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<p>In this paper, we formulated a mathematical model for the transmission dynamics of corruption by explicitly considering the behavior of the Criminal Justice System. The model was proven to be mathematically well posed. We used the next-generation matrix method to calculate the basic reproduction number regarding the corruption-free equilibrium and established the conditions for the local and global asymptotic stability of these equilibrium points. The analysis reveals a globally asymptotically stable corrupt-free equilibrium whenever <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal{R}&lt;1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">R</mi> <mo>&lt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> and a globally asymptotically stable endemic equilibrium if otherwise. The sensitivity analysis and numerical simulations showed that integrating a strategy aiming to strengthen the law and criminal justice system, as well as the campaigns to raise the awareness against corruption is the best approach to fight this phenomenon.</p>

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Corruption's diffusion and the criminal justice system: a dynamical model

  • 期刊论文

  • 发表日期：

    2026年1月16日

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  • Camilo Almanza Ramírez,
  • Jorge Eliecer Ospino Portillo,
  • José Luis Ramos Ruiz

摘要

In this paper, we formulated a mathematical model for the transmission dynamics of corruption by explicitly considering the behavior of the Criminal Justice System. The model was proven to be mathematically well posed. We used the next-generation matrix method to calculate the basic reproduction number regarding the corruption-free equilibrium and established the conditions for the local and global asymptotic stability of these equilibrium points. The analysis reveals a globally asymptotically stable corrupt-free equilibrium whenever \(\mathcal{R}<1\) R < 1 and a globally asymptotically stable endemic equilibrium if otherwise. The sensitivity analysis and numerical simulations showed that integrating a strategy aiming to strengthen the law and criminal justice system, as well as the campaigns to raise the awareness against corruption is the best approach to fight this phenomenon.