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.
Highlights
In this work we will treat the modeling and control of a system that describes the case of monogamous marriage
We introduce a control variable that characterizes the benefits of an awareness campaign to educate virgin men and women about the benefits of marriage for the individual and for the society, especially the legal procedures, administrative complications, the heavy financial and social consequences of divorces respectively in the above mentioned model ( )-( )
5 Conclusions In this paper, we consider a discrete-time marital status model, we treat the modeling and control of a system that describes the case of monogamous marriage
Summary
During longitudinal studies [ – ] and [ ], changes in mental, physical, moral and social functioning were assessed of married, unmarried and widowed women. . % of educated women know about divorce Using these statistical studies and the evolution of marital status, we define a discrete model VMDW which defines the evolution of the marital status of the marriage in a population. The second control is determined for the persons who have initiated the divorce proceedings. There are a number of different methods for calculating the optimal control for a specific mathematical model. We investigate an approach that determines an optimal control relative to a discrete marital status model which allows to inoculate a control (awareness), which allows to reduce the virgin individuals and to increase the number of married individuals with a minimal cost.
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