A Mathematical Model for Reducing Divorce Cases According to Social Indicators for Morocco: Optimal Control Approach

Abstract

In this research, we discuss a mathematical model for a person’s social status with a focus on marital status. In most societies, the marital status of men and women can be categorized as follows: Unmarried refers to a young man or woman of legal marriageable age who is neither married nor engaged. The second category is engagement, a stage that precedes marriage, often characterized by acquaintance and typically of short duration. The third status is marriage, which is customarily conducted according to the traditions and customs of each religion or culture. The next category is separation, referring to married couples who are experiencing difficulties and are living apart but are not legally divorced. Following that is divorce, which denotes a legal dissolution of marriage. The final status is widowed.
Our research aims to address and reduce the phenomenon of divorce, which has become widespread, withmore than 50 percent of marriages reportedly lasting less than a year.We identify two control strategies that help minimize the number of divorced individuals while increasing the number of married individuals. The optimal control problem is formulated and analyzed by applying a discrete version of Pontryagin’s Maximum Principle. Numerical simulations are performed to validate the theoretical results.