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Mathematical Analysis of the Impact of Poverty and Unemployment on Crime Trends in Sub-Saharan Countries

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  • Bilali Mataru

Abstract

Crime remains a persistent global challenge with profound socioeconomic implications. This paper develops a deterministic mathematical model to analyze crime dynamics in sub-Saharan Africa, specifically evaluating the impacts of poverty, unemployment, drug abuse, illiteracy, and socioeconomic inequality. Using the next-generation matrix method, we derive the crime threshold number (R0) to analyze the stability of equilibrium points. Numerical analysis demonstrates that the crime-free equilibrium is stable when the threshold number is less than unity, while center manifold theory reveals a transcritical bifurcation. Numerical simulations using ODE45 indicate that poverty, unemployment, inequality, drug abuse, and illiteracy significantly drive both property and violent crime. The findings suggest that sustainable crime reduction requires addressing these root causes; while imprisonment offers only a short-term solution due to recidivism, optimal vocational training and sustainable employment opportunities prove effective over the long term.

Suggested Citation

  • Bilali Mataru, 2026. "Mathematical Analysis of the Impact of Poverty and Unemployment on Crime Trends in Sub-Saharan Countries," Journal of Applied Mathematics, Hindawi, vol. 2026, pages 1-22, July.
    • Handle: RePEc:hin:jnljam:6608738
    DOI: 10.1155/jama/6608738
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