Fractional-order crime propagation model: a comparison between logistic and exponential growth

Abstract

Everyone is affected by crime in some manner. Criminal activity spreads through peer influence and is contagious. Several mathematical models for predicting crime transmission have been proposed in various studies. However, these models do not account for an individual’s logistic development, which is required to describe criminal behavior changes. As a result, this research present a fractional-order mathematical model of crime transmission that considers the logistic growth of law-abiding people. The existence and stability of the crime-free and crime persistence equilibrium have been investigated using the Routh-Hurwitz criterion. We also investigated the incidence of transcritical bifurcation in the proposed model system, including law enforcement. Numerical simulations have been preformed to validate the analytical findings, further supporting our qualitative conclusions and establish the role of different crucial parameters and variables used in the proposed model. The model with logistic growth outperforms the traditional one (exponential model). The results reveal that offenders survive as long as the coefficient of law enforcement remains below a specific threshold value. The criminals start vanishing once this value is achieved. The findings demonstrate that the offenders may persist if isolation and conversion rates remain low.