The fact that women are abused by their male partner is something that happens worldwide in the 21st century. In numerous cases, abuse only becomes publicly known when a fatal event occurs and is beyond any possible remedy, that is, when men murder their female partner. Since 2003, 793 (September 4, 2015) women have been assassinated by their significant other or excouple in Spain. Only 7.2% of murdered women had reported their fear and previous intimate partner violence (IPV) to the police. Even when the number of female victims is comparable to the number of victims by terrorism, the Government has not assigned an equal amount of resources to diminish the magnitude of this hidden social problem. In this paper, a mathematical epidemiological model to forecast intimate partner violence in Spain is constructed. Both psychological and physical aggressor subpopulations are predicted and simulated. The model’s robustness versus uncertain parameters is studied by a sensitivity analysis.
Violence against women occurs in all geographical areas and in all types of society. Violence affects girls and women of all ages and in all stages of life. In western societies, it has not been until quite recently (1979) that the intimate violence partner was institutionally identified and condemned. The origin is found in feminists in the 1950s [
Women abuse embraces different types of manifestations, such as physical violence, including sexual abuse, emotional-psychological violence, verbal abuse, religious discrimination, economic deprivation, isolation, gender privilege, and beating [
Women abuse takes place in different environments: workplace, public areas, family, and friends, and even at continuous and sustained connectability due to technological appliances. While the former type (workplaces and public areas) is more visible and socially condemned [
Moreover according to [
The incidence of violence against women in intimate relationships is difficult to diagnose. In fact, five different types can be identified: coercive controlling, violent resistance, situational couple violence, separation-instigated violence, and mutual violent control [
Even when progress is made from the justice viewpoint, the intimate violence problem remains mainly hidden for several reasons, such as low victimization acceptance, as it takes place at the heart of the couple. It produces social shame and a feeling of emotional failure experienced by women, which are the strength of a male chauvinist culture. There is also common victim tendency to forgive and forget lower levels of violence based on the myth of the romantic love that causes intimate partner violence (IPV) to persist [
It is difficult not only to identify the IPV problem, but to also quantify it in order to strength the claim for public answers to mitigate this social problem. In fact, the only available information is the casualties and police complaints made by victims [
As far as we know, previous studies have been qualitative in nature, have been based on sampling women populations by questionnaires [
For the particular case of Spain, more than 1,000 women have been murdered in the last 15 years by their significant others, a number that exceeds the number of victims murdered by the terrorist group ETA. For the time being, about 4,500 aggressors are in Spanish prisons for committing sexual abuse [
There exist recent studies modeling mathematically the domestic violence throughout continuous time differential equation models [
The aim of this paper was to construct a dynamic mathematical model by forecasting the amount of intimate partner aggressors over the 2012–2017 time horizon in Spain. By means of a population model that split the population into several categories according to different levels of violence and by quantifying by semester the main causes of IPV transits among subpopulations, a difference system provided dynamic quantification in a future time.
This paper is structured as follows: Section
Violence against women is transversal, with no distinction of social class or academic and professional qualification. We split the population of potential men abusers in Spain whose ages fell in the interval
Our study started in January 2012 and split the male population in Spain by semester into the four above-defined categories using the following notation: AS( AF(
The male population whose ages fell in the interval
Secondly, we estimated the AS subpopulation following [
The
Finally by subtracting the amounts of the three previous categories from the general population, we estimated the number of regular men (
Initial subpopulation in January 2012.
| | | |
---|---|---|---|
10.20% | 53% | 36% | 0.8% |
Among the factors that influence human behavior, we consider demographic, economic, and psychosocial factors. Some other possible factors are of the genetic type, which was not taken into account [
Our dynamic compartmental model was built by quantifying the semester transits between subpopulations throughout the study period (January 2012–December 2017).
We defined and quantified these transit coefficients. Changes in total population were due to demographic factors, in particular, birth (men who became 16 years old), death (naturally deceased or functional exit from the system when men became older than 75 years old), and emigration/immigration.
By obtaining the number of male births at each semester [
Subpopulation proportions of model incomers.
Egalitarian | 5.00% |
Regular | 58.57% |
Emotional-psychological abuser | 33.00% |
Physical aggressor | 3.43% |
This proportion in absolute values sized the quantities shown in Table
Number of model incomers per semester.
| | AS | AF | |
---|---|---|---|---|
01-Jul-12 | 4,667 | 54,675 | 30,805 | 3,202 |
01-Jan-13 | 4,753 | 55,674 | 31,368 | 3,260 |
01-Jul-13 | 4,753 | 55,674 | 31,368 | 3,260 |
01-Jan-14 | 4,725 | 55,348 | 31,185 | 3,241 |
01-Jul-14 | 4,725 | 55,348 | 31,185 | 3,241 |
01-Jan-15 | 4,894 | 57,323 | 32,297 | 3,357 |
01-Jul-15 | 4,894 | 57,323 | 32,297 | 3,357 |
01-Jan-16 | 5,140 | 60,209 | 33,923 | 3,526 |
01-Jul-16 | 5,140 | 60,209 | 33,923 | 3,526 |
01-Jan-17 | 5,220 | 61,143 | 34,450 | 3,581 |
01-Jul-17 | 5,220 | 61,143 | 34,450 | 3,581 |
Leaving the system occurred when the population became older than 74 years but also when males died in the age interval
Finally, the last demographic transit results from the net emigration impact due to economic reasons [
Apart from the demographic factors, the subpopulations’ dynamical behavior was influenced by the following. Women’s level of permissiveness against abusive behavior by their partners [ Men’s alcohol and drug consumption [ Jealousy as a factor promoted by the chauvinist culture [ Economic stress (long-term unemployment) [ The contagion effect on men caused by their close environment where examples of gender violence are experienced or suffered throughout [ Technology: the impact of new technologies on intimate partner psychological abuse (stalking) [
After we identified the main factors that influenced the intimate violence partners phenomenon, we proceeded to quantify the transit coefficients among categories from one period (
We began by measuring the transit from the subpopulation of regular
We assumed that this effect occurred only after a stable relationship among young partners. In our hypotheses, this possibility only occurred in a stable relationship between a young regular
There were two independent and different types of transit among the same subpopulations.
We considered the recovery effect due to therapy and the positive influence of a new egalitarian partner woman.
The above processed coefficient transit allowed the construction of the block diagram model shown in Figure
Block diagram model.
After defining the transit coefficients, the population dynamics were given by the set of difference equations, expressed as follows.
This system can be written in a matrix form as follows:
After we modeled the transit coefficients, the subpopulations were computed by solving the model. Thus by taking
Results of the model that corresponded to
| | | AS | AF |
---|---|---|---|---|
| 1,713,051 | 8,901,145 | 6,046,061 | 134,359 |
01-Jul-12 | 1,716,898 | 8,920,041 | 5,495,299 | 522,821 |
01-Jan-13 | 1,719,020 | 8,889,527 | 5,047,893 | 842,092 |
01-Jul-13 | 1,720,848 | 8,828,147 | 4,688,071 | 1,104,939 |
01-Jan-14 | 1,730,442 | 8,790,242 | 4,429,615 | 1,322,814 |
01-Jul-14 | 1,739,460 | 8,735,669 | 4,223,798 | 1,505,293 |
01-Jan-15 | 1,753,035 | 8,699,773 | 4,080,490 | 1,659,531 |
01-Jul-15 | 1,765,928 | 8,655,552 | 3,968,615 | 1,791,344 |
01-Jan-16 | 1,778,343 | 8,610,879 | 3,884,905 | 1,905,039 |
01-Jul-16 | 1,790,044 | 8,562,543 | 3,820,648 | 2,003,658 |
01-Jan-17 | 1,801,107 | 8,515,530 | 3,774,027 | 2,089,996 |
| 1,811,480 | 8,467,595 | 3,739,342 | 2,166,010 |
As Table
During the considered study period, the proportion of regular and egalitarian men remained fairly stable and changed less than 1%, while AS dropped by 12.90%. In contrast, the AF proportion grew considerably by about 12% (Table
Subpopulation results.
| | | AS | AF |
---|---|---|---|---|
01-Jan-12 | 10.20% | 53.00% | 36.00% | 0.80% |
01-Jul-17 | 11.19% | 52.32% | 23.10% | 13.38% |
The trend of the studied subpopulations is shown in Figure
Subpopulation trends.
Table
Robustness alcohol rate.
Alcohol rate | | | AS | AF |
---|---|---|---|---|
3 | 11.28% | 54.34% | 21.59% | 12.79% |
4 | 11.23% | 53.32% | 22.36% | 13.09% |
5 | 11.19% | 52.32% | 23.10% | 13.38% |
6 | 11.15% | 51.34% | 23.83% | 13.68% |
7 | 11.11% | 50.39% | 24.53% | 13.97% |
One important issue in the proposed model was the probability of the couple’s stability, explained when quantifying
Sensitivity analysis of the model versus the couple’s stability.
| | | AS | AF |
---|---|---|---|---|
1 | 11.11% | 50.39% | 24.53% | 13.97% |
2 | 11.52% | 58.83% | 18.22% | 11.43% |
4 | 12.08% | 68.15% | 11.60% | 8.17% |
6 | 12.41% | 72.82% | 8.47% | 6.29% |
8 | 12.64% | 75.56% | 6.69% | 5.12% |
Our model quantified the future population of psychological and physical aggressors in Spain by taking into account dynamic factors, such as demographic, economic, and sociocultural (alcohol, drugs, jealousy, marital separations, and poverty index) factors. However, it did not take into account important factors such as genetics and/or legal environments, which most likely had an impact on our results. Data about genetic factors is confidential, while legal environment data can be simulated, but it is a fixed unchangeable factor in location and time period terms.
An important underlying consequence of this study is the prevalent potential and preventive role played by women in each domestic violence event, to the extent that the main recommendation to overcome this dramatic problem lies in women’s active decision of breaking up their relationship in early stages of psychological abuse. This long-term recommendation requires strong willpower and Government action by investing in egalitarian education from early stage on childhood.
In the short-term the main recommendation to slow down this dramatic problem is sound and urgent public investment in education and media campaign (TV, social media, radio, public venues, and advertisements).
From our model, the hidden population of aggressors appears which is not quantified by official statistics and which reveals the problem when it is irreparable. Among the main reasons that explain this situation, we find poor recognition of abusive partners’ behaviors in early stages of the relationship, combined with the social shame and low levels of self-esteem experienced by abused women. Lack of security resources (economic, legal protection, housing, and psychological resources) means that women barely report their abusive partners.
One of the advantages of having such a model like that presented herein is that the results can be simulated according to certain parameters, such as level of alcoholism consumption and drug use.
The study can be applied to any other geographical area where data are available, and the study period can be changed. However, it is important to take into account that the longer the study period, the less reliable the obtained results.
The authors declare that they have no conflict of interests as to the publication of this paper.