Mathematical Model for the dynamics of Kidnapping in Nigeria with Optimal Control

Abstract

Kidnapping is regarded as one of the most terrifying types of banditry in the world. In Nigeria, it is a volent act use for perpetuating political objectives and interest by politicians. We developed a compartmentalized mathematical model for the dynamics of kidnapping activity. Total human population was sub-divided into S(t), I(t), U(t), R(t), K(t) and D(t), a system non-linear first order ordinary differential equations was developed. Two equilibrium points were established (kidnapper free equilibrium point and equilibrium point with kidnapping activity), stability analysis was carried out and the analytical result shows that the two equilibrium points are local asymptotically stable (LAS). The equilibrium point with kidnapping activity is globally asymptotically stable (GAS) provided that the condition of the Lyapunov function is satisfied. Additionally, the fundamental reproduction number or threshold number was calculated followed by numerical simulations to back up the analytical results.