A mathematical model to explore the role of tolerance in marriage stability and divorce dynamics

The purpose of this study is to develop a mathematical model to analyze the impact of tolerance on marriage stability and divorce dynamics. A deterministic mathematical model is formulated to describe marriage and divorce dynamics, incorporating tolerance as a modifying parameter. The standard incidence function is employed to represent the force of marital disunity. The local and global stability of the divorce-free equilibrium are examined using the Routh–Hurwitz criterion and the Metzler matrix approach, respectively, confirming its stability in both cases. Additionally, the global stability of the divorce endemic equilibrium is analyzed using a Lyapunov function, and the results indicate that it is globally stable. The divorce reproduction number R 0 is derived using the Next-Generation Matrix approach. To ensure model accuracy, model fitting is performed using empirical data by employing the Least squares method. The most influential parameters are identified using the normalized forward sensitivity index method. Both analytical and numerical results indicate that an increase in the tolerance factor is associated with a corresponding decrease in the divorce rate. The findings suggest that fostering tolerance in marriages could serve as a practical intervention to enhance marriage stability. Additionally, reducing contact between divorced individuals and married couples may help mitigate the spread of marital disunity. These insights provide valuable guidance for policymakers, marriage counselors, and social scientists in designing programs that promote enduring marital relationships.