Stability analysis of the corruption dynamics under fractional-order interventions

Abstract

This article proposes a nonlinear deterministic mathematical model that encapsulates the dynamics of the prevailing degree of corruption in a population. The objectives are attained by exploring the dynamics of the corruption model under fractional-order derivative in the Caputo sense. The outcomes of the research are facilitated by stratifying the population into five compartments: susceptible class, exposed class, corrupted class, recovered class, and honest class. The developed model is validated by proving pivotal delicacies such as positivity, invariant region, basic reproduction number, and stability analysis. The Ulam–Hyers stability technique is used to prove the stable solution. The Adam–Bashforth numerical scheme is employed to estimate the numerical solution. Moreover, the research environment is further enriched by studying each compartment with respect to a wide range of relevant parametric settings. The realizations of this study indicate that susceptible individuals remain subject to being influenced by corrupt individuals. In addition, it is observed that the population of exposed individuals, recovered individuals, and honest individuals asymptotically approach toward the corruption equilibrium point, whereas the magnitudes of susceptible individuals and corrupted individuals decrease asymptotically to the corruption equilibrium state. The compartment dynamics are witnessed to be sensitive for various fractional-orders indicating the utility of the fractional approach. The findings of this study support the fundamental understanding of conceptualizing corruption in accordance with the viral transmission of infectious disease.

Keywords

• corruption model
• caputo fractional derivative
• ulam–hyers stability
• adams–bashforth method
• numerical simulations