Disrupting the scammer lifecycle: A dynamically-consistent numerical analysis of a compartment model for scam-victim dynamics

Online deception and financial scams represent a pervasive threat in the digital age, yet a quantitative analysis and understanding of their propagation is lacking. This study introduces a novel model based on the framework of epidemiological models to describe the interaction between scammers and their victims. We propose a five-compartment deterministic model ($S-V-R-A_s-R_s$) calibrated using longitudinal data in fraud reports from the Canadian Anti-Fraud Centre. The model's theoretical properties are established, including the non-negativity of the state variables and the stability threshold defined by the basic reproduction number ($\mathcal{R}_0$). A non-standard finite difference scheme is developed for the numerical simulations to ensure dynamical consistency between the continuous deterministic model and its discrete equivalent. A key finding of the model sensitivity analysis indicates that the proliferation of scams is overwhelmingly driven by the lifecycle of scammers, their recruitment, attrition, and arrest, rather than the susceptibility of the victim population. The results of this study provide strong quantitative evidence that the most effective control strategies are those that directly disrupt the scammers' population. Overall, this study provides a crucial model for designing and evaluating evidence-based policies to combat the scourge of cybercrime.