Optimal Scheduling of Automated Warning Messages to Promote Primary Desistance from CSAM Offending: A Dual-Process Sensitisation–Habituation Model

Automated warning messages—pop-ups, interstitials and conversational agents that interrupt attempts to access child sexual abuse material (CSAM)—can produce substantial short-term reductions in offending behaviour. In criminological terms, the present model is concerned specifically with primary desistance: the initial lull, interruption or break in offending, rather than sustained cessation, secondary desistance or tertiary desistance. Repeated-warning exposure is governed by two opposing psychological forces that a recent review identified but did not reconcile: cumulative sensitisation, whereby repeated exposure raises perceived risk, and habituation, whereby repeated exposure erodes salience. We develop a dual-process (opponent-process) dynamical model in which perceived risk and attentional salience evolve across discrete warning events. The model admits closed-form periodic steady states, which we verify against a simulation and calibrate so that a fresh, credible warning produces event-level primary desistance on approximately 62% of attempts, matching the upper range of reported randomised-trial effects. We show that the two processes are oppositely monotone in the inter-exposure interval, so that per-warning efficacy can be non-monotone with an interior optimum. Under the illustrative baseline calibration, the model predicts that efficacy per warning peaks at about 0.82 at an interval of approximately 18 days. This is a mathematical optimum for the specified per-warning objective, not an empirically validated deployment rule: operationally preferred cadences may differ because social expectations, harm-reduction objectives, platform architectures and technical feasibility need not align with the same objective. We then formalise polymorphic warnings and relax the optimistic assumption that habituation is entirely variant-specific by allowing a proportion of habituation to generalise across warning variants. This shows when warning variety can preserve salience and when its benefit is eroded by cross-variant familiarity. The framework converts qualitative design hypotheses into quantitative, testable predictions that can guide the next generation of targeted repeated-exposure experiments. Because the calibration is anchored in single-exposure studies rather than repeated-warning schedules, the predicted cadence and repeated-exposure effects remain model-generated hypotheses requiring direct longitudinal validation.