On the global stability of a delayed epidemic model with transport-related infection.

Nonlinear Anal Real World Appl

Basque Center for Applied Mathematics, Bizkaia Technology Park, Building 500, E-48160, Derio, Spain.

Published: December 2011

We study the global dynamics of a time delayed epidemic model proposed by Liu et al. (2008) [J. Liu, J. Wu, Y. Zhou, Modeling disease spread via transport-related infection by a delay differential equation, Rocky Mountain J. Math. 38 (5) (2008) 1525-1540] 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.

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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7106529PMC
http://dx.doi.org/10.1016/j.nonrwa.2011.05.004DOI Listing

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