Optimal Control Problem of Treatment for Obesity in a Closed Population
Variety of intervention programs for controlling the obesity epidemic has been done worldwide. However, it is still not yet available a scientific tool to measure the effectiveness of those programs. This is due to the difficulty in parameterizing the human interaction and transition process of obes...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2014/273037 |
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| author | D. Aldila N. Rarasati N. Nuraini E. Soewono |
| author_facet | D. Aldila N. Rarasati N. Nuraini E. Soewono |
| author_sort | D. Aldila |
| collection | DOAJ |
| description | Variety of intervention programs for controlling the obesity epidemic has been done worldwide. However, it is still not yet available a scientific tool to measure the effectiveness of those programs. This is due to the difficulty in parameterizing the human interaction and transition process of obesity. A dynamical model for simulating the interaction between healthy people, overweight people, and obese people in a randomly mixed population is discussed in here. Two scenarios of intervention programs were implemented in the model, dietary program for overweight people with healthy life campaign and treatment program for obese people. Assuming all control rates are constant, disease free equilibrium point, endemic equilibrium point, and basic reproductive ratio (ℛ0) as the epidemic indicator were shown analytically. We find that the disease free equilibrium point is locally asymptotical stable if and only if ℛ0<1. From sensitivity analysis of ℛ0, we obtain that larger rate of dietary program and treatment program will reduce ℛ0 significantly. With control rates are continuous in time, an optimal control approach was applied into the model to find the best way to minimize the number of overweight and obese people. Some numerical analysis and simulations for optimal control of the intervention were shown to support the analytical results. |
| format | Article |
| id | doaj-art-26501e31065d4e11aae2d02de5cb02c1 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-26501e31065d4e11aae2d02de5cb02c12025-02-03T01:31:56ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252014-01-01201410.1155/2014/273037273037Optimal Control Problem of Treatment for Obesity in a Closed PopulationD. Aldila0N. Rarasati1N. Nuraini2E. Soewono3Department of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, P.O. Box 40132, Bandung, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, P.O. Box 40132, Bandung, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, P.O. Box 40132, Bandung, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, P.O. Box 40132, Bandung, IndonesiaVariety of intervention programs for controlling the obesity epidemic has been done worldwide. However, it is still not yet available a scientific tool to measure the effectiveness of those programs. This is due to the difficulty in parameterizing the human interaction and transition process of obesity. A dynamical model for simulating the interaction between healthy people, overweight people, and obese people in a randomly mixed population is discussed in here. Two scenarios of intervention programs were implemented in the model, dietary program for overweight people with healthy life campaign and treatment program for obese people. Assuming all control rates are constant, disease free equilibrium point, endemic equilibrium point, and basic reproductive ratio (ℛ0) as the epidemic indicator were shown analytically. We find that the disease free equilibrium point is locally asymptotical stable if and only if ℛ0<1. From sensitivity analysis of ℛ0, we obtain that larger rate of dietary program and treatment program will reduce ℛ0 significantly. With control rates are continuous in time, an optimal control approach was applied into the model to find the best way to minimize the number of overweight and obese people. Some numerical analysis and simulations for optimal control of the intervention were shown to support the analytical results.http://dx.doi.org/10.1155/2014/273037 |
| spellingShingle | D. Aldila N. Rarasati N. Nuraini E. Soewono Optimal Control Problem of Treatment for Obesity in a Closed Population International Journal of Mathematics and Mathematical Sciences |
| title | Optimal Control Problem of Treatment for Obesity in a Closed Population |
| title_full | Optimal Control Problem of Treatment for Obesity in a Closed Population |
| title_fullStr | Optimal Control Problem of Treatment for Obesity in a Closed Population |
| title_full_unstemmed | Optimal Control Problem of Treatment for Obesity in a Closed Population |
| title_short | Optimal Control Problem of Treatment for Obesity in a Closed Population |
| title_sort | optimal control problem of treatment for obesity in a closed population |
| url | http://dx.doi.org/10.1155/2014/273037 |
| work_keys_str_mv | AT daldila optimalcontrolproblemoftreatmentforobesityinaclosedpopulation AT nrarasati optimalcontrolproblemoftreatmentforobesityinaclosedpopulation AT nnuraini optimalcontrolproblemoftreatmentforobesityinaclosedpopulation AT esoewono optimalcontrolproblemoftreatmentforobesityinaclosedpopulation |