ID (desc)
JaLCDOI 10.18926/fest/11610 Sasaki, Toru| Ishikawa, Hirofumi| Kajiwara, Tsuyoshi| Watanabe, Masaji| 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. Kojima lake Water analysis Finite element method 岡山大学環境理工学部研究報告 1996-03 volume1 issue1 47 53 1341-9099 英語 publisher
JaLCDOI 10.18926/fest/11560 Sasaki, Toru| Kajiwara, Tsuyoshi| Ishikawa, Hirofumi| 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. Upwind-type Finite element method Kojima Lake 岡山大学環境理工学部研究報告 1998-01-14 volume3 issue1 31 36 1341-9099 英語 publisher
JaLCDOI 10.18926/fest/11557 Mathematical analysis of virus infectious diseases by ordinary differential equations Sasaki, Toru| Kajiwara, Tsuyoshi| 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. Virus Mathematica models HIV HCV HBV 岡山大学環境理工学部研究報告 2000-02-29 volume5 issue1 23 30 1341-9099 日本語 publisher
JaLCDOI 10.18926/fest/11555 Simulations of Heel Impact by Viscoelastic Models Kokubo, Masahito| Sasaki, Toru| The purpose of this study is to make some body models with viscoelastic model, to simulate the heel impact and to obtain the ground reaction force. In this paper, we build up body models of linear viscoelastic elements and mass elements to simulate heel impact. Here we consider the systems of linear differential equations numerically for the preparation of mathematical analysis in future. The simplest model with two mass elements is hardly able to simulate the heel impact if the rate of mass of elements is realistic. The models with more elements are suitable to simulate for actual rate of weight of body segments. The model with three mass elements makes it possible to guess the force to each body segment. Running Heel Impact Viscoelastic Model Biomechanics 岡山大学環境理工学部研究報告 2000-02-29 volume5 issue1 13 21 1341-9099 日本語 publisher
JaLCDOI 10.18926/fest/11553 Mathematical analysis of pathogenesis of viral hepatitis. Sasaki, Toru| Kajiwara, Tsuyoshi| 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. hepatitis mathematical model mutation 岡山大学環境理工学部研究報告 2000-02-29 volume5 issue1 7 11 1341-9099 日本語 publisher
JaLCDOI 10.18926/fest/11527 Random Bit Strings and Antigenic Diversity ― Simulations Sasaki, Toru| Transition of random bit strings is simulated by using pseudorandom numbers. Bit strings are considered as RNA of HIV virus here. Transition of random bit strings represents that of antigenic deversity. random bit string simulation of errors in RNA transcription antigenic diversity 岡山大学環境理工学部研究報告 2001-02-28 volume6 issue1 35 39 1341-9099 日本語 publisher
JaLCDOI 10.18926/fest/11515 Stability analysis of mathematical models of infectious disease Murase, Akiko| Sasaki, Toru| Kajiwara, Tsuyoshi| 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. mathematical model infectious disease dynamics in vivo stability analysis symbolic calculation 岡山大学環境理工学部研究報告 2002-03-22 volume7 issue1 17 21 1341-9099 日本語 publisher
JaLCDOI 10.18926/fest/11483 On Persistence in Dynamical Systems (Review) Sasaki, Toru| Kajiwara, Tsuyoshi| 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. persistence ordinary differential equation dynamical system 岡山大学環境理工学部研究報告 2005-02-28 volume10 issue1 13 21 1341-9099 日本語 publisher
JaLCDOI 10.18926/fest/11481 Kajiwara, Tsuyoshi| Sasaki, Toru| 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. Permanence dynamical system pathogen 岡山大学環境理工学部研究報告 2005-02-28 volume10 issue1 9 11 1341-9099 英語 publisher