<p>Corruption is a persistent social vice that undermines governance, equity, and economic development, particularly in developing and transitional economies. Motivated by the observation that corrupt behavior spreads through social influence, institutional norms, and perceived impunity, this study models corruption as a social contagion using a deterministic compartmental susceptible–exposed–corrupted–reformed (<i>SECR</i>) model. Basic qualitative properties are established, and a corruption influence threshold <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {R}_{0}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> is derived using the next-generation matrix method. Local and global stability results show that the corruption-free equilibrium is asymptotically stable locally when <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {R}_{0}&lt;1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> <mo>&lt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, and the corruption–endemic equilibrium is globally asymptotically stable when <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathcal {R}_{0}&gt;1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> <mo>&gt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. Sensitivity analysis highlights the dominant roles of the influence, recruitment, and transition rates in amplifying corruption, while enforcement intensity and exit rates suppress persistence. An optimal control problem with three interventions: prevention/awareness, targeted redirection of exposed individuals, and intensified enforcement/rehabilitation, is formulated and analyzed using Pontryagin’s maximum principle. Numerical simulations are conducted using the nonstandard finite difference (NSFD) method, which reveals that a combination of targeted redirection of exposed individuals and intensified enforcement/rehabilitation provides the strongest and fastest suppression of corruption and growth in reform. The results offer policy-relevant guidance for prioritizing early-stage interventions and sustained enforcement under realistic institutional constraints.</p>

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Modeling corruption as a social contagion: a mathematical approach to dynamics, thresholds, and control

  • Rwat Solomon Isa,
  • Kennedy Mensah,
  • Godwin Onuche Acheneje,
  • N. Jeeva,
  • Mehmet Gümüş,
  • Kashif Ali,
  • Ali Raza

摘要

Corruption is a persistent social vice that undermines governance, equity, and economic development, particularly in developing and transitional economies. Motivated by the observation that corrupt behavior spreads through social influence, institutional norms, and perceived impunity, this study models corruption as a social contagion using a deterministic compartmental susceptible–exposed–corrupted–reformed (SECR) model. Basic qualitative properties are established, and a corruption influence threshold \(\mathcal {R}_{0}\) R 0 is derived using the next-generation matrix method. Local and global stability results show that the corruption-free equilibrium is asymptotically stable locally when \(\mathcal {R}_{0}<1\) R 0 < 1 , and the corruption–endemic equilibrium is globally asymptotically stable when \(\mathcal {R}_{0}>1\) R 0 > 1 . Sensitivity analysis highlights the dominant roles of the influence, recruitment, and transition rates in amplifying corruption, while enforcement intensity and exit rates suppress persistence. An optimal control problem with three interventions: prevention/awareness, targeted redirection of exposed individuals, and intensified enforcement/rehabilitation, is formulated and analyzed using Pontryagin’s maximum principle. Numerical simulations are conducted using the nonstandard finite difference (NSFD) method, which reveals that a combination of targeted redirection of exposed individuals and intensified enforcement/rehabilitation provides the strongest and fastest suppression of corruption and growth in reform. The results offer policy-relevant guidance for prioritizing early-stage interventions and sustained enforcement under realistic institutional constraints.