Modelling and prevention of crime using age-structure and law enforcement

Every community experiences crime, therefore being aware of it is essential. It is natural to characterize individuals based on age when we consider the modelling of crime, as we do not expect a child to commit a crime. Also, a particular age group may be more prone to commit crimes. Keeping this in mind, we consider an age-structured model of the criminal and noncriminal-minded population in a society. The criminal-minded population is further divided into three categories. We develop a model and study the interaction between them. One crucial factor which we study is the effect of law enforcement. The global existence of steady state is shown using the method of induction on the real line. We check the stability of steady states by constructing appropriate Lyapunov functions. We have established the stability of the crime-free equilibrium. This equilibrium is more important as every society wants to achieve it. We also show the existence of forward bifurcation. It is interesting to see that the outcomes are very natural and enhance our understanding of such classes. Numerical simulations are also given for better illustration. & COPY; 2022 Elsevier Inc. All rights reserved.