The mathematical model for marital interactions in Ghana

Abstract

In this paper, a mathematical model is developed to explain changes in the ratios of married persons, adulterers, and divorcees. A formula for predicting the percentage of couples in the country using the inversion transformation was formulated using the equations expressing the proportions of adulterers and divorcees. The qualitative study revealed two threshold conditions: the basic reproductive numbers for a divorcee (RoY) and an adulterer (RoZ) in a married context. Based on these threshold conditions, it was found that, on average, a divorcee persuades a spouse to dissolve their marriage every year. However, we found that a significant fraction of couples were either divorcing or committing adultery, as shown by the instability of the divorce-adultery equilibrium point. Every month, a couple will occasionally spend 5 or 6 days apart sleeping outside of their union. The results of the sensitivity analysis revealed that the main cause of the country’s growing divorce problem is the rate at which spouses end their relationships while being influenced by others. On the other hand, the prevalence of adultery in the nation is largely influenced by the rate at which an adulterer divorces their spouse.