Geodesic
Global dynamics of a delay differential system of a two-patch SIS-model with transport-related infections
Mathematica Bohemica, Tome 140 (2015) no. 2, pp. 171-193.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We describe the global dynamics of a disease transmission model between two regions which are connected via bidirectional or unidirectional transportation, where infection occurs during the travel as well as within the regions. We define the regional reproduction numbers and the basic reproduction number by constructing a next generation matrix. If the two regions are connected via bidirectional transportation, the basic reproduction number R0 characterizes the existence of equilibria as well as the global dynamics. The disease free equilibrium always exists and is globally asymptotically stable if R01, while for R0>1 an endemic equilibrium occurs which is globally asymptotically stable. If the two regions are connected via unidirectional transportation, the disease free equilibrium always exists, but for R0>1 two endemic equilibria can appear. In this case, the regional reproduction numbers determine which one of the two is globally asymptotically stable. We describe how the time delay influences the dynamics of the system.
DOI : 10.21136/MB.2015.144324
Classification : 34K05, 34K20, 34K60, 92D30
Mots-clés : SIS model; asymptotically autonomous system; global asymptotic stability; Lyapunov functional; transport-related infection 
@article{10_21136_MB_2015_144324,
     author = {Nakata, Yukihiko and R\"ost, Gergely},
     title = {Global dynamics of a delay differential system of a two-patch {SIS-model} with transport-related infections},
     journal = {Mathematica Bohemica},
     pages = {171--193},
     publisher = {mathdoc},
     volume = {140},
     number = {2},
     year = {2015},
     doi = {10.21136/MB.2015.144324},
     mrnumber = {3368492},
     zbl = {06486932},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2015.144324/}
}
TY  - JOUR
AU  - Nakata, Yukihiko
AU  - Röst, Gergely
TI  - Global dynamics of a delay differential system of a two-patch SIS-model with transport-related infections
JO  - Mathematica Bohemica
PY  - 2015
SP  - 171
EP  - 193
VL  - 140
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2015.144324/
DO  - 10.21136/MB.2015.144324
LA  - en
ID  - 10_21136_MB_2015_144324
ER  - 
%0 Journal Article
%A Nakata, Yukihiko
%A Röst, Gergely
%T Global dynamics of a delay differential system of a two-patch SIS-model with transport-related infections
%J Mathematica Bohemica
%D 2015
%P 171-193
%V 140
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2015.144324/
%R 10.21136/MB.2015.144324
%G en
%F 10_21136_MB_2015_144324
Nakata, Yukihiko; Röst, Gergely. Global dynamics of a delay differential system of a two-patch SIS-model with transport-related infections. Mathematica Bohemica, Tome 140 (2015) no. 2, pp. 171-193. doi : 10.21136/MB.2015.144324. https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2015.144324/

Cité par Sources :