Modeling and Optimal Control Analysis on Armed Banditry and Internal Security in Zamfara State

Abstract

In Nigeria, Banditry which includes kidnapping, is currently a national threat that led to the loss of lives, livelihoods, crippled economic activities, broken social cohesion and above all led to a massive displacement of people especially in Zamfara State. We present a deterministic mathematical model for controlling the spread of armed banditry using job creation, ()1ut and efforts to make armed banditry unprofitable, ()2ut. We formulate a fixed time control problem subject to the model dynamics with aim to obtain the suitable optimal combination of the two control measures that will minimize the cost of the control efforts as well as the incidence of the menace. The simulations was carried out using the estimate initial conditions and parameter values obtained from the existing literature and hypothetical values. The Pontryagin’s maximum principle was employed to characterize the optimality system and solve the system numerically. The results obtained on simulations suggests that the application of any of the controls is effective in decreasing the population profile of the informers and the bandits in a finite time. Furthermore when both controls are combined that is efforts to make armed banditry unprofitable ()2utshould be at upper bound for a longer duration when compared with the job creation control, ()1ut.