Open AccessStability Analysis of Divorce Dynamics Models
Author(s) -
Syamsir Muaraf,
Syamsuddin Toaha,
Kasbawati Kasbawati
Publication year - 2020
Publication title -
jurnal matematika, statistika dan komputasi/jurnal matematika statistik dan komputasi
Language(s) - English
Resource type - Journals
eISSN - 2614-8811
pISSN - 1858-1382
DOI - 10.20956/jmsk.v17i2.11984
Subject(s) - linearization , stability (learning theory) , population , leslie matrix , equilibrium point , class (philosophy) , eigenvalues and eigenvectors , mathematics , vital rates , econometrics , demography , mathematical economics , economics , statistics , population growth , nonlinear system , computer science , sociology , mathematical analysis , physics , artificial intelligence , quantum mechanics , machine learning , differential equation
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.