start-ver=1.4 cd-journal=joma no-vol=19 cd-vols= no-issue=11 article-no= start-page=11047 end-page=11070 dt-received= dt-revised= dt-accepted= dt-pub-year=2022 dt-pub=20220802 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=Global stability of an age-structured infection model in vivo with two compartments and two routes en-subtitle= kn-subtitle= en-abstract= kn-abstract=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 > 1, the interior equilibrium is unique and globally stable, and if R-0 <= 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. en-copyright= kn-copyright= en-aut-name=KajiwaraTsuyoshi en-aut-sei=Kajiwara en-aut-mei=Tsuyoshi kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= en-aut-name=SasakiToru en-aut-sei=Sasaki en-aut-mei=Toru kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=2 ORCID= en-aut-name=OtaniYoji en-aut-sei=Otani en-aut-mei=Yoji kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=3 ORCID= affil-num=1 en-affil=Graduate School of Environmental and Life Sciences, Okayama University kn-affil= affil-num=2 en-affil=Faculty of Environmental and Life Science, Okayama University kn-affil= affil-num=3 en-affil=School of Engineering, Okayama University kn-affil= en-keyword=global stability kn-keyword=global stability en-keyword=two routes of infection kn-keyword=two routes of infection en-keyword=two compartments kn-keyword=two compartments en-keyword=type reproduction number kn-keyword=type reproduction number en-keyword=lyapunov functional kn-keyword=lyapunov functional END start-ver=1.4 cd-journal=joma no-vol=1 cd-vols= no-issue=1 article-no= start-page=47 end-page=53 dt-received= dt-revised= dt-accepted= dt-pub-year=1996 dt-pub=199603 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=Computational water analysis in an artificial lake: Kojima Lake case en-subtitle= kn-subtitle= en-abstract= kn-abstract=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. en-copyright= kn-copyright= en-aut-name=SasakiToru en-aut-sei=Sasaki en-aut-mei=Toru kn-aut-name=佐々木徹 kn-aut-sei=佐々木 kn-aut-mei=徹 aut-affil-num=1 ORCID= en-aut-name=IshikawaHirofumi en-aut-sei=Ishikawa en-aut-mei=Hirofumi kn-aut-name=石川洋文 kn-aut-sei=石川 kn-aut-mei=洋文 aut-affil-num=2 ORCID= en-aut-name=KajiwaraTsuyoshi en-aut-sei=Kajiwara en-aut-mei=Tsuyoshi kn-aut-name=梶原毅 kn-aut-sei=梶原 kn-aut-mei=毅 aut-affil-num=3 ORCID= en-aut-name=WatanabeMasaji en-aut-sei=Watanabe en-aut-mei=Masaji kn-aut-name=渡辺雅二 kn-aut-sei=渡辺 kn-aut-mei=雅二 aut-affil-num=4 ORCID= affil-num=1 en-affil= kn-affil=岡山大学 affil-num=2 en-affil= kn-affil=岡山大学 affil-num=3 en-affil= kn-affil=岡山大学 affil-num=4 en-affil= kn-affil=岡山大学 en-keyword=Kojima lake kn-keyword=Kojima lake en-keyword=Water analysis kn-keyword=Water analysis en-keyword=Finite element method kn-keyword=Finite element method END start-ver=1.4 cd-journal=joma no-vol=3 cd-vols= no-issue=1 article-no= start-page=31 end-page=36 dt-received= dt-revised= dt-accepted= dt-pub-year=1998 dt-pub=19980114 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=Computational analysis of contamination in Kojima Lake using upwind-type finite element method en-subtitle= kn-subtitle= en-abstract= kn-abstract=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. en-copyright= kn-copyright= en-aut-name=SasakiToru en-aut-sei=Sasaki en-aut-mei=Toru kn-aut-name=佐々木徹 kn-aut-sei=佐々木 kn-aut-mei=徹 aut-affil-num=1 ORCID= en-aut-name=KajiwaraTsuyoshi en-aut-sei=Kajiwara en-aut-mei=Tsuyoshi kn-aut-name=梶原毅 kn-aut-sei=梶原 kn-aut-mei=毅 aut-affil-num=2 ORCID= en-aut-name=IshikawaHirofumi en-aut-sei=Ishikawa en-aut-mei=Hirofumi kn-aut-name=石川洋文 kn-aut-sei=石川 kn-aut-mei=洋文 aut-affil-num=3 ORCID= affil-num=1 en-affil= kn-affil=岡山大学 affil-num=2 en-affil= kn-affil=岡山大学 affil-num=3 en-affil= kn-affil=岡山大学 en-keyword=Upwind-type kn-keyword=Upwind-type en-keyword=Finite element method kn-keyword=Finite element method en-keyword=Kojima Lake kn-keyword=Kojima Lake END start-ver=1.4 cd-journal=joma no-vol=5 cd-vols= no-issue=1 article-no= start-page=23 end-page=30 dt-received= dt-revised= dt-accepted= dt-pub-year=2000 dt-pub=20000229 dt-online= en-article= kn-article= en-subject= kn-subject= en-title=Mathematical analysis of virus infectious diseases by ordinary differential equations kn-title=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 en-subtitle= kn-subtitle= en-abstract= kn-abstract=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. en-copyright= kn-copyright= en-aut-name=SasakiToru en-aut-sei=Sasaki en-aut-mei=Toru kn-aut-name=佐々木徹 kn-aut-sei=佐々木 kn-aut-mei=徹 aut-affil-num=1 ORCID= en-aut-name=KajiwaraTsuyoshi en-aut-sei=Kajiwara en-aut-mei=Tsuyoshi kn-aut-name=梶原毅 kn-aut-sei=梶原 kn-aut-mei=毅 aut-affil-num=2 ORCID= affil-num=1 en-affil= kn-affil=岡山大学 affil-num=2 en-affil= kn-affil=岡山大学 en-keyword=Virus kn-keyword=Virus en-keyword=Mathematica models kn-keyword=Mathematica models en-keyword=HIV kn-keyword=HIV en-keyword=HCV kn-keyword=HCV en-keyword=HBV kn-keyword=HBV END start-ver=1.4 cd-journal=joma no-vol=5 cd-vols= no-issue=1 article-no= start-page=13 end-page=21 dt-received= dt-revised= dt-accepted= dt-pub-year=2000 dt-pub=20000229 dt-online= en-article= kn-article= en-subject= kn-subject= en-title=Simulations of Heel Impact by Viscoelastic Models kn-title=粘弾性モデルを用いた着地衝撃シミュレーション en-subtitle= kn-subtitle= en-abstract= kn-abstract=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. en-copyright= kn-copyright= en-aut-name=KokuboMasahito en-aut-sei=Kokubo en-aut-mei=Masahito kn-aut-name=小久保雅仁 kn-aut-sei=小久保 kn-aut-mei=雅仁 aut-affil-num=1 ORCID= en-aut-name=SasakiToru en-aut-sei=Sasaki en-aut-mei=Toru kn-aut-name=佐々木徹 kn-aut-sei=佐々木 kn-aut-mei=徹 aut-affil-num=2 ORCID= affil-num=1 en-affil= kn-affil=岡山大学 affil-num=2 en-affil= kn-affil=岡山大学 en-keyword=Running kn-keyword=Running en-keyword=Heel Impact kn-keyword=Heel Impact en-keyword=Viscoelastic Model kn-keyword=Viscoelastic Model en-keyword=Biomechanics kn-keyword=Biomechanics END start-ver=1.4 cd-journal=joma no-vol=5 cd-vols= no-issue=1 article-no= start-page=7 end-page=11 dt-received= dt-revised= dt-accepted= dt-pub-year=2000 dt-pub=20000229 dt-online= en-article= kn-article= en-subject= kn-subject= en-title=Mathematical analysis of pathogenesis of viral hepatitis. kn-title=ウイルス性肝炎発病の数理モデル en-subtitle= kn-subtitle= en-abstract= kn-abstract=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. en-copyright= kn-copyright= en-aut-name=SasakiToru en-aut-sei=Sasaki en-aut-mei=Toru kn-aut-name=佐々木徹 kn-aut-sei=佐々木 kn-aut-mei=徹 aut-affil-num=1 ORCID= en-aut-name=KajiwaraTsuyoshi en-aut-sei=Kajiwara en-aut-mei=Tsuyoshi kn-aut-name=梶原毅 kn-aut-sei=梶原 kn-aut-mei=毅 aut-affil-num=2 ORCID= affil-num=1 en-affil= kn-affil=岡山大学 affil-num=2 en-affil= kn-affil=岡山大学 en-keyword=hepatitis kn-keyword=hepatitis en-keyword=mathematical model kn-keyword=mathematical model en-keyword=mutation kn-keyword=mutation END start-ver=1.4 cd-journal=joma no-vol=6 cd-vols= no-issue=1 article-no= start-page=35 end-page=39 dt-received= dt-revised= dt-accepted= dt-pub-year=2001 dt-pub=20010228 dt-online= en-article= kn-article= en-subject= kn-subject= en-title=Random Bit Strings and Antigenic Diversity ― Simulations kn-title=ランダムビットストリングと抗原多様性 ―コンピュータ・シミュレーション en-subtitle= kn-subtitle= en-abstract= kn-abstract=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. en-copyright= kn-copyright= en-aut-name=SasakiToru en-aut-sei=Sasaki en-aut-mei=Toru kn-aut-name=佐々木徹 kn-aut-sei=佐々木 kn-aut-mei=徹 aut-affil-num=1 ORCID= affil-num=1 en-affil= kn-affil=岡山大学 en-keyword=random bit string kn-keyword=random bit string en-keyword=simulation of errors in RNA transcription kn-keyword=simulation of errors in RNA transcription en-keyword=antigenic diversity kn-keyword=antigenic diversity END start-ver=1.4 cd-journal=joma no-vol=7 cd-vols= no-issue=1 article-no= start-page=17 end-page=21 dt-received= dt-revised= dt-accepted= dt-pub-year=2002 dt-pub=20020322 dt-online= en-article= kn-article= en-subject= kn-subject= en-title=Stability analysis of mathematical models of infectious disease kn-title=感染症数理モデルの安定性解析 en-subtitle= kn-subtitle= en-abstract= kn-abstract=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. en-copyright= kn-copyright= en-aut-name=MuraseAkiko en-aut-sei=Murase en-aut-mei=Akiko kn-aut-name=村瀬晶子 kn-aut-sei=村瀬 kn-aut-mei=晶子 aut-affil-num=1 ORCID= en-aut-name=SasakiToru en-aut-sei=Sasaki en-aut-mei=Toru kn-aut-name=佐々木徹 kn-aut-sei=佐々木 kn-aut-mei=徹 aut-affil-num=2 ORCID= en-aut-name=KajiwaraTsuyoshi en-aut-sei=Kajiwara en-aut-mei=Tsuyoshi kn-aut-name=梶原毅 kn-aut-sei=梶原 kn-aut-mei=毅 aut-affil-num=3 ORCID= affil-num=1 en-affil= kn-affil=岡山大学 affil-num=2 en-affil= kn-affil=岡山大学 affil-num=3 en-affil= kn-affil=岡山大学 en-keyword=mathematical model kn-keyword=mathematical model en-keyword=infectious disease kn-keyword=infectious disease en-keyword=dynamics in vivo kn-keyword=dynamics in vivo en-keyword=stability analysis kn-keyword=stability analysis en-keyword=symbolic calculation kn-keyword=symbolic calculation END start-ver=1.4 cd-journal=joma no-vol=10 cd-vols= no-issue=1 article-no= start-page=13 end-page=21 dt-received= dt-revised= dt-accepted= dt-pub-year=2005 dt-pub=20050228 dt-online= en-article= kn-article= en-subject= kn-subject= en-title=On Persistence in Dynamical Systems (Review) kn-title=力学系のパーシステンスについて(レビュー) en-subtitle= kn-subtitle= en-abstract= kn-abstract=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. en-copyright= kn-copyright= en-aut-name=SasakiToru en-aut-sei=Sasaki en-aut-mei=Toru kn-aut-name=佐々木徹 kn-aut-sei=佐々木 kn-aut-mei=徹 aut-affil-num=1 ORCID= en-aut-name=KajiwaraTsuyoshi en-aut-sei=Kajiwara en-aut-mei=Tsuyoshi kn-aut-name=梶原毅 kn-aut-sei=梶原 kn-aut-mei=毅 aut-affil-num=2 ORCID= affil-num=1 en-affil= kn-affil=岡山大学 affil-num=2 en-affil= kn-affil=岡山大学 en-keyword=persistence kn-keyword=persistence en-keyword=ordinary differential equation kn-keyword=ordinary differential equation en-keyword=dynamical system kn-keyword=dynamical system END start-ver=1.4 cd-journal=joma no-vol=10 cd-vols= no-issue=1 article-no= start-page=9 end-page=11 dt-received= dt-revised= dt-accepted= dt-pub-year=2005 dt-pub=20050228 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=A permanence theorem for a mathematical model for dynamics of pathogens and cells in vivo using elementary methods en-subtitle= kn-subtitle= en-abstract= kn-abstract=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. en-copyright= kn-copyright= en-aut-name=KajiwaraTsuyoshi en-aut-sei=Kajiwara en-aut-mei=Tsuyoshi kn-aut-name=梶原毅 kn-aut-sei=梶原 kn-aut-mei=毅 aut-affil-num=1 ORCID= en-aut-name=SasakiToru en-aut-sei=Sasaki en-aut-mei=Toru kn-aut-name=佐々木徹 kn-aut-sei=佐々木 kn-aut-mei=徹 aut-affil-num=2 ORCID= affil-num=1 en-affil= kn-affil=岡山大学 affil-num=2 en-affil= kn-affil=岡山大学 en-keyword=Permanence kn-keyword=Permanence en-keyword=dynamical system kn-keyword=dynamical system en-keyword=pathogen kn-keyword=pathogen END