A Mathematical Overview of the Monogamous Marriage in a Multiregion Framework: Modelling and Control

Abstract

The main objective of this paper is to develop a new mathematical model to study, analyze, and control the family status in several regions and to discuss the impact of the connectivity of regions and the mobility of residents on the marital status of the family, by adopting a multiregion discrete-time model. The modelling and the control process of the system that describes the case of monogamous marriages in a multiregion framework are considered. Two combined control strategies are proposed, which allow reducing the virgin and divorced individuals and increasing the number of married individuals in a specific region. The first control is considered as the impact of public awareness campaigns to educate virgin men and women about the benefits of marriage for the individual and the society; the second control characterizes the legal procedures, administrative complications, and the heavy financial and social consequences of divorces. The optimal control theory is applied to characterize such optimal strategies and determined numerically using a progressive-regressive discrete scheme to discuss the obtained results.

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

“…Proof. In order to derive the necessary condition for optimal control, the Pontryagins maximum principle in discrete time given in [8,9,14,15] was used. We obtain the following adjoint equations:…”

“…Different simulations can be carried out using various values of parameters. In the present numerical approach, we use the following parameters values taken from [9]: α 1 = 0.0023, α 2 = 0.0015, α 3 = 0.0018, α 4 = 0.00013, β 1 = 0.000022, β 2 = 0.000026, β 3 = 0.000027, β 4 = 0.000024, β 5 = 0.000025, λ 1 = 0.00003, λ 2 = 0.00002, λ 3 = 0.00018, λ 4 = 0.00004, δ 1 = 0.00002, δ 2 = 0.00002, δ 3 = 0.00022, δ 4 = 0.000028, µ 1 = 0.0002, µ 2 = 0.0003, µ 3 = 0.0004, µ 4 = 0.0004, γ 1 = 0.00035, γ 2 = 0.0001, γ 3 = 0.0001, τ 1 = 2000, and τ 2 = 3290.…”

“…M. Lhous in [8] have discussed Discrete mathematical modeling and optimal control of the marital status for the monogamous marriage case. And in [9] M. Lhous have develop a new mathematical model to study, analyze, and control the family status in several regions and the impact of the connectivity of regions and the mobility of residents on the marital status of the family, by adopting a multi-region discrete-time model. The civil status of a person in islamic family and society can be classified for women into one of four categories: virgin, married, divorced or widowed.…”