Insight into the optimal control strategies on corruption dynamics using fractional order derivatives

Abstract

The fractional-order design for conceptualizing corruption offers several advantages on the corruption spreading over the integer-order corruption models such as acknowledgement of the intricate dynamics of corruption, including corruption super-spreading aspects, variable corruption transmission rates, it capture the persistence of memory effects, accounting for the past trajectory of corruption epidemic, and also providing a more accurate explanation of corruption dynamics. The author of the study has formulated the fractional order model on corruption dynamics by dividing the total population into five sub-groups namely the susceptible group, the exposed group, the moderately corrupted group, the highly corrupted group, and the corruption repented group. In the qualitative analyses section the author of this study has: shown the model solutions existence and uniqueness by applying the well-known Picard–Lindelöf criteria, computed the model basic reproduction number using the next generation approach, computed the model equilibrium points and investigated their stabilities, re-formulated the corresponding fractional order optimal control problem using the proposed three time-dependent controlling variables (prevention measure, moderate corruption treatment measure and high corruption treatment measure). The necessary optimality conditions for the fractional order optimal control problem and the existence of optimal control strategies are derived and presented by applying Pontryagin's Maximum Principle. Eventually, the study demonstrated the effectiveness of the combinations of the three controlling strategies through numerical methods (simulations) and the analysis results shows that the implementation of the three time-dependent controlling strategies significantly minimizes the number of corrupted individuals in the community.