Global dynamics of a delay differential system of a two-patch SIS-model with transport-related infections

Title:

Global dynamics of a delay differential system of a two-patch SIS-model with transport-related infections

Creator:

Nakata, Yukihiko and Röst, Gergely

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:252ebb95-8eb2-44e7-ae58-6c044641249e
uuid:252ebb95-8eb2-44e7-ae58-6c044641249e
doi:10.21136/MB.2015.144324

Subject:

SIS model, asymptotically autonomous system, global asymptotic stability, Lyapunov functional, and transport-related infection

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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 R0 < 1, 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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

171-193

Source:

Mathematica bohemica | 2015 Volume:140 | Number:2

Harvested from:

CDK

Metadata only:

false