David Katerndahl, University of Texas Health Science Center at San Antonio, TX
Sandra Burge, University of Texas Health Science Center at San Antonio, TX
Robert Ferrer, University of Texas Health Science Center at San Antonio, TX
Johanna Becho, University of Texas Health Science Center at San Antonio, TX
Robert Wood, University of Texas Health Science Center at San Antonio, TX
Maria D. M. Villacampa, University of Texas Health Science Center at San Antonio, TX

Abstract: The purpose of this study was to develop a mathematical model of mutual partner violence and assess impact of her controllable behaviors on reducing violence. An agent-based model was created of couples with history of violence based upon results of two multiple time series studies of partner violence. To explore factors that may alter model results, eight continuous variable parameters were created based upon significant (p=.05) but discrepant (opposite directions) results from previous studies. To assess the potential impact that random stress and her behavior (arguments, forgiveness, alcohol use, violence) could have on violence and stalking, the impact of variable parameter settings of these factors were also assessed. The model identified 18 unique patterns were observed, grouped into five general categories. Added random stress contributed to his violence in only two patterns. Although avoiding participation in arguments had no effect, her forgiveness and elimination of alcohol use often reduced her violence only. However, consistent violence or nonviolence on her part sometimes affected his violence and stalking. In conclusion, while increasing forgiveness and reducing alcohol intake could reduce her violence, they generally had little effect on his. However, if she eliminated her violence, it could eliminate his violence and stalking in some situations.

Keywords: nonlinear dynamics, battered women, domestic violence, spousal abuse, mathematical modeling