Stability Analysis of Divorce Dynamics Models

Abstract

This article examines the mathematical model of divorce. This model consists of four population classes, namely the Married class (M), the population class who experiences separation of separated beds (S), the population class who is divorced by Divorce (D), and the population class who experiences depression or stress due to divorce Hardship (H). This study focuses on the stability analysis of divorce-free and endemic equilibrium points. Local stability was analyzed using linearization and eigenvalues ​​methods. In addition, the basic reproduction number is provided via the next generation matrix method. The existence and stability of the equilibrium point are determined from . The results showed that the rate of interaction between population M and populations other than H is very influential on efforts to minimize divorce. Divorce can be minimized when the transmission rate is reduced to . Reducing the transmission rate and increasing the rate of transfer from split bed class to married class can turn divorce endemic cases into non-endemic cases. A numerical simulation is given to confirm the analysis results.

Multiple dynamics in a delayed predator‐prey model with asymmetric functional and numerical responses

“…All the above situations were explained numerically as well as graphically. Toaha 32 proved that at most two outcomes R1 and R2 are possible when the model does not involve the intraspecific competition among predators, and both the functional and numerical responses are of Holling type I. We arrived at the same conclusion with Toaha 32 when the intraspecific competition is present among predators (analytical proof is given in Appendix ).…”

“…Toaha 32 proved that at most two outcomes R1 and R2 are possible when the model does not involve the intraspecific competition among predators, and both the functional and numerical responses are of Holling type I. We arrived at the same conclusion with Toaha 32 when the intraspecific competition is present among predators (analytical proof is given in Appendix ). Therefore, we conclude that the variety of such delay‐induced dynamical behaviors in a single and relatively simple model are due to the presence of the distinct numerical response function.…”

“…It is found that intra‐specific competition has no role in inducing stability switching. The dynamical behaviors of system () are on par with the outcomes of system () studied by Toaha 32 …”

“…Very interestingly, Toaha 32 also considered the Wangersky‐Cunningham (WC) model linked with linear harvesting term, which is similar to $$$$ {\displaystyle \begin{array}{cc}\hfill \dot{x}(t)& = rx(t)\left(1-\frac{x(t)}{K}\right)-\alpha x(t)y(t)- Ex(t),\hfill \\ {}\hfill \dot{y}(t)& =\beta x\left(t-\tau \right)y\left(t-\tau \right)- my(t)- Ey(t),\hfill \end{array}} $$$$ where $$$ E $$$ is the combined (equal) harvesting effort. He established that two distinct dynamics, viz., (R1) and (R2) hold in the WC model.…”

Asymptotic Study of Divorce Model with Pre-Marriage Preparedness as Control

“…They concluded that harmonization and limitation of social contagion will reduce the rate of divorce. A model of three compartments; married, divorced, and separated was formulated by [9] which was extended by [20]. In their study, they concluded that increasing the number of marriages that go into separation and educating them along with reducing contact with infectious divorcees help in combating the divorce epidemic.…”