Disease dynamics for the hometown of migrant workers

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2014, 11(5): 1175-1180. doi: 10.3934/mbe.2014.11.1175

Disease dynamics for the hometown of migrant workers

Ram P. Sigdel ^1, and C. Connell McCluskey ^1,

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

Received January 2014 Revised January 2014 Published June 2014

Abstract
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A recent paper by L. Wang, X. Wang J. Theoret. Biol. 300:100--109 (2012) formulated and studied a delay differential equation model for disease dynamics in a region where a portion of 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 that for 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.

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

Mathematics Subject Classification: Primary: 34K20, 92D30; Secondary: 34D2.

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

References:

[1]	J. P. LaSalle, The Stability of Dynamical Systems, SIAM, Philadelphia, 1976.
[2]	C. C. McCluskey, Global stability for an SEIR epidemiological model with varying infectivity and infinite delay, Math. Biosci. and Eng., 6 (2009), 603-610. doi: 10.3934/mbe.2009.6.603.
[3]	C. C. McCluskey, Complete global stability for an SIR epidemic model with delay - distributed or discrete, Nonlinear Anal. RWA, 11 (2010), 55-59. doi: 10.1016/j.nonrwa.2008.10.014.
[4]	B. Nepal, Population mobility and spread of {HIV} across the Indo-Nepal border, J. Health Popul. Nutr., 25 (2007), 267-277.
[5]	United Nations Entity for Gender Equality and the Empowerment of Women (UN Women), Asia Pacific and Arab States Regional Programme on Empowering Women Migrant Workers in Asia, 2013. Available from: http://migration-unifem-apas.org/nepal/index.html.
[6]	L. Wang and X. Wang, Influence of temporary migration on the transmission of infectious diseases in a migrants' home village, J. Theoret. Biol., 300 (2012), 100-109. doi: 10.1016/j.jtbi.2012.01.004.
[7]	World Bank, HIV/AIDS in Nepal, 2012. Available from: http://www.worldbank.org/en/news/feature/2012/07/10/hiv-aids-nepal.

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References:

[1]	J. P. LaSalle, The Stability of Dynamical Systems, SIAM, Philadelphia, 1976.
[2]	C. C. McCluskey, Global stability for an SEIR epidemiological model with varying infectivity and infinite delay, Math. Biosci. and Eng., 6 (2009), 603-610. doi: 10.3934/mbe.2009.6.603.
[3]	C. C. McCluskey, Complete global stability for an SIR epidemic model with delay - distributed or discrete, Nonlinear Anal. RWA, 11 (2010), 55-59. doi: 10.1016/j.nonrwa.2008.10.014.
[4]	B. Nepal, Population mobility and spread of {HIV} across the Indo-Nepal border, J. Health Popul. Nutr., 25 (2007), 267-277.
[5]	United Nations Entity for Gender Equality and the Empowerment of Women (UN Women), Asia Pacific and Arab States Regional Programme on Empowering Women Migrant Workers in Asia, 2013. Available from: http://migration-unifem-apas.org/nepal/index.html.
[6]	L. Wang and X. Wang, Influence of temporary migration on the transmission of infectious diseases in a migrants' home village, J. Theoret. Biol., 300 (2012), 100-109. doi: 10.1016/j.jtbi.2012.01.004.
[7]	World Bank, HIV/AIDS in Nepal, 2012. Available from: http://www.worldbank.org/en/news/feature/2012/07/10/hiv-aids-nepal.

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