Document Type : Research Paper
Authors
1
Department of Mathematics, School of Advanced Sciences, VIT-AP University, Amaravati, 522237, India.
2
Department of Mathematics, Birla Institute of Technology and Science, Pilani, 333031, India.
Abstract
Crime, a complex and dynamic phenomenon influenced by various factors such as social, economic, and environmental variables, has been the focus of numerous studies aiming to model and mitigate delinquent behavior while fostering prosocial growth. However, existing mathematical models, predominantly based on ordinary and fractional differential equations, often overlook the intricate dynamics of gang warfare and competition effects among different gangs, crucial for accurately representing criminal behavioral changes. Hence, the proposed model incorporates competition effects among different gang members and categorizes the total population into five clusters using an epidemiological population-based approach: non-criminals (N ), criminals (C), gang-1 (G1), gang-2 (G2), and prisoners (P ). The article establishes the wellposedness and stability of the proposed
model. Additionally, the criminal generation number, a key metric for eradicating crime transmission, is calculated using the next-generation matrix technique, offering insights into optimal crime-control strategies. Equilibrium points, including criminal-free, gangs-free, gang-1 free, gang-2 free, and an endemic equilibrium, are examined. The criminal-free equilibrium is globally asymptotically stable if the criminal generation number is less than one, while the gangs-free, gang-1 free, gang-2 free, and endemic equilibrium are locally asymptotically stable if the criminal generation number exceeds one. A sensitivity analysis is employed to assess the impact of various model parameters on crime transmission control. Theoretical conclusions are validated through numerical simulations, concluding with a discussion on the societal consequences inferred from the model’s findings.
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