An interactive bi-disruption model for marital instability with stability analysis

Abstract

Marital instability has a devastating effect on our society. In general, marital disruption results in negative physical and psychological health outcomes, as well as adverse economic consequences for children, adolescents and adults. An all-interactive bi-disruption state model is proposed and the stability of the disruption-free equilibrium of the model is explored. The aim is to examine the effects of both homogenous and heterogenous interactions on the propagation potential (the basic reproductive number) of marital disruptions. The homogenous interaction epitomizes couples’ own interaction in the marriage, while heterogenous interactions represent couples’ interactions with individuals of other unstable states. Stability analysis of the marital disruption-free equilibrium was established using both the Routh Stability and Castilos-Chavez GAS criteria. It was revealed that the marital disruption-free is locally and globally asymptotically stable whenever the basic reproductive number is less than unity. The dynamics were further demonstrated through sensitivity analysis of the parameters using the RK4 simulation technique, achieved with codes implemented in R. As the simulation results evince, increases of 33% and 17% in the rates of homogenous resolution and remarriage, as well as 13% and 15% decreases in the rates of heterogenous contacts respectively between individuals of states M and P; and M and D are enough to ensure stability of marriages. The study therefore, has crucial guidelines to minimize marital instability.

Keywords

• Bi-disruptions
• Interactive
• Resolution
• Remarriage
• Basic reproductive number
• Asymptotic stability