Authors: E. Leal-Enríquez; Aime Renata Gutiérrez-Antúnez
Addresses: Department of ICE-CONTROL ESIME Zacatenco, Instituto Politécnico Nacional I.P.N., Unidad Profesional Adolfo López Mateos, Ciudad de México, México ' Department of Educación, Universidad de Baja California, Tepic, Nayarit, México
Abstract: A dynamic indicator to measure the level of violence between a perpetrator and victim of intimate partner violence is developed in this paper. Herein it is considered that violence can be measured through the rates of change over time of the violent interactions, considering the weight of severity of the violence committed. These rates of change are modelled by a logistic differential equation with a probabilistic parameter, the principle being the self-regulation of a perpetrator. This parameter of self-regulation is modelled by two changes of states: one of self-control and the other being a loss thereof. The transition of each state is modelled by a discrete Markov chain. With the proposed dynamic indicator, computational simulations are created to generate probable scenarios of partner violence with varying levels of severity. This dynamic indicator is then applied to a specific study of physical violence, using the prevalence of violence to approximate a state of loss of control. With the results obtained from the simulation, a qualitative analysis is made of the probable behaviours, controllable (semi-stable) and uncontrollable (potentially deadly), that can occur in a time interval of 3 and 12 months.
Keywords: dynamic indicator; mathematical model; violent scenarios; self-regulation; intimate partner violence.
International Journal of Mathematical Modelling and Numerical Optimisation, 2019 Vol.9 No.4, pp.366 - 381
Received: 23 Apr 2018
Accepted: 10 Oct 2018
Published online: 23 May 2019 *