Sensitivity and threshold analysis of a juvenile delinquency model with multiple exposure pathways
##semicolon##
juvenile delinquency, mathematical modeling, peer influence, social media exposure, family dynamics##article.abstract##
We analyze a compartmental model of juvenile delinquency that includes three exposure pathways (peer, social, family) and multiple infectious/delinquent compartment’s EPJ , ESJ , EFJ , IJ , AJ , CJ together with recovered and cumulative classes. Using the next-generation matrix method we derive the threshold parameter R0 (the basic reproduction number) in closed, computable form and prove that the delinquency-free equilibrium (DFE) is locally asymptotically stable if R0 < 1 and unstable if R0 > 1. We also establish global stability of the DFE under R0 < 1 by the comparison theorem. Finally, we present a rigorous sensitivity-analysis framework for R0 (normalized forward sensitivities / elasticity’s using eigenvector formulas) and discuss policy implications: which exposure pathways and parameters should be targeted for effective control. Numerical implementation steps, suggested parameter values for illustrative simulations, and policy recommendations are provided.
