Bifurcation and stability analysis with numerical simulations of a social model for marriage and divorce under fear effect

This manuscript adds a divorce term to a divorce-marriage model that has a fear effect. With MATLAB simulations (ode45), the entire time-dependent system of ordinary differential equations is solved numerically. Line and surface plots with varying sets of parameter values illustrate population variation over time. Equilibrium analysis is done for different cases (such as populations with no divorce, female-only, and male-only populations), and the stability analysis is made using Jacobian eigenvalues. The innovation of this study lies in the explicit incorporation of a divorce compartment into the developed marriage–divorce–fear model, providing an improved representation of social dynamics. Our expansion offers a deeper comprehension of the interplay between fear, divorce, and remarriage in shap- ing long-term population dynamics, unlike previous models that examined fear effects without directly incorporating divorce. This contribution enhances the mathematical modeling of social systems by elucidating novel bifurcation thresholds and stability requirements that encapsulate pivotal transitions in marital dynamics.
- Helal MA. Mathematical Modeling of Marital Dynamics.Springer;2024.
- Amato PR. The consequences of divorce for adults andchildren. J Marriage Fam. 2000;62(4): 1269–1287.
- Kelly JB. Children’s adjustment in conflicted marriage anddivorce: a decade review of research. J Am Acad Child &Adolesc Psychiatry 2000;39(8):963–973.
- McElroy M. Marriage markets and peer influence: Socialcontagion in marital decisions. Soc Sci Res. 2021.
- Karney BR, & Bradbury TN. The longitudinal course ofmarital quality and stability: a review of theory, methods, andresearch. PsycholBull. 2007;118:3–34.
- Brines J, & Joyner K. (1997). The ties that bind: principlesof cohesion in marriage and cohabitation. Am Soc Rev. 1997;62(3):333–355.
- Cherlin AJ. The deinstitutionalization of American marriage.J Marriage Fam. 2004;66(4):848–861.
- Whisman MA. Marital distress and DSM-IV psychiatricdisorders in a population-based national survey. J AbnormalPsychol. 2007; 116(3): 638–643.
- Amato PR. Research on divorce: continuing trends and newdevelopments. J Marriage Fam. 2010;72(3):650–666.
- Rogers SJ. Divorce and remarriage: the roles of gender andrace. J Marriage Fam. 1995;57(4):1083–1097.
- Bracher M, & Santow G. Divorce and remarriage inAustralia: recent trends and determinants. Popul Stud.1993;47(3):403–421.
- Times of India. “Forever gets shorter as Hyderabad sees rise indivorce filings.” The Times of India, February 2024. Available at: https://timesofindia.indiatimes.com/city/hyderabad/ forevergets-shorter-as-hyderabad-see-rise-in-divorcefilings/articleshow/123081008.cms [Accessed: 19 August2025].
- ThinkRSP Law. “The Growing Trend of Divorce Casesin India.” ThinkRSP Law Blog, 2024. Available at: https://www.thinkrsplaw.com/the-growing-trend-of-divorce-cases-in-india/ [Accessed: 19 August 2025].
- Echelaw. “Divorce Rate in India: AnInsightful Analysis.” Echelaw, 2024. Available at: https://www.echelaw.com/divorce-rate-in-india-aninsightful-analysis/ [Accessed: 19 August 2025].
- Forever News. “Untying the Knot: Changing Landscapeof Divorce in India.” Forever News, 2024. Available at: https://www.forevernews.in/fn-premium/untying-the-knot-changing-landscape-of-divorce-in-india-839846 [Accessed:19 August 2025].
- Gottman JM. What Predicts Divorce? The Relationship BetweenMarital Processes and Marital Outcomes. Lawrence ErlbaumAssociates; 1994.
- Tessema GM, Alemayehu G, Getachew T. Mathematicalmodeling of marriage and divorce dynamics. J Appl Math.2021 2021;2021:1–12.
- Duato J, Odar M. A mathematical model of divorcepropagation. Physica A 5272019;121215.
- Gambrah CA, Adzadu S. A nonlinear mathematical model forthe dynamics of divorce epidemics in Ghana. Math Biosci Eng.19 2022;2022(3):2675–2694.
- Tessema H, Haruna I, Osman S, Kassa E. A mathematical modelanalysis of marriage divorce. Commun Math Biol Neurosci. 20222022; Article ID 15. https://doi.org/10.28919/cmbn/6851
- Karaagac B. A numerical investigation of marriagedivorce model. Results Appl Math. 20 2023; 100329.https://www.sciencedirect.com/science/article/pii/S2468227623003290
- Gweryina RI, Yusuf SM, Yusuf JA. Qualitative analysis of amathematical model of divorce epidemic with anti-divorcetherapy. East Afr Sch J Eng Comput Sci. 4 2; 2021.https://pisrt.org/psr-press/journals/easl/05-vol-4-2021-issue-2/qualitative-analysis-of-a-mathematical-model-ofdivorce-epidemic-with-anti-divorce-therapy/
- Barnes B, Adzadu S, Gambrah C. The mathematical modelfor marital interactions in Ghana. Results Appl Math. 19 2023:100354. https://www.sciencedirect.com/science/article/ pii/S2468227622003544
- Mathematical control of divorce stressamong marriages. Maths J. 65; 2021.https://www.mathsjournal.com/pdf/2021/vol6issue5/PartB/6-3-19-859.pdf
- Murray JD. Mathematical Biology I: An Introduction, 3rd ed.Springer; 2002.