A mathematical model of corruption dynamics endowed with fractal–fractional derivative

Abstract

Numerous organisations across the globe have significant challenges about corruption, characterised by a systematic, endemic, and pervasive nature that permeates various societal establishments. Hence, we propose the fractional order model of corruption, which encompasses the involvement of corrupt individuals across various stages of education and employment. Specifically, we examine the presence of corruption among children in elementary schools, youths in tertiary institutions, adults in civil services, adults in government and public offices, and individuals who have renounced their involvement in corrupt practices. The basic reproduction number of the system was determined by utilising the next-generation matrix. The strength number was obtained by calculating the second derivative of the corruption-related compartments. The examined model solution’s existence, uniqueness, and stability were established using the Krasnoselski fixed point theorem, the Banach contraction principle, and the Ulam–Hyers theorem, respectively. Based on the numerous figures presented, our simulations indicate a positive correlation between the decline in fractal–fractional order and the increase in the number of individuals susceptible to corruption. This phenomenon results in an increase in the prevalence of corruption among designated sectors of the general population. The persistence of corruption in society is a significant challenge to its eradication, as individuals who see personal gains from engaging in corrupt practices tend to exhibit a recurring inclination towards such behaviour. Nevertheless, it is recommended that to mitigate corruption within various corruption-prone subcategories, there is a need to enhance the level of consciousness and promotion of anti-corruption measures throughout all societal establishments.