A mathematical approach on the dynamics of kidnapping with apprehended kidnappers

Abstract

Kidnapping has emerged as a critical security challenge in Nigeria and other parts of the world. This study formulates a compartmental mathematical model that divides the population into vulnerable individuals V (t), kidnappers Q(t), hostages H(t), and apprehended kidnappers A(t). We introduce a Crime Propagation Number (CPN ) to assess the risk of kidnapping. Analysis of the model shows that if CPN < 1 and λ > μ, the kidnapping-free equilibrium is locally and globally asymptotically stable. Numerical simulations indicate that increasing the apprehension and rescue rates reduces the incidence of kidnapping.