VIDA: A simulation model of domestic VIolence in times of social DistAncing
Lígia Mori Madeira, Bernardo Alves Furtado, Alan Rafael Dill
VVIDA: A simulation model of domestic VIolencein times of social DistAncing
L´ıgia Mori Madeira , Bernardo Alves Furtado , and Alan RafaelDill
Department of Political Science at Federal University of RioGrande do Sul (UFRGS) National Council for Technological Development (CNPq) Institute for Applied Economic Research (Ipea)January 12, 2021
Abstract
Violence against women occurs predominantly in the family and do-mestic context. The COVID-19 pandemic led Brazil to recommend and,at times, impose social distancing, with the partial closure of economicactivities, schools, and restrictions on events and public services. Prelimi-nary evidence shows that intense coexistence increases domestic violence,while social distancing measures may have prevented access to public ser-vices and networks, information, and help. We propose an agent-basedmodel (ABM), called VIDA, to illustrate and examine multi-causal factorsthat influence events that generate violence. A central part of the model isthe multi-causal stress indicator, created as a probability trigger of domes-tic violence occurring within the family environment. Two experimentaldesign tests were performed: (a) absence or presence of the deterrencesystem of domestic violence against women and (b) measures to increasesocial distancing. VIDA presents comparative results for metropolitan re-gions and neighbourhoods considered in the experiments. Results suggestthat social distancing measures, particularly those encouraging stayingat home, may have increased domestic violence against women by about10%. VIDA suggests further that more populated areas have compara-tively fewer cases per hundred thousand women than less populous capi-tals or rural areas of urban concentrations. This paper contributes to theliterature by formalising, to the best of our knowledge, the first modelof domestic violence through agent-based modelling, using empirical de-tailed socioeconomic, demographic, educational, gender, and race data atthe intraurban level (census sectors).
Keywords:
Domestic Violence, Violence against Women, Agent-basedModels (ABMs), Pandemics, Simulation, Metropolitan Regions1 a r X i v : . [ c s . M A ] J a n Introduction
Domestic violence is a global public health and human rights violation issue(OPAS and WHO 2017). It is estimated that around 30% of women in the worldsuffer, or have suffered violence, usually committed by intimate male partners.Many cases result in homicides, with almost 40% of female murders committedby their partners. UN Women estimates that in countries like France, Cyprus,Singapore, and Argentina, social distancing has increased cases of domesticviolence by 25% to 30% (Women 2020). A report by WHO and PAHO alsodenounces that domestic violence against women tends to increase in times ofemergency, including epidemics, victimising more vulnerable female groups suchas the elderly, women with disabilities, refugees, and those living in conflict-affected areas (WHO and OPAS 2020).Under normal circumstances, this panorama reveals the seriousness withwhich the problem must be addressed. During the pandemic with the rec-ommendations for isolation and social distancing, authorities, media, and re-searchers have pointed to an increase in domestic violence rates in many coun-tries. This is also the case in Brazil, if not worse (Warken 2020). Data releasedby the National Ombudsman for Human Rights, office linked to the Ministryof Women, Family, and Human Rights, indicate that calls to the hotline grew14%, with an increase of 37.6% in April compared to the same month in 2019(Antunes 2020).Social distancing alters the internal dynamics of domestic violence againstwomen by intensifying the factors at the root of this violence, such as gen-der inequality, the patriarchal system, the macho culture, and misogyny. Also,domestic violence may increase in the context of the pandemic due to the con-sequent economic impact, the overload of reproductive labour on women, stressand other emotional effects, alcohol or drug abuse, and the reduction of helplinesand services (Alencar et al. 2020).This study seeks to illustrate situations of domestic violence against womenbefore and after the COVID-19 pandemic using agent-based simulation mod-elling, reproducing the main findings in the literature regarding the causes ofdomestic violence. The model proposed (called VIDA) contributes to under-standing the mechanisms behind the hypothesis that staying at home as a so-cial distancing measure affects the magnitude of numbers related to domesticviolence. Our experimental design introduces deterrence and social distancingmeasures in the model, to compare with the baseline model that reflected thecontext before the pandemic.The simulation demonstrated that the difference in the effects of deterrencein each cohort due to the availability of the criminal justice system and informalcontrol networks (community) was the mechanism guiding the explanation forthe increase in cases of domestic violence against women while following socialdistancing measures. Specifically, the study estimated metrics for the economicdecline and for the behaviour of staying at home as a social distancing measurethat allows comparing Brazilian metropolitan regions. Therefore, the simulationcould grasp regional differences while contributing to understanding the main2actors around social distancing and economic decline, as well as the existenceand features of deterrence measures.Section two provides an overview of the literature on the causes of domesticviolence committed by intimate partners. Section three describes the method-ology and presents the model VIDA. We explain the model’s idea, assumptions,and implementation based on the construction of the indicator of stress andthe characterisation of the artificial population. Also, we discuss the model’svalidation, calibration, and tests of policies that illustrate domestic violence,before and during the application of social distancing measures. Section fourshows the general results and analysis, based on weighted areas, for each of theBrazilian metropolitan regions. Section five closes this article, presenting ourfinal considerations.
The literature review on partner abuse perpetration (Rothman 2018) lists sev-eral causes and determinants of this type of violence. The discussion startsfrom the definition of the very concept of dating abuse, now understood asphysical, sexual, verbal, and emotional abuse directed at a partner (present orex), occurring in relationships of people of the opposite or same sex (Center forDisease Control 2019), not distinguishing between the type of abuse, its severity,the consequences of these acts, the frequency with which they occur, or differ-entiating the gender of perpetrator and victim. This concept does not includeviolence characterised as being chronic, severe, resulting in physical or sexual in-jury, caused by a person in a position of advantage over the victim. These typesgenerally characterise the domestic violence against women and are taken bysocial movements as a core element in their definition, given the characteristicof power and control, involving what the literature calls patriarchal terrorism,of the abuser towards the victim.Based on a sociological perspective, Johnson (1995) demonstrates two differ-ent ways to approach the issue of domestic violence. One is the family violenceperspective, in which the object refers to family conflicts due to their frequency,the role of stress, and the adherence to normative standards that would acceptsome form of violence in a family context. The other is the feminist perspec-tive, which restricts the focus to specific factors of the perpetration of violenceagainst women by intimate partners, prevailing the historical, cultural, andsocial patterns of patriarchy. Other concepts observed in the literature are in-timate terrorism, a form of violence aimed at controlling the relationship; andsituational violence between partners, which does not result from patterns ofabuse and control but escalates to violence in the emergence of specific situationsof conflict (Johnson and Leone 2005).According to Stark (2012), the conceptualisation and, consequently, how toaddress domestic violence, are divided into two models, the “violent incident3odel” and the “coercive control model”. The first defines violence betweenpartners as a criminal offence since the late 1990s. It considers measures suchas restricting access to victims, children, and firearms, and is based on shelterprograms, legal assistance, and other support for victims. In the violent incidentmodel, incarceration is the preferred response for offenders, and the level of dan-ger observed is the main factor determining how the police respond to domesticabuse. Abusers who continue their actions – with sufficient time between eachevent – are considered, by analogy to criminals in general, as repeat offenders.Despite the contribution to reducing severe forms of violence, scholars questionwhether incarceration and judicial protection can have a long-term impact.The coercive control model is defended as a more comprehensive approach.It considers that most female victims of violence are subjected to a patternof dominance that includes techniques of isolation, degradation, exploitation,control, and physical violence. It is a pattern of psychological and emotionalabuse that the literature calls patriarchal or intimate terrorism (Johnson 2008),or coercive control (Stark and Hester 2019; Stark 2020). Stark shares that“this gap between what the law defines as the crime of domestic violence andthe actual tactics abusers use to subjugate their partners severely limits theefficacy of even the most dedicated and well-trained police” (2012, p. 201).For advocates of this model, it is necessary to change from a pattern based onspecific incident response to a proactive response that redefines partner abuseas ongoing conduct. It is crucial to apply appropriate sanctions to stop thecourse of such conduct and the risk of escalation. Studies have advanced inunderstanding the risk to children living in environments of domestic violence(Katz 2016). Despite criticism, scholars argue that police intervention in eventsof domestic violence has prevented thousands of injuries and deaths, in additionto changing the normative pattern regarding violence against women (Stark2012).The concern with causal explanations for violence between intimate part-ners began in the last century, involving different mechanisms, ranging frompsychoanalytic theories, explanations of intergenerational transmission, and so-cial learning, to theories of situational background. Bell and Naugle (2008)review the main theories of intimate partner violence (IPV) with variables ofinterest and theoretical limitations. The main explanations encompass (a) theidea that frustration in one area of life can lead to aggression – for example,low autonomy in the workplace could lead to abusive compensation at home–, (b) the assumption that childhood and the environment where a person wasraised play a role in predicting future abusive partners, and (c) the theoriesmixing explanations of distal background, such as childhood abuse, exposure tointerparental aggression, and situations that trigger violence (alcohol consump-tion, jealousy, and other conflicts with the partner). The authors propose aframework that, based on different theories, offers a contextual analysis of IPVincluding distal and proximal aspects, proposing that the perpetration of abusecan be explained by antecedent factors, motivators, unwritten rules, and legaland social consequences of violent behaviour (Bell and Naugle 2008). Accord-ing to the authors, the advantage of this integrating theoretical framework is4he flexibility in presenting common points between apparently contradictoryfindings.Sociocultural theories range from economic explanations to approaches ofstructural inequality (present in explanations of feminist theories). Modelsbased on inequality consider that domestic abuse reflects the power structure insociety, taking into account income, unemployment, culture, race, and gender.Feminist theories share the understanding that an unequal society influencesthe emergence of incidents of violence. They emphasise, however, that maleprivilege overcomes any other social inequality in a society with a patriarchalstructure. Feminist theories originally proposed that the primary reasons fordomestic violence were related to a reinforcement of gender standards, but lateradjustments suggested the need to accommodate inter-gender relations. Be-cause of the prevalence of feminists in the political coalitions that formulatedprograms against this type of violence, these initiatives tend to assume thatgender norms and traditional roles lead to perpetration and victimisation.Criminology theories have taken advantage of recent developments in thestudy of urban crime and criminal “hot spots” and have relied on the routineactivity theory of criminal events and on the explanations related to target orvictim suitability to understand domestic and intimate violence (Mannon 1997).These approaches consider crime as predatory, involving a motivated offender,an available target, and the absence of capable guardians. Family isolationalso contributes to increasing victimisation, making the home one of the mostdangerous places for women and children.Finally, socio-ecological models organise multiple determinants at differentlevels (individual, family, peer, community, institutional, and societal). Violentbehaviour cannot be attributed to a single factor but to a wide range of possiblegrouped factors, including biological and psychological risk factors, childhoodexperiences, economic status, substance use, social characteristics (friends, forinstance), aspects of the intimate relationship with the partner, workplace cul-ture, and level of involvement with education, public policies, disadvantagedneighbourhood, violence in the community, access to weapons, cultural normsrelated to aggression, the woman’s social status, intersectional nature, and mul-tiple forms of oppression (Rothman 2018).More recent studies have distinguished the lethal risk of IPV from domesticand family violence (DFV). The prediction of each of these types of violence hasdifferent numbers and causes. For Ferguson and McLachlan (2020), many toolsto access risk are designed to predict violence and its escalation, including re-victimisation and repeated offences, not necessarily to predict homicides. WhileIPV is consistently identified as one of the high-risk factors for femicides, therisk factors may not be the same, for example, for the use and abuse of drugs andalcohol. The prevalence of drugs and alcohol abuse is much higher in cases ofphysical violence than in the prediction of femicides (Ferguson and McLachlan2020). On the other hand, having a gun increases the risk of femicide by 1000%,but such a risk would not be confirmed in cases of domestic violence. Also, thecharacteristics of the relationship, the presence of children, marital status, andthe duration of the relationship do not appear to be significant risk factors for5emicides, although they may contribute to the risk of intimate violence.
This section explains the concept of agent-based models (ABMs) and describesthe proposed model, VIDA. After this introductory part, subsection 3.1 willaddress the model’s intuition, followed by subsection 3.2 that describes thegeneration of the indicator of stress. Subsection 3.3 explains the experimentaldesign and the proposed changes in parameters related to measures of socialdistancing and deterrence of domestic violence. Finally, subsection 3.4 presentsthe model’s sensitivity analysis and validation.Agent-based models (ABMs) are built by describing agents (individual andactive subjects) and the interrelationship between them, as well as the envi-ronment where these interactions occur (Epstein and Axtell 1996). ABMs areartificial simulations made in a computational environment. They mimic thecore mechanisms of a phenomenon under examination (Abdou et al. 2012).Therefore, ABMs are simulacra, artificial, in silico, reduced to core aspects ofthe phenomenon, and their purpose is well-defined.Epstein and Axtell (1996) synthesise ABMs as the analysis of the functions oftransformation of agents and environment, as a result of the present interactionbetween the agents and the environment. These transformation algorithms, thesequence, and how interactions occur, are formally described and can be verifiedand reproduced through the computational code provided, which is considereda best practice (Grimm et al. 2010, 2020). ABMs are subject to verificationand scrutiny of the background theory, and the processes and empirical dataadopted.Understanding criminal processes is an area of criminology in which ABMscan be useful and contribute to the construction of public policies and the ac-tion of public managers. Among the aspects of criminology, opportunity theo-ries investigate the motivations of aggressors to understand the environmentalcontexts in which crimes occur. When developing models to test these opportu-nities, it is necessary to predict the dynamic interactions of individuals involvedin each criminal event, their interactions with other agents and the environment.A criminal system is guided by a wide range of interrelated factors. Thesefactors include and are not limited to the individual perception of the offender,the configuration and knowledge of the physical environment, the convenienceand attractiveness of the target or victim, the cognitive representation of theenvironment, and other factors related to the community.The criticisms and importance of ABMs result from the difficulty of criminol-ogy theories hitherto addressing the importance of individual incidents locatedin specific time and space. The theories have always been concerned with gen-eral and aggregate standards, making it difficult to draw conclusions regardingthe behaviour of victims and offenders that could affect crime rates and occur-rence. It is necessary to examine the individual actors who play essential rolesin criminal events in order to understand the patterns and characteristics of6rimes better.
In normal circumstances, the reality of families encompasses individual mem-bers participating in professional or social activities, most of the time outside thehome. During a pandemic where society is upstanding social distancing mea-sures, family reality changes, and individuals are at home most of the time, evenwhen carrying out work activities. Environmental and socioeconomic factorscontinue to contribute to this experience, intensifying social and pathologicalfactors such as the use and abuse of drugs and alcohol.Regarding the issue of domestic violence against women, it is noted that thedeterrent mechanisms are compromised in a context of social distancing by atleast two aspects. First, it is hard or even impossible to be distant from theabuser. Second, there are fewer opportunities to denounce the abusive situationto the community, as well as less access to the police and reduced response bythe justice system.The purpose of the model VIDA is to illustrate causal elements intrinsicto the domestic and family environment that favours the likelihood of violenceagainst women. It contributes to the increase in the theory’s explanatory ca-pacity and offers quantitative elements to support the validity of the causalelements embedded in the model. When the general behaviour of conditionsfor violence is calibrated according to the figures available for Brazil, it is pos-sible to construct indicators of the magnitude of adverse effects resulting froma specific contextual situation. In this study, VIDA explicitly tested the in-crease in families’ permanence at home due to social distancing measures takento prevent the spread of the virus Sars-CoV-2 in the context of the COVID-19pandemic and the restriction to deterrence systems available to women victimsof domestic abuse.The model is based on the following family situation: male abuser and femalevictim, with or without children. The characteristics of men, women, and thefamily environment are derived as samples of the population as observed in thecensus of 2010 conducted by the Brazilian Institute of Geography and Statistics(IBGE), for Brazilian metropolitan regions. Based on the family nucleus, webuild a risk indicator (stress) that accumulates additively (Berge et al. 2014)theoretical hypotheses that contribute as a trigger to domestic violence. Thisrisk indicator serves as a probabilistic factor that leads to violence.
The indicator of stress is the central part of the model and aims at systematicallyweighing in the findings of the literature. The indicator is created successivelyadding: (a) exogenous characteristics of each family member (model’s agents),(b) endogenous agents’ variables that accumulate throughout the simulation,and (c) variables chosen by the modeller.7spects related to income, gender, years of education, age, race, and the typ-ical size of families are exogenously included. The variables are collected fromcensus sectors and weighted statistical areas. Endogenous variables result fromother variables or the interaction promoted by the model’s algorithm. The mod-eller may change some variables to assess the model’s response. These variablesinclude the proportion of those staying at home (before and during the pan-demic), the relevance of gender to the indicator of stress, level of employment,the possession or not of weapons, and presence of substance use disorder.The starting point to establish the indicator of stress is gender, consideringthat being male leads to a higher indicator (see table 1). After that, we addindividual, household and per capita income influence, specifying that lowerincome leads to comparatively higher indicators. Household income works as aproxy for neighbourhood quality and income per capita as a proxy for domestic(dis)comfort.The literature review in section two further suggests four hypotheses relatedto the composition of the indicator of stress. The variable years of schoolingis added to the indicator based on the hypothesis that fewer than six years ofstudy leads to a higher indicator of stress of 60%, and the greater the numberof years of schooling, the lower the indicator. Another hypothesis is that beingolder than 18 and younger than 29 years old is a characteristic relevant to theindicator of stress. The third hypothesis concerns the victim’s race. In this case,black agents receive a proportional increase of 30% in the indicator of stress.Finally, the fourth hypothesis leads to an increase in the indicator of stress forwomen who are employed.Some factors undergo multiplicative proportionality of the value to be added,according to their relevance (see table 1). Those considered highly relevantare multiplied by ten, and medium relevant, by five. For years of schooling(which ranges from 0 to 17) and history of domestic abuse (number of eventsof violence), values are divided by a constant (10). These values were chosento maintain a sensible balance among factors influencing the indicator of stressand were validated via the sensitivity analysis performed.Access to firearms and substance use disorder are included as aggravatingfactors. Firearms are considered twice as highly relevant. Access to firearms,once confirmed, is deterministic (always added to the indicator). Substance usedisorder, in turn, is implemented as a random additional factor because it mayor may not occur.As such, the indicator of stress is the result of the addition and multiplicationof a number of composition individual and familial census characteristics thatfollow existing literature reasoning and degree of relevance. The compositemeasure is then used probabilistically as a violence trigger that accumulatesendogenously. This tentative construction captures the subjective findings ofthe literature in a systemic way and enables our implementation of a deterrencesystem mechanism.VIDA is a model with simple dynamics. In each simulation, VIDA starts bygenerating the artificial population sample according to the choices made by themodeller. The model then runs for a brief period of 10 steps. During this pe-8ndicator of stress Values added Observations Source RelevanceGender Male 0.8, female 0.2 Initial value ModellerIncome 1 – income IBGE 2010 HighHousehold income – household income IBGE 2010 MediumIncome per capita 1 – income pc IBGE 2010 MediumYrs. of schooling 1 – (schooling / 10) + 60% if < >
18 age <
29 IBGE 2010 HighSpouse’s race 1, if black female + 30% IBGE 2010Employment 1, if employed Def.: 80% pop. Modeller MediumStaying at home 0.67, if no work; 0.34 Endogenous MediumFirearms 1, if access; 0 Def.: 10% pop. Modeller High * HighSubstance use 1, if addicted; 0 Def.: 10% pop. Modeller High, randomHist. domestic abuse Events violence / 10 Endogenous HighTable 1: The table lists the components of the indicator of stress, how they affectit, the source of the data and the relevance of the multiplicative proportionality.riod, there is some stochastic neutral volatility associated with employment andincome. Moreover, there is enough time for an endogenous history of violenceto build up. After 200 steps, the violence levels have stabilized and the modelis interrupted and output is generated. The model also includes a fixed modelscale that divides the indicator by a 1,000 so to calibrate the cases of attacks tothe available empirical data. The execution of each step of the model consistsof: 1. Update of the indicator of stress for all agents.2. Verification of the violence trigger.3. Verification of the need to seek help from public policies against violence,the deterrence process.The full model is available at the COmSES platform and GitHub. It is builtupon the Mesa framework (Masad and Kazil 2015). The reader interested inusing VIDA should focus on the ’violence’ folder. Basically, the constructionof the stress indicator is included as an agent step at agents.py and the cre-ation of the sampled families from data is made within model.py , using dataand processes from the folder ’input’.
Generalization.py iterates the model200 times and tests the experimental design. Outputs are also included in therepository.
When the model appropriately represents the phenomena researched, it is pos-sible to ask what-if questions. Therefore, it is possible to test the likely effects of9ndicator of stress Values added Source RelevanceDenounce – 1 Endogenous MediumProtective measure – 1 Endogenous HighConviction – 1 Endogenous HighTable 2: Influence of deterrence system on aggressor’s indicator of stress.interventions that have not yet taken place. Our experimental design includestwo consequences of the pandemic: (a) the imposition of social distancing mea-sure of staying at home, and (b) the access (or lack thereof) of the victim toprotective measures in case of domestic violence (deterrence system).Victims searching for help when suffering from domestic violence typicallyhave three similarly-sized behaviour patters, according to data compiled by theBrazilian Senate. The first group is of victims that never denounce. Victimsfrom the second group in contrast denounce immediately after the first caseof violence. Victims from the third group denounce after the third event ofviolence. Following this segmentation, the victims in the model VIDA are dis-tributed equally among these three groups and act accordingly.The model then considers that women who denounce have a 50% chance ofobtaining protection. Among those who denounce and obtain protection, 50%have the chance to see their abuser convicted. The victim’s situation (denounce,protection, or abuser conviction) is included in the model as an element thatreduces the abuser’s indicator of stress (see table 2. Therefore, it works toreduce the chances of further violence cases, and each request for support in thedeterrence system reduces the likelihood of future violent events.
VIDA is simulated with different sampled data. The results presented referto the median of results obtained after the 200-fold simulation. The modelwas calibrated in order to approximate the number of notifications of domesticviolence against women made by health agencies in 2011, using data from the2010 census. In 2011, data from the Senate indicated 73.7 notifications per100,000 women.The literature offers different concepts of model validation (Gal´an et al.2009; Guerini and Moneta 2017; Moss 2008; Ngo and See 2012; Wilensky andRand 2015). However, there is some consensus around the idea that modelsare validated according to their purpose, context and ontology (Edmonds andMeyer 2017). A model proposed for predicting is expected to offer accurateand confirmed results that were not part of the model beforehand. A modeldesigned to help to understand a given mechanism does not have to prove apredicted empirical data. In any case, a model must be anchored in its purposeand reflect the available literature. 10ccordingly, VIDA’s purpose is to illustrate causal elements that are sub-jectively present in the literature, thus helping understand the phenomena andenable the implementation of what-if analysis. As a first tentative to systemati-cally represent a multi-causal intricate theoretical mechanism – that of domesticviolence trigger – and the empirical foundation of the input of the model, webelieve VIDA results are sufficiently validated to enable comparisons amongmetropolitan regions and insights into intraurban differences.The sensitivity analysis results presented in the next section contributesto demonstrate the robustness of the model as it assesses how the variationof parameters and processes interfere in the results. Moreover, the analysisof parameter changes contributes to comprehending the effects these changesgenerate.The modeller running VIDA can control the variation of the parametersthat are not endogenous or derived directly from the IBGE population sam-pling. Thus, the modeller may alter data on: relevance of gender; employmentpercentage (and consequently the population staying at home and whether re-ceiving salaries); access to firearms, and substance use disorder. It is possibleto test volatility of employment and income value, increasing the chances ofmoving from employed to unemployed and vice versa, as well small increases ordecreases in income.
First, we present the results of the sensitivity analysis, where the parameterschosen by the modeller are submitted to variation. Second, we present the base-line results and those for the experimental design. Then, we show a comparisonof results across 46 metropolitan regions in Brazil. Finally, we detail intraurbanresults for Bras´ılia and Porto Alegre. Once the model was calibrated with na-tionwide data from 2011, showing 73.7 reports of violence per 100,000 women,it was possible to observe the differences resulting from the implicit variationof race, gender, age, family size, presence of weapons, and economic capacityof families in different metropolitan regions and intrametropolitan neighbour-hoods.
The results presented adopt the standard parameters of the model for themetropolitan region of Bras´ılia (see table 3), with the presence of deterrenceand absence of social distancing measures, that is, the situation before the pan-demic. The model runs 200 simulations for each tested parameter.The indicator of stress according to gender, fixed at 0.2 for women andvarying for men between 0.1 and 0.9, has little influence on the results relatedto increasing cases and denounces. The percentage increase between the lowestand highest value was 2.24% for cases of violence and 2.48% for denounces.11ndicator component level Cases DenouncesGender stress0.1 169.57 60.050.44 172.28 61.720.9 173.45 61.58Percentage of employed0.1 165.66 58.650.44 169.14 60.810.9 174.11 61.98Firearms0.1 173.33 62.40.44 368.05 115.290.9 628.79 186.41Substance use disorder0.01 170.99 60.940.22 178.09 63.680.5 184.73 66.14Table 3: Sensitivity analysis: results of cases and denounces per 100,000 womenwhen varying modeller choices of indicator os stress components.The percentage of employment between 0.1 and 0.9, led to an increase of4.85% in domestic violence against women, and an increase of 5.36% in thenumber of denounces. This slight increase is in accordance with the suggestionof the literature that working women are more subject to domestic violence.As expected, the introduction of a high * high relevance multiplicative pro-portionality for access to firearms into the model resulted in an increase in casesand denouncing. Varying from 0.1 to 0.9, access to firearms increased violencecases significantly by 72.43% and denouncing by 66.52%.The occurrence of cases of domestic violence related to substance use disorderincluded an additional random factor, considering that such cases may or maynot occur. Thus, the increase (from 0.01 to 0.5) in the chances of being addictedresulted in an increase in violence cases of 7.44% and the number of denouncesof 7.86%.
The model VIDA with typical parameters (see table 1) was simulated 200 timesto report the average numbers obtained. The average number of denounceswas 61.73, in an environment with 174.49 domestic violence cases per 100,000women.Table 4 shows the results for the experimental design tests. Social distancingmeasures, which forces the agents to stay at home, regardless of whether they12eterrence Social distancing Cases DenouncesFALSE FALSE 180.38 0FALSE TRUE 197.35 0TRUE FALSE 173.62 61.97TRUE TRUE 190.74 47.38Table 4: Results per 100,000 women for different alternatives of social distancingand deterrence system.are working, leads to an increase in violence cases of 8.86%. At the same time,denounces reduced by almost a third (29.25%), compared with the baselinesimulated model with the default parameters.Additionally, the inclusion of the deterrence system in the model demon-strated a reduction in domestic violence cases by only 3.53%, when comparedwith its absence (178.89 versus 172.79 cases per 100,000 women). These findingscorroborate the literature (Campbell et al. 2003), which states that judicial pro-tection and incarceration have a greater long-term impact and work to reducesevere forms of violence, especially femicides. According to the literature, otheraspects contribute to reducing the risk of severe forms of domestic violence,such as the expansion of employment, preventing substance use disorder, andrestricting access to weapons.A relevant contribution of the simulation is the ability to compare the re-sults across different metropolitan regions with varying composing attributes,such as age and gender, family size, average wages, years of schooling, and racedistribution, according to the 2010 demographic census sample data. Figure 1shows the number of cases of domestic violence per 100,000 women in the high-populated areas in Brazilian metropolitan regions. The data simulated in themodel suggest that larger and wealthier metropolitan regions have proportion-ately fewer cases of domestic violence against women than regions with smallerand poorer populations.Empirical analysis for Brazil have shown increasing rates in the regions Northand Northeast, and decreasing rates in the South and Southeast of Brazil inthe past decade. When shifting the focus of analysis to the size of the mu-nicipalities, there is a general decrease in homicides in large cities (with morethan 500,000 inhabitants) and an increase in medium-sized (between 100,000and 500,000 inhabitants) and small municipalities (with less than 100,000 in-habitants) (Cerqueira et al. 2019). Despite their sizes, another important ex-planatory element that may affect the results is the lack of infrastructure anddeterrence systems in regions with a larger number of domestic violence cases(Madeira et al. 2018). Our simulation results reveal patterns that are similar tothe empirical data, showing notably fewer cases in metropolitan regions of theSouth and Southeast. When cases are more frequent in these regions, they areidentified in metropolitan regions that encompass smaller cities, located inlandand with less access to deterrence apparatus.13igure 1: Number of domestic violence cases per 100,000 women in Brazilianhigh-populated areas metropolitan regions as classified by the IBGE.Further, we compared intraurban simulation results with the current reality(see figure 2). The comparison data was retrieved from the database of Indica-tors of Violence Against Women — Maria da Penha Law, for the year 2019. The analysis from the municipalities located in the metropolitan region of PortoAlegre suggest that results show similar patterns of domestic violence whencomparing the simulation and reality. Neighbourhoods corresponding to munic-ipalities with high rates of violence, such as Viam˜ao, Taquara, Cachoeirinha andGua´ıba figure in the simulation among the groups with the highest incidence.Alvorada, with a proven record of violence, appears in the simulation with an Retrieved from https://atlassocioeconomico.rs.gov.br/regiao-metropolitana-de-porto-alegre-rmpa
This article presents a first attempt to formalise a multi-causal model of domes-tic violence, based on a series of family characteristics and comparable artifi-cial data, generated from intra-urban (large neighbourhoods) census data. Themodel illustrates theoretical mechanisms and quantifies explanatory aspects ofviolence against women. Additionally, it incorporates aspects that emerged withthe COVID-19 pandemic – forced coexistence in the home environment due tosocial distancing measures – and elements of the deterrence system to addressdomestic abuse. As such, the paper contributes to the understanding of thecomplex mechanisms encompassing violence against women in Brazil.The results suggest an increase in violence against women of about 10% withthe implementation of social distancing measures emphasising staying at home,16hich is confirmed by recent data that point to a 30% decrease in denounces inseveral countries and 25% in some Brazilian states (Bueno et al. 2020). Moredensely populated metropolitan regions appear to have fewer violence cases per100,000 women compared to smaller metropolitan regions. The same compara-tive pattern appears in the intra-metropolitan analysis between high-populatedareas and rural or peripheral areas.In addition, the model, its codification, and the process of generating ar-tificial population samples based on census data are publicly available. Thispractice aims to facilitate the dissemination of the model and its use by thescientific community, analysts, and public policy managers.Future work involves detailing empirical data in the model, specifically iden-tifying possession of firearms per household, and feedback effects within theneighbourhood. Data on the access of firearms can greatly contribute to the re-liability of the proposed spatial analysis because the presence of firearms seemsto be the strongest among the causes of femicides.The elaboration of public policies depends on the right diagnoses capableof supporting appropriate interventions. The area of violence and crime rou-tinely deals with the problem of lack of data, even more so in cases of highunderreporting such as domestic violence. The ethical limitations of producingexperiments in the area can also be overcome by using agent-based simulatingmodels, which make it possible to replicate reality and illustrate different effectsin an auspicious way. However, researchers who have been trying to understandthe risks related to domestic abuse, especially in the context of the pandemic,have suggested the need to use data parsimoniously since it takes time to un-derstand the changes in the dynamics of collecting and recording information.The model demonstrated to be useful to simulate and anticipate data, allowingto illustrate this type of violence and its georeferenced disparities. This toolproves to be of great importance in this particular moment where all kinds ofinequalities stand out in the country.
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