Discrete mathematical modeling and optimal control of the marital status: Islamic polygamous marriage model case

Abstract

In this paper, we discuss a discrete mathematical model of Islamic polygamy and the social position of Muslims. In eleven compartments we explain the social situation and give an explanation of the marital status of each Males and females in Islamic societies that allow polygamy. In order to controlling and reducing the number of virgins men and women, divorced men and women we implement two control variables. The first control characterizes the benefits of an awareness campaign to educate virgin men and women about the benefits marriage to the individual and society, and the second control is about the legal procedures, administrative complexities and the grave financial and social implications of divorce. After that, we applied the optimal control theory to describe such an optimal strategies and finally a numerical simulation was performed to verify the theoretical analysis using a progressive-regressive discrete schema that converges following a convenient test related to the Forward–Backward Sweep Method (FBSM).