TY  - JOUR
AU  - Pippal, Sarita
AU  - Ranga, Ajay
PY  - 2026
DA  - 2026/07/24
TI  - Modeling Marital Stability: A Dynamical Systems Analysis of Extramarital Affairs and Divorce
JO  - Journal of Mathematics and Interdisciplinary Applications
T2  - Journal of Mathematics and Interdisciplinary Applications
JF  - Journal of Mathematics and Interdisciplinary Applications
VL  - 2
IS  - 3
SP  - 164
EP  - 191
DO  - 10.62762/JMIA.2026.666866
UR  - https://www.icck.org/article/abs/JMIA.2026.666866
KW  - dynamical systems
KW  - marital stability
KW  - extramarital affairs
KW  - divorce dynamics
KW  - equilibrium analysis
KW  - sensitivity analysis
AB  - This study develops and analyzes a nonlinear mathematical model to describe the dynamics of marriage, extramarital affairs, marital breakdown, and divorce. The population is divided into five compartments: single $S(t)$, married $M(t)$, individuals in extramarital affairs $A(t)$, broken marriages $B(t)$, and divorced $D(t)$. The model is formulated as a system of nonlinear ordinary differential equations capturing transitions between these states through parameters representing marriage formation, affair initiation, reconciliation, separation, and divorce. Basic qualitative properties, including positivity and boundedness of solutions, are established to ensure the model is well posed. Equilibrium analysis reveals the trivial equilibrium $E_T=(0,0,0,0,0)$, the divorce-free equilibrium $E_0=(S^0,M^0,0,0,0)$, and a positive endemic equilibrium $E^*=(S^*,M^*,A^*,B^*,D^*)$. Stability is investigated via the Jacobian matrix and characteristic equation. The basic reproduction number $R_0$, derived using the next-generation matrix method, determines whether marital instability spreads in the population. The divorce-free equilibrium is locally asymptotically stable when $R_01$. Sensitivity analysis and numerical simulations are performed to examine the influence of key parameters, including marriage formation rate $\alpha$, affair initiation rate $\gamma$, instability rate $\sigma$, and reconciliation rate $\xi$. Phase portraits, parameter variation diagrams, and reproduction number plots confirm the analytical results. The findings highlight the roles of extramarital affairs and reconciliation in shaping marital stability and provide a quantitative framework for understanding long-term marriage and divorce dynamics.
SN  - 3070-393X
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  - 

@article{Pippal2026Modeling,
  author = {Sarita Pippal and Ajay Ranga},
  title = {Modeling Marital Stability: A Dynamical Systems Analysis of Extramarital Affairs and Divorce},
  journal = {Journal of Mathematics and Interdisciplinary Applications},
  year = {2026},
  volume = {2},
  number = {3},
  pages = {164-191},
  doi = {10.62762/JMIA.2026.666866},
  url = {https://www.icck.org/article/abs/JMIA.2026.666866},
  abstract = {This study develops and analyzes a nonlinear mathematical model to describe the dynamics of marriage, extramarital affairs, marital breakdown, and divorce. The population is divided into five compartments: single \$S(t)\$, married \$M(t)\$, individuals in extramarital affairs \$A(t)\$, broken marriages \$B(t)\$, and divorced \$D(t)\$. The model is formulated as a system of nonlinear ordinary differential equations capturing transitions between these states through parameters representing marriage formation, affair initiation, reconciliation, separation, and divorce. Basic qualitative properties, including positivity and boundedness of solutions, are established to ensure the model is well posed. Equilibrium analysis reveals the trivial equilibrium \$E\_T=(0,0,0,0,0)\$, the divorce-free equilibrium \$E\_0=(S^0,M^0,0,0,0)\$, and a positive endemic equilibrium \$E^*=(S^*,M^*,A^*,B^*,D^*)\$. Stability is investigated via the Jacobian matrix and characteristic equation. The basic reproduction number \$R\_0\$, derived using the next-generation matrix method, determines whether marital instability spreads in the population. The divorce-free equilibrium is locally asymptotically stable when \$R\_01\$. Sensitivity analysis and numerical simulations are performed to examine the influence of key parameters, including marriage formation rate \$\alpha\$, affair initiation rate \$\gamma\$, instability rate \$\sigma\$, and reconciliation rate \$\xi\$. Phase portraits, parameter variation diagrams, and reproduction number plots confirm the analytical results. The findings highlight the roles of extramarital affairs and reconciliation in shaping marital stability and provide a quantitative framework for understanding long-term marriage and divorce dynamics.},
  keywords = {dynamical systems, marital stability, extramarital affairs, divorce dynamics, equilibrium analysis, sensitivity analysis},
  issn = {3070-393X},
  publisher = {Institute of Central Computation and Knowledge}
}