An Extended Compartmental Model for Divorce Dynamics with Reconciliation, Counseling and Socioeconomic Factors

This paper develops an extended mathematical framework for the analysis of divorce dynamics within a structured population. The proposed model is formulated as a linear inhomogeneous deterministic seven-compartment system that characterizes transitions among single, married, estranged, divorced, reconciled, counseling, and other related social states. Unlike many existing nonlinear social models, the present formulation admits explicit analytical tractability while incorporating behavioral control parameters that capture the effects of financial stress, social support, and digital media influence. The total population is rigorously shown to remain bounded, thereby ensuring the positivity and invariance of the feasible region. Explicit closed-form expressions for the equilibrium states are derived, together with a divorce reproduction threshold parameter, Rd, which governs the persistence or eradication of divorce dynamics. In particular, the divorce-free equilibrium is proven to be locally asymptotically stable when Rd < 1 and unstable when Rd > 1, thereby establishing a clear threshold condition for long-term marital stability. Stability properties are established through eigenvalue analysis of the associated system matrix and are further substantiated via Lyapunov-based arguments and parametric sensitivity analysis. Numerical simulations implemented using a fourth-order Runge–Kutta scheme validate the theoretical findings and demonstrate the stabilizing influence of reconciliation mechanisms and enhanced social support interventions. Overall, the study provides a mathematically rigorous and analytically tractable framework for understanding divorce persistenceand offers quantitative insights that may inform evidence-based social and policy interventions.