Optimal Control of Multiple Transmission of Water-Borne Diseases
A controlled SIWR model was considered which was an extension of the simple SIR model by adjoining a compartment (𝑊) that tracks the pathogen concentration in the water. New infections arise both through exposure to contaminated water as well as by the classical SIR person-person transmission pathwa...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/421419 |
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| author | G. Devipriya K. Kalaivani |
| author_facet | G. Devipriya K. Kalaivani |
| author_sort | G. Devipriya |
| collection | DOAJ |
| description | A controlled SIWR model was considered which was an extension of the simple SIR model by adjoining a compartment (𝑊) that tracks the pathogen concentration in the water. New infections arise both through exposure to contaminated water as well as by the classical SIR person-person transmission pathway. The controls represent an immune boosting and pathogen suppressing drugs. The objective function
is based on a combination of minimizing the number of infected individuals and the cost of the drugs dose. The optimal control is obtained by solving the optimality system which was composed of four nonlinear ODEs with initial conditions and four nonlinear adjoint ODEs with transversality conditions. The results were analysed and interpreted numerically using MATLAB. |
| format | Article |
| id | doaj-art-f2aec22d59b24372ae9c5a5382434a34 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f2aec22d59b24372ae9c5a5382434a342025-02-03T06:08:47ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/421419421419Optimal Control of Multiple Transmission of Water-Borne DiseasesG. Devipriya0K. Kalaivani1P. G. Department of Mathematics, Women's Christian College, Chennai 600006, IndiaP. G. Department of Mathematics, Women's Christian College, Chennai 600006, IndiaA controlled SIWR model was considered which was an extension of the simple SIR model by adjoining a compartment (𝑊) that tracks the pathogen concentration in the water. New infections arise both through exposure to contaminated water as well as by the classical SIR person-person transmission pathway. The controls represent an immune boosting and pathogen suppressing drugs. The objective function is based on a combination of minimizing the number of infected individuals and the cost of the drugs dose. The optimal control is obtained by solving the optimality system which was composed of four nonlinear ODEs with initial conditions and four nonlinear adjoint ODEs with transversality conditions. The results were analysed and interpreted numerically using MATLAB.http://dx.doi.org/10.1155/2012/421419 |
| spellingShingle | G. Devipriya K. Kalaivani Optimal Control of Multiple Transmission of Water-Borne Diseases International Journal of Mathematics and Mathematical Sciences |
| title | Optimal Control of Multiple Transmission of Water-Borne Diseases |
| title_full | Optimal Control of Multiple Transmission of Water-Borne Diseases |
| title_fullStr | Optimal Control of Multiple Transmission of Water-Borne Diseases |
| title_full_unstemmed | Optimal Control of Multiple Transmission of Water-Borne Diseases |
| title_short | Optimal Control of Multiple Transmission of Water-Borne Diseases |
| title_sort | optimal control of multiple transmission of water borne diseases |
| url | http://dx.doi.org/10.1155/2012/421419 |
| work_keys_str_mv | AT gdevipriya optimalcontrolofmultipletransmissionofwaterbornediseases AT kkalaivani optimalcontrolofmultipletransmissionofwaterbornediseases |