start-ver=1.4
cd-journal=joma
no-vol=40
cd-vols=
no-issue=6
article-no=
start-page=3981
end-page=3995
dt-received=
dt-revised=
dt-accepted=
dt-pub-year=2020
dt-pub=202006
dt-online=
en-article=
kn-article=
en-subject=
kn-subject=
en-title=
kn-title=Axisymmetric traveling fronts in balanced bistable reaction-diffusion equations
en-subtitle=
kn-subtitle=
en-abstract=
kn-abstract=For a balanced bistable reaction-diffusion equation, the existence of axisymmetric traveling fronts has been studied by Chen, Guo, Ninomiya, Hamel and Roquejoffre [4]. This paper gives another proof of the existence of axisymmetric traveling fronts. Our method is as follows. We use pyramidal traveling fronts for unbalanced reaction-diffusion equations, and take the balanced limit. Then we obtain axisymmetric traveling fronts in a balanced bistable reaction-diffusion equation. Since pyramidal traveling fronts have been studied in many equations or systems, our method might be applicable to study axisymmetric traveling fronts in these equations or systems.
en-copyright=
kn-copyright=

en-aut-name=TaniguchiMasaharu
en-aut-sei=Taniguchi
en-aut-mei=Masaharu
kn-aut-name=
kn-aut-sei=
kn-aut-mei=
aut-affil-num=1
ORCID=

affil-num=1
en-affil= Research Institute for Interdisciplinary Science, Okayama University
kn-affil=
en-keyword= Traveling front
kn-keyword= Traveling front
en-keyword= reaction-diffusion equation
kn-keyword= reaction-diffusion equation
en-keyword=axisymmetric
kn-keyword=axisymmetric
en-keyword=balanced
kn-keyword=balanced
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