Mathematical modeling and optimal control of corruption dynamics

Abstract

The problem of corruption is of serious concern in all the nations, more so in the developing countries. This paper presents the formulation of a corruption control model and its analysis using the theory of differential equations. We found the equilibria of the model and stability of these equilibria are discussed in detail. The threshold quantity [Formula: see text] which has a similar implication here as in the epidemiological modeling is obtained for the present model. The corruption free equilibrium is found to be stable when [Formula: see text] is less than [Formula: see text] and unstable for [Formula: see text]. The endemic equilibrium which signifies the presence of corrupted individuals in the society exists only when [Formula: see text]. This equilibrium point is locally asymptotically stable whenever it exists. We perform extensive numerical simulations to support the analytical findings. Furthermore, we extend the model to include optimal control and the optimal control profile is obtained to get the maximum control within a stipulated period of time. Our presented results show that the level of corruption in the society can be reduced if corruption control efforts through media/punishments etc. are increased and put in place.