Corruption, a pervasive societal ill, hinders economic, social, and political progress globally. This study develops a novel mathematical model to analyze the transmission dynamics of corruption. Utilizing Corruption Index data, the model introduces the Corruption Influence Number (CIN), a metric quantifying corruption’s societal impact. Numerical simulations using MATLAB ODE solvers validate the model and investigate parameter effects on corruption dynamics. The findings reveal how corruption contact rates influence the transition of susceptible individuals to corruption. Moreover, the results underscore the effectiveness of prevention and punishment strategies in reducing corruption. This research concludes with the formulation of an optimal control solution, offering a foundation for future cost-effectiveness analyses of corruption mitigation strategies.