Mathematical modeling of intimate partner violence: Simulations of loss of control scenarios

摘要

In this study, we developed a mathematical model to help predict the level of violence between a perpetrator and the submissive victim of intimate partner violence. We consider that violence can be measured based on the violence accumulated in previous months starting from an initial condition of violence. The proposed model is based on a difference equation with a probabilistic parameter, which is referred to as the perpetrator’s loss of control parameter. This loss of control parameter is modeled as a discrete Markov chain with two states: self-control and loss of control. Another important factor that is incorporated in the model is a proportionality factor for considering the proportion of loss of control by the perpetrator, which is manifested as violence or injury toward the partner in a probable cycle of violence. Using this dynamic indicator, computational simulations can be performed to generate probable scenarios of intimate partner violence with various levels of severity. A qualitative analysis was performed of the probable behaviors, i.e., controllable (semi-stable) and uncontrollable (potentially deadly), that can occur at different monthly intervals. This dynamic indicator was then applied in a specific study of physical violence, where the prevalence of violence was used to approximate the loss of control state for the perpetrator.