Modeling Crime Transmission with Fear Effect: A Fractional-Order Approach for Effective Crime Control Strategies

Crime poses a formidable global challenge, prompting extensive research that has proposed multiple mathematical models employing ordinary differential equations and fractional differential equations to forecast the transmission of criminal activity. However, these models do not include the fear effect of the judiciary on the offender, which is necessary to depict the behavioral changes of criminals. Therefore, this research proposes a fractional-order mathematical model of crime transmission that includes the fear effect of the judiciary on offenders. In this study, the total population is categorized into six clusters using an epidemiological population-based approach, namely vulnerable individuals (S), free criminals (C), prisoners (P), convicted criminals (Cv\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_v$$\end{document}), judiciary (J), and law enforcement officers (L). This article discusses that the proposed model is well-posed as well as stable. The criminal generation number for eradicating crime transmission has been calculated using the next-generation matrix technique, which provides insight into the best crime-control strategies. A sensitivity analysis has been used to determine the impact of various model parameters on crime transmission control. Theoretical conclusions have been validated using numerical simulations, followed by a description of the societal consequences.