Modelling the Dynamics of Sara-Suka Crime with Rehabilitation Strategy in Bauchi State

Abstract

As in other states in Nigeria, there is a reasonable number of young men and women without jobs in Bauchi State. These individuals have few opportunities to improve their socioeconomic status. Some of them joined Sara-Suka Boys, loosely organized criminal gangs. In this work, we developed a model based on mathematical techniques, resulting in a system of ordinary differential equations, to analyze the dynamics of the Sara-Suka crime while accounting for the State's rehabilitation programme. We used the Lipchitz condition to test for the existence and uniqueness of the solution for the model, determining the solution's positivity and the invariant region, respectively. The basic reproduction number (Ro) was calculated using a next-generation matrix technique. According to the study, the Sara-Suka Crime-Free Equilibrium (SSCFE) is unstable whenever Ro exceeds one and locally asymptotically stable (LAS) whenever it is less than 1. The SSCFE's global stability was also attained. Numerical investigations illustrated that an increase in the arrest rate of Sara-Suka boys, a reduction in the Sara-Suka conversion rate, and a boost in the rehabilitation programme will significantly help reduce and, with time, completely eradicate the Sara-Suka thuggery.