Disease dynamics for the hometown of migrant workers

Ram P. Sigdel; C. Connell McCluskey

doi:10.3934/mbe.2014.11.1175

Mathematical Biosciences and Engineering, 2014, 11(5): 1175-1180. doi: 10.3934/mbe.2014.11.1175. Primary: 34K20, 92D30; Secondary: 34D23.

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Disease dynamics for the hometown of migrant workers

Ram P. Sigdel, C. Connell McCluskey

1. Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario

Received date: , Published date:

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A recent paper by L. Wang, X. Wang J. Theoret. Biol. 300:100--109 (2012) formulatedand studied a delay differential equation model for disease dynamics in a region where a portionof the population leaves to work in a different region for an extended fixed period. Upon return,a fraction of the migrant workers have become infected with the disease.The global dynamics were not fully resolved in that paper, but are resolved here. We show thatfor all parameter values and all delays, the unique equilibrium is globally asymptotically stable,implying that the disease will eventually reach a constant positive level in the population.

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Keywords: Delay; migrant workers; epidemiology.; global stability; Lyapunov functional

Citation: Ram P. Sigdel, C. Connell McCluskey. Disease dynamics for the hometown of migrant workers. Mathematical Biosciences and Engineering, 2014, 11(5): 1175-1180. doi: 10.3934/mbe.2014.11.1175

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Copyright Info: 2014, Ram P. Sigdel, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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