start-ver=1.4 cd-journal=joma no-vol=4 cd-vols= no-issue=1 article-no= start-page=77 end-page=80 dt-received= dt-revised= dt-accepted= dt-pub-year=1999 dt-pub=19990226 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=Hilbert C* -bimodules and countably infinite continuous graphs en-subtitle= kn-subtitle= en-abstract= kn-abstract=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. 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= affil-num=1 en-affil= kn-affil=岡山大学 en-keyword=Hilbert bimodule kn-keyword=Hilbert bimodule en-keyword=C* -algebras kn-keyword=C* -algebras en-keyword=continous graph kn-keyword=continous graph END start-ver=1.4 cd-journal=joma no-vol=11 cd-vols= no-issue=1 article-no= start-page=19 end-page=26 dt-received= dt-revised= dt-accepted= dt-pub-year=2006 dt-pub=20060315 dt-online= en-article= kn-article= en-subject= kn-subject= en-title=Hydrodynamic and structural simulation by a particle approach kn-title=粒子的アプローチによる構造・流体シミュレーション en-subtitle= kn-subtitle= en-abstract= kn-abstract=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. en-copyright= kn-copyright= en-aut-name=MoritaToshimasa en-aut-sei=Morita en-aut-mei=Toshimasa kn-aut-name=守田利昌 kn-aut-sei=守田 kn-aut-mei=利昌 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=(株)日本総合研究所 affil-num=2 en-affil= kn-affil=岡山大学 en-keyword=Particle kn-keyword=Particle en-keyword=Simulation kn-keyword=Simulation en-keyword=Hydrodynamic analysis kn-keyword=Hydrodynamic analysis en-keyword=Structural analysis kn-keyword=Structural analysis END start-ver=1.4 cd-journal=joma no-vol=9 cd-vols= no-issue=1 article-no= start-page=45 end-page=51 dt-received= dt-revised= dt-accepted= dt-pub-year=2004 dt-pub=20040227 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=The qualitative properties of mathematical models for HIV infection en-subtitle= kn-subtitle= en-abstract= kn-abstract=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. en-copyright= kn-copyright= en-aut-name= en-aut-sei= en-aut-mei= kn-aut-name=IuchiTakuma kn-aut-sei=Iuchi kn-aut-mei=Takuma 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=HIV kn-keyword=HIV en-keyword=Mathematical model kn-keyword=Mathematical model en-keyword=Stability kn-keyword=Stability en-keyword=Liapunov function kn-keyword=Liapunov function END start-ver=1.4 cd-journal=joma no-vol=17 cd-vols= no-issue=1 article-no= start-page=1 end-page=6 dt-received= dt-revised= dt-accepted= dt-pub-year=2012 dt-pub=201203 dt-online= en-article= kn-article= en-subject= kn-subject= en-title=Basic Reproductive Ratio for Epdiemic Models (Review) kn-title=感染症数理モデルの再生産数(レビュー) en-subtitle= kn-subtitle= en-abstract= kn-abstract=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. en-copyright= kn-copyright= en-aut-name=SumitaMasanori en-aut-sei=Sumita en-aut-mei=Masanori kn-aut-name=住田正憲 kn-aut-sei=住田 kn-aut-mei=正憲 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=岡山大学環境理工学部 affil-num=2 en-affil= kn-affil=岡山大学環境理工学部 en-keyword=Basic reproductive ratio kn-keyword=Basic reproductive ratio en-keyword=epidemic model kn-keyword=epidemic model en-keyword=Non negative matrix kn-keyword=Non negative matrix en-keyword=M-matrix kn-keyword=M-matrix 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 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=8 cd-vols= no-issue=1 article-no= start-page=19 end-page=22 dt-received= dt-revised= dt-accepted= dt-pub-year=2003 dt-pub=200303 dt-online= en-article= kn-article= en-subject= kn-subject= en-title=A note on the effect of quadratic term on final pattern in Turing model kn-title=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 en-subtitle= kn-subtitle= en-abstract= kn-abstract=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. en-copyright= kn-copyright= en-aut-name=YamauchiKen-ichi en-aut-sei=Yamauchi en-aut-mei=Ken-ichi kn-aut-name=山内憲一 kn-aut-sei=山内 kn-aut-mei=憲一 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=Turing instability kn-keyword=Turing instability en-keyword=Reaction Diffusion equation kn-keyword=Reaction Diffusion equation en-keyword=Quadratic term kn-keyword=Quadratic term 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=6 cd-vols= no-issue=1 article-no= start-page=17 end-page=23 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=Speeds of travelling wave solutions in a mathematical model of some infectious disease in predator-prey system kn-title=捕食系の感染症数理モデルにおける進行波解の速度 en-subtitle= kn-subtitle= en-abstract= kn-abstract=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. 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=OkitaTomoki en-aut-sei=Okita en-aut-mei=Tomoki kn-aut-name=沖田知毅 kn-aut-sei=沖田 kn-aut-mei=知毅 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=Travelling wave kn-keyword=Travelling wave en-keyword=Infectious disease kn-keyword=Infectious disease END start-ver=1.4 cd-journal=joma no-vol=1 cd-vols= no-issue=1 article-no= start-page=43 end-page=46 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=Hilbert C*-Bimodules Given From Bundle Constructions en-subtitle= kn-subtitle= en-abstract= kn-abstract=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. 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= affil-num=1 en-affil= kn-affil=岡山大学 en-keyword=Hilbert bimodule kn-keyword=Hilbert bimodule en-keyword=bundle kn-keyword=bundle en-keyword=tensor product kn-keyword=tensor product 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=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=3 cd-vols= no-issue=1 article-no= start-page=25 end-page=29 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=Coaction crossed products of Hilbert C*-bimodules by finite groups en-subtitle= kn-subtitle= en-abstract= kn-abstract=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]. 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= affil-num=1 en-affil= kn-affil=岡山大学 en-keyword=Hilbert bimodule kn-keyword=Hilbert bimodule en-keyword=Coaction kn-keyword=Coaction en-keyword=Crossed product kn-keyword=Crossed product 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=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=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