Stability Analysis of Divorce Dynamics Models

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.