### Mathematical Biosciences and Engineering

2014, Issue 5: 1175-1180. doi: 10.3934/mbe.2014.11.1175

# Disease dynamics for the hometown of migrant workers

• Received: 01 January 2014 Accepted: 29 June 2018 Published: 01 June 2014
• MSC : Primary: 34K20, 92D30; Secondary: 34D23.

• 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.

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

### Related Papers:

• 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.

 [1] SIAM, Philadelphia, 1976. [2] Math. Biosci. and Eng., 6 (2009), 603-610. [3] Nonlinear Anal. RWA, 11 (2010), 55-59. [4] J. Health Popul. Nutr., 25 (2007), 267-277. [5] Available from: http://migration-unifem-apas.org/nepal/index.html. [6] J. Theoret. Biol., 300 (2012), 100-109. [7] Available from: http://www.worldbank.org/en/news/feature/2012/07/10/hiv-aids-nepal.
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