Stability Analysis of Divorce Dynamics Models


  • Syamsir Muaraf Depertemen Matematika
  • Syamsuddin Toaha Hasanuddin University
  • Kasbawati Kasbawati Hasanuddin University



Divorce Dynamics, Mathematical Model, Equilibrium Point, Stability Analysis, Pontryagin Minimum Principle, Forward-Backward Sweep Method, Optimal Control


This article examines the mathematical model of divorce. This model consists of four population classes, namely the Married class (M), the population class who experiences separation of separated beds (S), the population class who is divorced by Divorce (D), and the population class who experiences depression or stress due to divorce Hardship (H). This study focuses on the stability analysis of divorce-free and endemic equilibrium points. Local stability was analyzed using linearization and eigenvalues ​​methods. In addition, the basic reproduction number  is provided via the next generation matrix method. The existence and stability of the equilibrium point are determined from . The results showed that the rate of interaction between population M and populations other than H is very influential on efforts to minimize divorce. Divorce can be minimized when the transmission rate is reduced to . Reducing the transmission rate and increasing the rate of transfer from split bed class to married class can turn divorce endemic cases into non-endemic cases. A numerical simulation is given to confirm the analysis results.


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