A Stochastic Crime-Victim Model with Fear Effect and Information-Driven Control
DOI:
https://doi.org/10.62054/ijdm/0302.01Abstract
To explore the dynamics of crime-victim interactions under uncertainty, we propose and analyze a stochastic crime model incorporating fear effects and information-driven control mechanisms. The model is formulated as a stochastic differential system in which criminals, susceptible victims, and information levels interact through a nonlinear incidence rate that is reduced by both fear-induced behavioral responses and information dissemination, while being further perturbed by nonlinear white noise. Firstly, the existence, positivity, and boundedness of the solution of the model are investigated to ensure biological and social feasibility. Secondly, sufficient conditions for extinction, persistence in mean, and the existence of a stationary distribution are established. In particular, the density behavior in the neighborhood of the positive equilibrium of the corresponding deterministic system is studied to characterize the long-term dynamics. Finally, numerical simulations are carried out to support the analytical results and to illustrate the effects of fear, information, and stochastic perturbations on the system dynamics. The results demonstrate that fear effects, information dissemination, and environmental noise play significant and sometimes competing roles in determining the persistence and suppression of criminal activity within the system.
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