Modeling the Dynamics of Corruption and Optimal Control in Public Sectors

Abstract

 We introduce a Susceptible-Corrupted-Paying Well-Recovered (SCPwR) model specifically designed to analyze corruption dynamics within the public sector. This model is demonstrated to be well posed both epidemiologically and mathematically. Our results show that all model solutions remain positive and bounded given initial conditions within a meaningful set. We investigate the existence of unique corruption-free and endemic equilibrium points and calculate the basic reproduction number. The local and global stability of these equilibrium points is then analyzed. Our findings indicate that the system has a locally asymptotically stable corruption-free equilibrium when  R_e < 1 and unstable when R_e > 1 . Additionally, the corruption endemic equilibrium point  E^*  is globally asymptotically stable only if dL/dt< 0 . Numerical implementation of the model suggests that corruption will persist in public sectors if civil servants are not adequately compensated.