DOI: 10.11648/j.ajam.20261405.17 ISSN: 2330-006X

Mathematical Model Analysis of Marriage Divorce Incorporating Counselling and Medical Attention

Felicien Habiyaremye
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This paper has investigated the mathematical model analysis of marriage divorce taking into consideration the effect of counselling and medical attention in order to minimize the divorce cases. The research aimed at developing the deterministic mathematical model of marriage divorce incorporating the counselling and medical attention(treatment), determining the divorce free and endemic equilibrium points, determining the sensitivity analysis and finding numerical simulation. The system of the differential equations of the model was proved to be well posed which showed that the mathematical model of marriage divorce was re-searchable. The differential equations were linearized using Jacobean matrix and It was found that the divorce free equilibrium point to be locally asymptotically stable when the reproduction number is less than one, and divorce endemic equilibrium point to be globally asymptotically unstable when the reproduction number is greater than one, . The sensitivity analysis was done to get the numerical values of the parameters involved in the model. The numerical simulations were done using Runge Kutta fourth order and MATLAB in order to generate the graphs. It was found that the number of divorced individuals reduced as results of individuals got counselling sessions and medical attention (treatment). It was equally observed, the active interaction between married and divorced individuals resulted in the increase of the divorced individuals due to the fact that the reproduction number is greater than one. The number of married individuals increased as a result of individuals got counselling sessions and separated individuals renewed their relationship. This research is of the great help of the community that with good communication, assume responsibility in the family, fidelity as couples, considering diversity in family and avoiding violence of any kind in the family as key factors of avoiding divorce in marriage.

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