Dynamics and optimal control strategies of Corruption model

Abstract

In this work, we propose a nonlinear mathematics effect model of media on the phenomenon of corruption. We suggest a model that is more general than the ones we are familiar with in this domain, as we work in a structure of nine compartments. This model is important because it explains how corruption spreads in society. Moreover, we have proved the existence and the uniqueness of the solution through the fixed point theorem. The equilibria of the model are determined, and their stability is thoroughly studied. We argue that the corruption-free equilibrium is stable when R0 is less than one. The endemic equilibrium, which indicates the presence of corruption in the community, exists only when R0 > 1. Based on the principle of Pontryagin's maximum, an assessment of the requirements for optimal control of corruption spread. We perform extensive numerical simulations to support the analytical results.