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A mathematical approach to Xenophobia: The case of South Africa

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  • Mhlanga, A.

Abstract

Xenophobia is a social evil which leaves a trail of destruction wherever it passes through. A mathematical model is formulated and analyzed to gain an understanding of xenophobia in order to come up with strategies on how we can best control it. The xenophobia-free equilibrium is shown to be globally asymptotically stable when the corresponding threshold parameter is less than unity. Furthermore, the xenophobic equilibrium point exists only when the corresponding threshold parameter is greater than unity and is locally asymptotically stable when the corresponding threshold parameter is greater than unity. The results from the model analysis suggest that negative peer influence promotes the development of xenophobia while counseling and incarceration inhibit its growth. The results from the numerical simulations suggest that although counseling and incarceration can singly reduce xenophobia, the use of counseling of the exposed and the xenophobic coupled with incarceration may be the ideal strategy to stop this menace.

Suggested Citation

  • Mhlanga, A., 2021. "A mathematical approach to Xenophobia: The case of South Africa," Mathematical Social Sciences, Elsevier, vol. 110(C), pages 44-52.
    • Handle: RePEc:eee:matsoc:v:110:y:2021:i:c:p:44-52
    DOI: 10.1016/j.mathsocsci.2021.02.001
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    References listed on IDEAS

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    1. Ebenezer O. Oni & Samuel K. Okunade, 2018. "The Context of Xenophobia in Africa: Nigeria and South Africa in Comparison," Advances in African Economic, Social and Political Development, in: Adeoye O. Akinola (ed.), The Political Economy of Xenophobia in Africa, chapter 0, pages 37-51, Springer.
    2. A. Mhlanga & C. P. Bhunu & S. Mushayabasa, 2014. "HSV-2 and Substance Abuse amongst Adolescents: Insights through Mathematical Modelling," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-17, November.
    3. Jonathan Crush & Sujata Ramachandran, 2010. "Xenophobia, International Migration and Development," Journal of Human Development and Capabilities, Taylor & Francis Journals, vol. 11(2), pages 209-228.
    4. Mubayi, Anuj & Greenwood, Priscilla E. & Castillo-Chávez, Carlos & Gruenewald, Paul J. & Gorman, Dennis M., 2010. "The impact of relative residence times on the distribution of heavy drinkers in highly distinct environments," Socio-Economic Planning Sciences, Elsevier, vol. 44(1), pages 45-56, March.
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