acta Medica Okayama1341-9099712002感染症数理モデルの安定性解析1721ENAkikoMuraseToruSasakiTsuyoshiKajiwara10.18926/fest/11515Dynamics 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.No potential conflict of interest relevant to this article was reported.岡山大学環境理工学部Acta Medica Okayama1341-9099612001捕食系の感染症数理モデルにおける進行波解の速度1723ENTsuyoshiKajiwaraTomokiOkita10.18926/fest/11524In 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.No potential conflict of interest relevant to this article was reported.岡山大学環境理工学部Acta Medica Okayama1341-9099512000微分方程式モデルによるウイルス感染症の数理的解析：レビュー2330ENToruSasakiTsuyoshiKajiwara10.18926/fest/11557Some 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.No potential conflict of interest relevant to this article was reported.岡山大学環境理工学部Acta Medica Okayama1341-9099512000ウイルス性肝炎発病の数理モデル711ENToruSasakiTsuyoshiKajiwara10.18926/fest/11553Simple 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.No potential conflict of interest relevant to this article was reported.岡山大学環境理工学部Acta Medica Okayama1341-9099411999Hilbert C* -bimodules and countably infinite continuous graphs7780ENTsuyoshiKajiwara10.18926/fest/19724In 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.No potential conflict of interest relevant to this article was reported.岡山大学環境理工学部Acta Medica Okayama1341-9099311998Computational analysis of contamination in Kojima Lake using upwind-type finite element method3136ENToruSasakiTsuyoshiKajiwaraHirofumiIshikawa10.18926/fest/11560We 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.No potential conflict of interest relevant to this article was reported.岡山大学環境理工学部Acta Medica Okayama1341-9099311998Coaction crossed products of Hilbert C*-bimodules by finite groups2529ENTsuyoshiKajiwara10.18926/fest/11558In 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].No potential conflict of interest relevant to this article was reported.岡山大学環境理工学部Acta Medica Okayama1341-9099111996Hilbert C*-Bimodules Given From Bundle Constructions4346ENTsuyoshiKajiwara10.18926/fest/11608This 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.No potential conflict of interest relevant to this article was reported.岡山大学環境理工学部Acta Medica Okayama1341-9099111996Computational water analysis in an artificial lake: Kojima Lake case4753ENToruSasakiHirofumiIshikawaTsuyoshiKajiwaraMasajiWatanabe10.18926/fest/11610We 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.No potential conflict of interest relevant to this article was reported.