Mathematical modeling of trauma dynamics: Exploring the impact of therapeutic interventions

Abstract

Trauma resulting from sustained external violence, such as that seen in protracted conflicts, poses a severe public health challenge. While mathematical models have been used to study social contagions, few have explicitly addressed scenarios where a community is persistently traumatized by a distinct, external group of perpetrators. This paper introduces a novel deterministic compartmental model that conceptualizes this dynamic as a predator-prey interaction. The model incorporates a multi-stage healing process augmented by a therapeutic intervention parameter (η). Qualitative analysis of the model demonstrates that a trauma-free equilibrium is impossible under conditions of constant external influx of perpetrators (Π). Instead, the system always converges to a unique, globally stable endemic equilibrium where trauma persists. Numerical simulations illustrate the model’s dynamics, showing that while therapeutic interventions (η > 0) dramatically reduce the endemic level of trauma. The results underscore that the most effective public health strategy is a dual approach: simultaneously implementing measures to reduce the external threat (e.g., targeting perpetrator influx and activity) and, of course, intensifying therapeutic interventions - Cognitive
Behavioral Therapy (CBT) and Eye Movement Desensitization and Reprocessing (EMDR) at a parameter value η = 0.25 and above.