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A mathematical approach to xenophobia: the case of South Africa. (English) Zbl 1461.91213

Summary: 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.

MSC:

91D10 Models of societies, social and urban evolution
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[1] Aremu, O. J., Responses to the 1983 expulsion of aliens from Nigeria: A critique, Afr. Res. Rev., 7, 3, 340-341 (2013)
[2] Arriola, L. M.; Hyman, J. M., Being sensitive to uncertainty, Comput. Sci. Eng., 9, 2, 10-20 (2007)
[3] Benedict, B., Modelling alcoholism as a contagious disease: how infected buddies spread problem drinking, Indian Math. Soc. News, 40, 3 (2007)
[4] Bhunu, C. P., Modelling the spread of street kids in Zimbabwe, J. Biol. Systems, 22, 3, 429-447 (2014) · Zbl 1303.91135
[5] Bhunu, C. P., Homelessness and drug misuse in developing countries: A mathematical approach, Commun. Nonlinear Sci. Numer. Simul., 19, 1908-1917 (2014) · Zbl 1457.92157
[6] Bhunu, C. P., Modelling the spread of street kids in Zimbabwe, J. Biol. Systems, 22, 3, 429-447 (2014) · Zbl 1303.91135
[7] Bhunu, C. P.; Mushayabasa, S., A theoretical analysis of smoking and alcoholism, J. Math. Model. Algorithms, 11, 4, 387-408 (2012) · Zbl 1270.34118
[8] Bhunu, C. P.; Mushayabasa, S., Prostitution and drug (alcohol) misuse: the menacing combination, J. Biol. Systems, 20, 2, 177-193 (2012) · Zbl 1279.92070
[9] Campell, J., Zulu King and South Africa’s wave of xenophobia, Afr. Trans. (2015), https://www.cfr.org/blog/zulu-king-and-south-africas-wave-xenophobia
[10] Carr, J., Applications Centre Manifold Theory (1981), Springer-Verlag: Springer-Verlag New York · Zbl 0464.58001
[11] Castillo-Chavez, C.; Feng, Z.; Huang, W., On the computational of \(R_0\) and its role on global stability, (Castillo-Chavez, C.; etal., Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, and Theory, Vol. 126 (2002), Ed., IMA), 215-230
[12] Castillo-Chavez, C.; Song, B., Dynamical models of tuberculosis and their applications, Math. Biosci. Eng., 1, 2, 361-404 (2004) · Zbl 1060.92041
[13] Charney, C., Voices of New Democracy: African Expectations in the New South Africa (1995), Centre for Policy Studies: Centre for Policy Studies Johannesburg
[14] Chinomona, E.; Maziriri, E. T., Examining the phenomenon of Xenophobia as experienced by African Immigrant Entrepreneurs in Johannesburg, South Africa: Intensifying the Spirit of ’Ubuntu’, Int. J. Res. Bus. Stud. Manage., 2, 6, 20-31 (2015)
[15] Choane, M.; Shulika, L. S.; Mthombeni, M., An analysis of the causes, effects and Ramifications of Xenophobia in South Africa, Insight Afr., 3, 2, 129-142 (2011)
[16] Claassen, C., Explaining South African Xenophobia, AFRO BAROMETER, Let the People Have a SayWorking Paper No. 173 (2017)
[17] Crush, J., The dark side of democracy: migration, xenophobia and human rights in South Africa, Int. Migr., 38, 6, 103-131 (2000)
[18] Crush, Jonathan; Pendleton, Wade, South African Migration Project 30: Regionalizing Xenophobia? Citizen Attitudes To Immigration and Refugee Policy in Southern Africa, (PDF) (2016), Institute for Democracy in South Africa, Retrieved 1 November 2016
[19] Crush, J.; Ramachandran, S., Xenophobia, international migration and development, J. Human Dev. Capabilities, 11, 2, 209-228 (2010)
[20] Diekman, O.; Heesterbeek, J. A.P.; Roberts, M., The construction of next-generation matrices for compartmental epidemics models, J. R. Soc. Interface, 7, 47, 873-885 (2010), (2010)
[21] Van den Driesche, P.; Watmough, J., Reproduction number and sub-threshold endemic equilibria for the compartmental models of disease transmission, Math. Biosci., 180, 1-2, 29-48 (2002) · Zbl 1015.92036
[22] Van den Driesche, P.; Watmough, J., Further notes on the reproduction number, (Mathematical Biology (2008), Springer), 159-178 · Zbl 1206.92038
[23] Van den Driessche, P.; Zou, X., Modeling relapse in infectious diseases, Math. Biosci., 207, 1, 89-103 (2007) · Zbl 1114.92047
[24] Fabricius, P., ISS today: Xenophobia once again jeopardises South Africa’s interests in Africa (2017), viewed 21 July 2017, from https://www.dailymaverick.co.za/article/2017-03-02-iss-today-xenophobia-once-again-jeopardises-south-africasinterests-in-africa
[25] Fanon, F., The Wretched Earth (1990), Penguin: Penguin London
[26] Gonzalez, B.; Huerta-Sanchez, E.; Ortiz-Nieves, A.; Vzquez-Alvarez, T.; Kribs-Zaleta, C., Am i too fat? Bulimia as an epidemic, J. Math. Psych., 47, 515-526 (2003) · Zbl 1037.92019
[27] Harper, M., Somalis in Kenya, they call us ATM machines, Afr. Argum., 7 (2010)
[28] Hsier, Y. H.; Wang, Y. S., Basic reproduction number for HIV model incorporating commercial sex and behavior change, Bull. Math. Biol., 68, 551-575 (2006) · Zbl 1334.92405
[29] Prohibited Persons, Abuse of Undocumented Migrants, Asylum Seekers and Refugees in South Africa (1998), Human Rights Watch.: Human Rights Watch. New York
[30] They have robbed me of my life, (Xenophobic Violence Against Non-Nationals in South Africa (2020)), https://www.hrw.org/report/2020/09/17/they-have-robbed-me-my-life/xenophobic-violence-against-non-nationals-south
[31] Jamison, D. T.; Feachmen, M. W.; Bos, E. R.; Baingana, F. K.; Hofman, K. J.; Rogo, K. O., Disease and Mortality in Sub-Saharan Africa (2006), World Bank: World Bank Washington, DC
[32] Kodaira, J. Y.; de Souza Passos, J. R., The basic reproduction number in SI staged progression model: a probabilistic approach, (Dynamics Days South America 2010 International Conference on Chaos and Nonlinear Dynamics (2010))
[33] Marsella, A. J.; Ring, E., Human migration and immigration: An overview, (Adler, L. L.; Gielen, U. P., Migration: Immigration and Emigration in International Perspective (2003), Praeger: Praeger Westport, CT), 3-22
[34] Masenya, M. J., Afrophobia in South Africa: A general perspective of xenophobia, Bangladesh J. Sociol., 14, 1, 81-88 (2017)
[35] Mavhinga, D., Human Rights Watch, South Africa launches plan to combat xenophobia and racism, (Crucial Step in South African Path To Justice and Equity (2019)), https://reliefweb.int/report/south-africa/south-africa-launches-plan-combat-xenophobia-and-racism
[36] Mhlanga, A.; Bhunu, C. P.; Mushayabasa, S., HSV-2 and substance abuse amongst adolescents: Insights through mathematical modelling, J. Appl. Math., Article 104819 pp. (2014) · Zbl 1437.92131
[37] Misago, J. P., Disorder in a changing society: Authority and the micro-politics of violence, (Landau, L. B., Exorcising the Demons Within (2012), Wits University Press: Wits University Press Johannesburg), 90-108
[38] Mubayi, A.; Greenwood, P. E.; Castillo-Chavez, C.; Gruenewald, D. M., The impact of relative residence times on the distribution of heavy drinkers in highly distinct environments, Socio-Econ. Plann. Sci., 44, 45-56 (2010)
[39] Neocosmos, M., The politics of fear and the fear of politics: Reflections on xenophobic violence in South Africa, J. Asian Afr. Stud., 43, 6, 586-594 (2008)
[40] Oni, E. O.; Okunade, S. K., The context of Xenophobia in Africa: Nigeria and South Africa in Comparison, (Akinola, A., The Political Economy of Xenophobia in Africa (2018), Advances in African Economic, Social and Political Development. Springer: Advances in African Economic, Social and Political Development. Springer Cham)
[41] Peil, M., Ghana’s aliens, Int. Migr. Rev., 8, 3 (1974)
[42] Powell, D.R., Fair, J., Le Claire, R.J., Moore, L.M., Thompson, D., 2005. Sensitivity analysis of an infectious disease model. In: Proceedings of the International System Dynamics Conference, Boston, Mass, USA.
[43] Sanchez, F.; Wang, X.; Castillo-Chavez, C.; Gorman, D. M.; Gruenewald, P. G., Drinking as an epidemic a simple mathematical model with recovery and relapse, (Witkiewitz, K.; Marlatt, G. A., Guide To Evidence-Based Relapse Prevention (2007), Elsevier: Elsevier New York, NY)
[44] Simeon, R., Consideration on the Design of Federation: The South African Constitution in Comparative Perspective (1998), Institute of Intergovernmental Relations, Gueen’s University: Institute of Intergovernmental Relations, Gueen’s University Kingston
[45] Solomon, H.; Kosaka, H., Xenophobia in South Africa, Narrative and recommendations, South. Afr. Peace Secur. Stud., 2, 2, 5-30 (2016)
[46] Steinberg, J., ISS Monograph No 117: Mozambican and Congolese Refugees in South Africa: A mixed reception (2008), Institute for Security Studies, Archived from the original (PDF) on 3 October 2008. Retrieved 5 September2008
[47] Zhao, X. Q., Dynamical Systems in Population Biology (2013), Springer Science and Business Media: Springer Science and Business Media New York, NY, USA
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