Mathematical Analysis of Corruption Dynamics Incorporating the Corrupt Individuals Under Investigation Class and Recidivism

Abstract

Corruption is a complicated social, political, and economic phenomenon that impacts both public and private officials, as well as the nation as a whole. Several studies have likened it to an harrowing contagious disease because of its propensity to proliferate in the society by replicating itself from one individual to another and it causes debilitating effects to a country's economy. Despite the fact that many nations employ a variety of strategies to curb the spread of corruption, the vice incessantly persists. To ascertain the impact of control measures on corruption's propagation, a nonlinear deterministic mathematical model that describes its dynamics is developed and analyzed in this study. The study incorporates rigorous analysis to verify the existence, positivity, and boundedness of the solution, as well as the stability of the equilibrium points. It is confirmed that whenever the corruption reproduction number R₀ is less than one, the corruption-free equilibrium (CFE) is globally asymptotically stable. Using the normalized forward sensitivity approach, we determined the prerequisite for the optimal approach to mitigate the propagation of corruption. It is evident that 10% increase in corruption initiation rate β causes a corresponding 10% increase in R₀, while 10% increase in efficacy of anti-corruption and religious instructions ψ as well as incarceration rate γ₃ causes a reduction of R₀ by 6.462% and 1.686% respectively. On the numerical segment, python software was utilized to illustrate the time series solution. The numerical findings were in concurrence with the analytical results. This study recommends a tripartite approach to eradicating corruption over time. This involves effective anti-graft campaigns and religious teaching, establishment of an efficient and robust whistle-blowing protocols and lastly the imprisonment of individuals found culpable of committing corruption regardless of their socio-economic statuses.