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On the global stability of a delayed epidemic model with transport-related infection. (English) Zbl 1231.34128
Summary: We study the global dynamics of a time delayed epidemic model proposed by J. Liu, J. Wu and Y. Zhou [Rocky Mt. J. Math. 38, No. 5, 1525–1540 (2008; Zbl 1194.34111)] describing disease transmission dynamics among two regions due to transport-related infection. We prove that if an endemic equilibrium exists then it is globally asymptotically stable for any length of time delay by constructing a Lyapunov functional. This suggests that the endemic steady state for both regions is globally asymptotically stable regardless of the length of the travel time when the disease is transferred between two regions by human transport.

##### MSC:
 34K20 Stability theory of functional-differential equations 37N25 Dynamical systems in biology 34D23 Global stability of solutions to ordinary differential equations 92D30 Epidemiology
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##### References:
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