Disease dynamics for the hometown of migrant workers
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 migr...
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| Format: | Article |
| Language: | English |
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AIMS Press
2014-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.1175 |
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| author | Ram P. Sigdel C. Connell McCluskey |
| author_facet | Ram P. Sigdel C. Connell McCluskey |
| author_sort | Ram P. Sigdel |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-28b043ac37ba41afb8a4b756e60a14bb |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-28b043ac37ba41afb8a4b756e60a14bb2025-01-24T02:28:54ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-05-011151175118010.3934/mbe.2014.11.1175Disease dynamics for the hometown of migrant workersRam P. Sigdel0C. Connell McCluskey1Department of Mathematics, Wilfrid Laurier University, Waterloo, OntarioDepartment of Mathematics, Wilfrid Laurier University, Waterloo, OntarioA 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.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.1175delaymigrant workersepidemiology.global stabilitylyapunov functional |
| spellingShingle | Ram P. Sigdel C. Connell McCluskey Disease dynamics for the hometown of migrant workers Mathematical Biosciences and Engineering delay migrant workers epidemiology. global stability lyapunov functional |
| title | Disease dynamics for the hometown of migrant workers |
| title_full | Disease dynamics for the hometown of migrant workers |
| title_fullStr | Disease dynamics for the hometown of migrant workers |
| title_full_unstemmed | Disease dynamics for the hometown of migrant workers |
| title_short | Disease dynamics for the hometown of migrant workers |
| title_sort | disease dynamics for the hometown of migrant workers |
| topic | delay migrant workers epidemiology. global stability lyapunov functional |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.1175 |
| work_keys_str_mv | AT rampsigdel diseasedynamicsforthehometownofmigrantworkers AT cconnellmccluskey diseasedynamicsforthehometownofmigrantworkers |