Mathematical modeling and analysis of kidnapping as a communicable disease

Abstract

Kidnapping affects most African countries, including Nigeria, and has become a pressing national issue. This study develops and analyzes a mathematical model of kidnapping dynamics, treating it as a communicable process. The model incorporates key compartments including susceptible individuals, kidnappers, abductees, and rescued individuals. The basic reproduction number R0R_0 is derived and used as a threshold parameter. Stability analyses is carried out using linearization and Lyapunov functions are performed to determine the conditions under which the kidnapping-free and endemic equilibria are stable. Sensitivity analysis identifies the most influential parameters on R0R_0, notably the direct recruitment rate of kidnappers. Numerical simulations validate the model and reveal that when R0<1R_0 < 1, all kidnapping-related compartments diminish over time, indicating that kidnapping can be eradicated under appropriate conditions. Conversely, when R0>1R_0 > 1, kidnapping becomes endemic. The results underscore the significance of reducing the recruitment rate of kidnappers and enhancing rescue operations as effective strategies to combat the spread of kidnapping. These findings provide valuable insight for policymakers and security agencies to design informed and impactful interventions.