A nonlinear compartmental model is developed to analyze crime dynamics in a structured society. The population is stratified into eight compartments: \(S(t)\) (susceptible), \(E(t)\) (exposed), \(C(t)\) (active criminals), \(C_v(t)\) (convicted criminals), \(P_h(t)\) (passive-honest), \(P_c(t)\) (committed-honest), \(J_h(t)\) (honest judges), and \(J_c(t)\) (corrupt judges). The model incorporates nonlinear mechanisms such as institutional corruption (\(\kappa_1\)), judicial correction (\(\kappa_2\)), recidivism feedback (\(\rho_1,\rho_2\)), exposure intensity (\(\eta_1\)), and rehabilitation (\(r_2\)), providing a realistic portrayal of crime--justice interactions. Solutions remain positive... More >

This study introduces an age-structured compartmental model that analyzes transitions among stable marriages, long-distance relationships, extra-marital affairs, and divorce. Key behavioral parameters include $\lambda$ (transition to long-distance), $\delta$ (reunification), $\alpha_1$ and $\alpha_2$ (affair formation), $\beta$ (reconciliation), $\gamma$ (affair-driven divorce), and $\mu$ (non-affair divorce). The unmarried women's pool is structured by age, governed by an engagement function $\theta(a)$ and inflow $\Lambda(a)$. A nonlinear differential equation system captures how behavioral mechanisms collectively drive marital dynamics over time. Numerical simulations show that higher $\b... More >