Discrete mathematical modeling and optimal control of the marital status: the monogamous marriage case
Abstract In this paper, we consider a discrete model of the marital status of the family dynamics. It is assumed that individuals in the society can be classed in one of the eight compartments: virgin men, virgin women, married men, married women, divorced men, divorced women, widowed men and widowe...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-10-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-017-1390-0 |
| _version_ | 1819207965425532928 |
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| author | Mustapha Lhous Mostafa Rachik Hassan Laarabi Ahmed Abdelhak |
| author_facet | Mustapha Lhous Mostafa Rachik Hassan Laarabi Ahmed Abdelhak |
| author_sort | Mustapha Lhous |
| collection | DOAJ |
| description | Abstract In this paper, we consider a discrete model of the marital status of the family dynamics. It is assumed that individuals in the society can be classed in one of the eight compartments: virgin men, virgin women, married men, married women, divorced men, divorced women, widowed men and widowed women. The objective of this work is to treat the modeling and control the system that describes the case of monogamous marriage. We determine two controls which allow to reduce the number of virgin, divorced individuals and increase the number of married individuals. The first control is the benefits of an awareness campaign to educate virgin men and women about the benefits of marriage for the individual and for the society, the second control characterizes the legal procedures, administrative complications and the heavy financial and social consequences of divorces. The optimal control problems are procured based on a discrete version of Pontryagin’s maximum principle and determined numerically using a progressive-regressive discrete schema that converges following a convenient test related to the Forward-Backward Sweep Method (FBSM) on the optimal control. |
| first_indexed | 2024-12-23T05:31:52Z |
| format | Article |
| id | doaj.art-081d382ec45c4090b078dc58152ed7b4 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-23T05:31:52Z |
| publishDate | 2017-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-081d382ec45c4090b078dc58152ed7b42022-12-21T17:58:27ZengSpringerOpenAdvances in Difference Equations1687-18472017-10-012017111610.1186/s13662-017-1390-0Discrete mathematical modeling and optimal control of the marital status: the monogamous marriage caseMustapha Lhous0Mostafa Rachik1Hassan Laarabi2Ahmed Abdelhak3Laboratory of Modelling, Analysis, Control and Statistics, Department of Mathematics and Computer Science, Faculty of Sciences Ain Chock, Hassan II University of CasablancaLaboratory of Analysis Modelling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University of CasablancaLaboratory of Analysis Modelling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University of CasablancaDepartment of Mathematics, Faculty of Sciences, University Ibn TofailAbstract In this paper, we consider a discrete model of the marital status of the family dynamics. It is assumed that individuals in the society can be classed in one of the eight compartments: virgin men, virgin women, married men, married women, divorced men, divorced women, widowed men and widowed women. The objective of this work is to treat the modeling and control the system that describes the case of monogamous marriage. We determine two controls which allow to reduce the number of virgin, divorced individuals and increase the number of married individuals. The first control is the benefits of an awareness campaign to educate virgin men and women about the benefits of marriage for the individual and for the society, the second control characterizes the legal procedures, administrative complications and the heavy financial and social consequences of divorces. The optimal control problems are procured based on a discrete version of Pontryagin’s maximum principle and determined numerically using a progressive-regressive discrete schema that converges following a convenient test related to the Forward-Backward Sweep Method (FBSM) on the optimal control.http://link.springer.com/article/10.1186/s13662-017-1390-0discrete marital status modelmonogamous marriagePontryagin’s maximum principleoptimal control |
| spellingShingle | Mustapha Lhous Mostafa Rachik Hassan Laarabi Ahmed Abdelhak Discrete mathematical modeling and optimal control of the marital status: the monogamous marriage case Advances in Difference Equations discrete marital status model monogamous marriage Pontryagin’s maximum principle optimal control |
| title | Discrete mathematical modeling and optimal control of the marital status: the monogamous marriage case |
| title_full | Discrete mathematical modeling and optimal control of the marital status: the monogamous marriage case |
| title_fullStr | Discrete mathematical modeling and optimal control of the marital status: the monogamous marriage case |
| title_full_unstemmed | Discrete mathematical modeling and optimal control of the marital status: the monogamous marriage case |
| title_short | Discrete mathematical modeling and optimal control of the marital status: the monogamous marriage case |
| title_sort | discrete mathematical modeling and optimal control of the marital status the monogamous marriage case |
| topic | discrete marital status model monogamous marriage Pontryagin’s maximum principle optimal control |
| url | http://link.springer.com/article/10.1186/s13662-017-1390-0 |
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