Mathematical Modelling and Analysis of the Dynamics of Corruption Incorporating Anti – Corruption Agencies

Abstract

Corruption is a global problem that affects many countries, undermining economic, social, and political development. To better understand the control measures that can reduce corruption transmission, we have formulated and analyzed a mathematical model incorporating anti – corruption agencies. To verify the model's validity, we explored the basic properties of the model in terms of existence, uniqueness, positivity and boundedness, and results showed that the solution exists, is unique, positive and bounded. The basic reproduction number, , was computed using the next-generation matrix method. Furthermore, the model was studied analytically to explore corruption dynamics. The stability analysis of the formulated model showed that the corruption-free equilibrium is locally and globally asymptotically stable if, but the corruption-endemic equilibrium is globally asymptotically stable if . A sensitivity analysis of the model parameters with respect to the threshold quantity measuring the spread of corruption was conducted to identify the most influential parameters driving the spread of corruption. The results revealed that reducing the values of parameters with positive indices will contribute in controlling the spread of corruption. Conversely, the sensitivity results suggest that increasing the values of parameters with negative indices will also help to mitigate the spread of corruption.