A mathematical model of corruption dynamics endowed with fractal–fractional derivative
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Date
2023-08
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Elsevier
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.
Description
This article is published by Elsevier 2023 and is also available at https://doi.org/10.1016/j.rinp.2023.106894
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Citation
Results in Physics 52 (2023) 106894