Abstract
In the context of mathematical models applied to social sciences, we present and analyze a model based on differential equations for the intimate partner violence (IPV). Such a model describes the dynamics of a heterosexual romantic couple in which the man perpetrates violence against the woman. We focus on incorporating different key factors reported in the literature as causal or motivational factors to perpetrate IPV. Among the main factors included are the failures in self-regulation, the man’s need to control the woman, the social pressure on the woman to remain married, and empowerment programs. Another aspect that we include is periodic alcohol consumption for the man. The discussion of the model includes a stability analysis of its equilibrium points and the asymptotic behavior of its solutions. Also, the interpretation of results is presented in terms of IPV phenomenon. Finally, a brief review is given on different scales to quantify human behavioral traits and numerical simulations for some IPV scenarios.
Highlights
Violence against woman is a social problem that afflicts all societies, without distinction of race, socioeconomic level or academic degree
Our objective is to model mathematically the dynamics of the intimate partner violence (IPV) problem in one couple in order to contribute to a better understanding of this social phenomenon
We present the development of a first mathematical model in ordinary differential equations, which allows us to predict the possible violent situations that a woman could face in the relationship
Summary
Violence against woman is a social problem that afflicts all societies, without distinction of race, socioeconomic level or academic degree. We search for models to describe the evolution in time of violence or related variables With this approach, we find models such as the one reported by Poza et al [9] which is an epidemiological type model that describes the evolution of the populations of different types of men, who were classified according to their level of woman abuse in Spain. Important and pioneer work which is supported by a long and deep research on human behavior for marital couples is reported in [10,11] by Gottman et al Let us say, that this article is not directly related to violence levels, but it presents and analyzes a model to predict a possible marital dissolution
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