Browsing by Author "Etsehiwot Gobezayewu"

Filter results by typing the first few letters
Now showing 1 - 1 of 1
  • No Thumbnail Available
    Item
    Analysis of Unhealthy Attitude on Marriage and its Impact on the Dynamics of Divorce using Mathematical Model
    (HAWASSA UNIVERSITY, 2024-06) Etsehiwot Gobezayewu
    Divorce is the dissolution of two partners marriage, which is a serious problem challenging the establishment of the family in a routine manner and causing severe impacts on the emotional and mental health of the individual. In this thesis, we modified and analyzed a mathematical model that describes the spread of unhealthy attitude on marriage and its impact on the dynamics of divorce. The population was divided in to six compartments and analyzed using a system of non-linear ordinary differential equations. The basic reproduction number R0 is calculated using next generation matrix operator. We have found two equilibrium points, namely the unhealthy attitude free equilibrium point and the unhealthy attitude present equilibrium point. We have established the conditions for the stability of equilibrium points. The unhealthy attitude free equilibrium point is both locally and globally stable if R0 < 1, and the unhealthy attitude present equilibrium point is also both locally and globally stable if R0 > 1. The modified model exhibits a forward bifurcation whenever R0 < 1, which indicates the threshold parameter plays an important role in reducing the spread of unhealthy attitude on marriage. Secondary data sources for divorce case were collected from Hawassa first instance court. The data were fitted to the model to estimate some parameter values using Least Square optimization method. Sensitivity analysis was performed to identify parameters which are sensitive to the reproduction number. According to this the contact rate between married and individuals who have unhealthy attitude β1 and the rate of transfer from unhealthy attitude to healthy counseling φ plays an important role in reducing R0 less than unity. Finally, we performed numerical simulations using ODE 45 codes to support the analytical results in agreement with numerical solutions.