Stochastic Agent-Based Models of Intimate Partner Violence

TL;DR

The study investigates IPV dynamics within couples using two stochastic ABMs where each partner occupies one of four states $s_i \in \{-1,0,1,2\}$ (passive, normal, upset, violence). Model 1 analyzes short-term evolution after an upsetting episode with absorbing outcomes, while Model 2 examines long-term dynamics under social support; both are extended with self-consistent mean-field feedback linking aggressiveness $a$, perceived violence $v$, and threshold $v_c$. Phase diagrams show how low versus high aggressiveness and symmetric versus asymmetric social influence steer the system toward normal, dominance, or mutual-violence regimes, in line with Cycle of Violence theory. The results highlight the protective role of social support and demonstrate how social norms, via mean-field feedback, can shape IPV trajectories, offering quantitative guidance for prevention strategies.

Abstract

Intimate partner violence (IPV) is a significant public health problem and social issue that involves couples from all socioeconomic and cultural contexts. IPV may affect women and men, but these latter are the most common perpetrators of IPV. We developed stochastic Agent-Based models of IPV focused on the couple dynamics, determined by the parallel, individual behaviour of partners. Based on the psychological theory of the Cycle of Violence, we have developed a model based on four discrete states: passivity, normal situation, upset and physical assault. The individual transition probability depends on the previous state of the subject and that of the partner, and on a control parameter, the aggressiveness. We then let this parameter evolve depending on the perceived violence from past experiences (polarisation) or from the support received from the environment (social influence). From the analysis of the phase diagrams we observe the emergence of characteristic patterns, in agreement with the observations of IPV in the literature.

Figures (10)

• Figure 1: The transition diagram of couple dynamics for Model 1. The ovals represent the 16 possible states $(s_1, s_2)$ of the couple and the arrows the transitions $M(s'_1, s_2|s_1, s_2; a_1, a_2)=\tau(s'1|s_1,s_2;a_1)\tau(s'_2|s_2, s_1;a_2)$. The initial state is coloured in red and marked by the START label. The green ovals are unreachable "garden of Eden" states, which can only be the starting states of the dynamics, and the corresponding transition probabilities are dashed. The four absorbing states normal $(0,0)$, separation $(2,2)$, male violence $(2,-1)$, female violence $(-1,2)$ are marked in yellow.
• Figure 2: An example of a stochastic trajectory.
• Figure 3: Basin of attraction of the four absorbing states of Model 1 for all possible values of male ($a_1$) and female ($a_2$) aggressiveness. The absorbing states are the asymptotic states of the probability distribution $P(s_1, s_2)$ corresponding to: normal $P(0,0)$, separation $P(2,2)$, male violence $P(2,-1)$, female violence $P(-1,2)$. The asymmetry between male and female is only due to the initial state $P(1,0;0)=1$.
• Figure 4: The evolution function of aggressiveness $a'=f(a;v,v_c)$ for different levels of perceived violence $v$, with $v_c=0.1$.
• Figure 5: Absorbing states of Model 1 with a mean-field (self-consistent) evolution of the aggressiveness with $v_c=0.1$. Axes and plots as in Fig. \ref{['fig:model1-phase']}. Averages over 20 runs.