Abstract

Marriage and divorce are pivotal aspects of societal dynamics, influencing family structures and individual well-being. This research introduces an advanced mathematical model to comprehend the intricate dynamics of marital relationships. Unlike conventional models, which often overlook the unpredictability inherent in human interactions, our model integrates stochastic elements and real-world factors such as mental distress and family issues. Mathematical modeling unveils the dynamics of marriage and divorce, guiding interventions to foster relationship stability and societal cohesion amidst multifaceted influences. However, the deterministic approach is limited due to the randomness of virus behavior. To address this issue, a more realistic stochastic model for computer viruses is considered, which can better capture the unpredictability of virus spread and establish effective preventive measures. The positivity and uniqueness of the model are checked, and the extinction and persistence theorems are proved using Ito's method. Numerical simulation shows that when the value of increases the divorces increases in the population while by increasing the value of the broken individuals recovered from their conflict and came back to its married lifestyle.