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:
| [1] |
Luju Liu, Jianhong Wu, Xiao-Qiang Zhao .
The impact of migrant workers on the tuberculosis transmission: General models and a case study for
China. Mathematical Biosciences and Engineering, 2012, 9(4): 785-807.
doi: 10.3934/mbe.2012.9.785
|
| [2] |
Peter Witbooi, Gbenga Abiodun, Mozart Nsuami .
A model of malaria population dynamics with migrants. Mathematical Biosciences and Engineering, 2021, 18(6): 7301-7317.
doi: 10.3934/mbe.2021361
|
| [3] |
Xue Liu, Xin You Meng .
Dynamics of Bacterial white spot disease spreads in Litopenaeus Vannamei with time-varying delay. Mathematical Biosciences and Engineering, 2023, 20(12): 20748-20769.
doi: 10.3934/mbe.2023918
|
| [4] |
Gang Huang, Edoardo Beretta, Yasuhiro Takeuchi .
Global stability for epidemic
model with constant latency and infectious periods. Mathematical Biosciences and Engineering, 2012, 9(2): 297-312.
doi: 10.3934/mbe.2012.9.297
|
| [5] |
Ardak Kashkynbayev, Daiana Koptleuova .
Global dynamics of tick-borne diseases. Mathematical Biosciences and Engineering, 2020, 17(4): 4064-4079.
doi: 10.3934/mbe.2020225
|
| [6] |
Mostafa Adimy, Abdennasser Chekroun, Claudia Pio Ferreira .
Global dynamics of a differential-difference system: a case of Kermack-McKendrick SIR model with age-structured protection phase. Mathematical Biosciences and Engineering, 2020, 17(2): 1329-1354.
doi: 10.3934/mbe.2020067
|
| [7] |
Yu Ji .
Global stability of a multiple delayed viral infection model with general incidence rate and an application to HIV infection. Mathematical Biosciences and Engineering, 2015, 12(3): 525-536.
doi: 10.3934/mbe.2015.12.525
|
| [8] |
Vanessa Steindorf, Sergio Oliva, Jianhong Wu .
Cross immunity protection and antibody-dependent enhancement in a distributed delay dynamic model. Mathematical Biosciences and Engineering, 2022, 19(3): 2950-2984.
doi: 10.3934/mbe.2022136
|
| [9] |
Rundong Zhao, Qiming Liu, Huazong Zhang .
Dynamical behaviors of a vector-borne diseases model with two time delays on bipartite networks. Mathematical Biosciences and Engineering, 2021, 18(4): 3073-3091.
doi: 10.3934/mbe.2021154
|
| [10] |
Cruz Vargas-De-León, Alberto d'Onofrio .
Global stability of infectious disease models with contact rate as a function of prevalence index. Mathematical Biosciences and Engineering, 2017, 14(4): 1019-1033.
doi: 10.3934/mbe.2017053
|
-
Abstract
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.
References
|
[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.
|
-
-
This article has been cited by:
| 1.
|
C. Connell McCluskey,
Global stability for an $SEI$ model of infectious disease with age structure and immigration of infecteds,
2016,
13,
1551-0018,
381,
10.3934/mbe.2015008
|
|
| 2.
|
Ram P. Sigdel, C. Connell McCluskey,
Global stability for an SEI model of infectious disease with immigration,
2014,
243,
00963003,
684,
10.1016/j.amc.2014.06.020
|
|
| 3.
|
Gang Huang, Chenguang Nie, Yueping Dong,
Global stability for an SEI model of infectious diseases with immigration and age structure in susceptibility,
2019,
12,
1793-5245,
1950042,
10.1142/S1793524519500426
|
|
| 4.
|
Wei Yang, Zhan Shu, James Lam, Chengjun Sun,
Global dynamics of an HIV model incorporating senior male clients,
2017,
311,
00963003,
203,
10.1016/j.amc.2017.05.030
|
|
| 5.
|
Xiao Wang, Zhaohui Yang, Xiongwei Liu,
Periodic and almost periodic oscillations in a delay differential equation system with time-varying coefficients,
2017,
37,
1553-5231,
6123,
10.3934/dcds.2017263
|
|
| 6.
|
Hebai Chen, Lan Zou,
How to control the immigration of infectious individuals for a region?,
2019,
45,
14681218,
491,
10.1016/j.nonrwa.2018.07.018
|
|
| 7.
|
Hong Zhang, Xiongwei Liu, Mingquan Yang,
Global exponential stability of a delay reduced SIR model for migrant workers’ home residence,
2015,
50,
08939659,
119,
10.1016/j.aml.2015.06.014
|
|
-
-
DownLoad: