Mathematical Modeling and Optimal Control of Intervention Strategies for A Banditry Model

Abstract

This paper presents an optimal control of intervention strategies for the menace of Banditry taking into account media campaign against Banditry  rehabilitation of Bandits detainees and use of military force against Banditry  as control strategies. The Banditry free equilibrium, Banditry present equilibrium and the basic reproduction number of Banditry  were obtained. The stability analysis results suggest that the Banditry free equilibrium is locally asymptotically stable when   and otherwise when . The Boko Haram presence equilibrium is globally asymptotically stable when  and unstable if . We used the three control strategies and updated the Banditry menace model. The optimal control issue was resolved using Pontryagin's Maximum Principle (PMP).It was discovered that there is a significant decrease in the population of Bandits and increase in the number of rehabilitated Bandits and detained Bandits when the control measures are implemented compared to the case without control. We solved the optimality control using a forward-backward sweep strategy implemented in MATLAB for numerical simulation. Additionally, we saw that the number of people detained fluctuates as the number of people receiving rehabilitation rises. We argue that in order to lessen or completely erase the menace caused by Bandits in society, the government should fund media campaigns and rehabilitation initiatives.