Modeling the Phenomenon of Xenophobia in Africa


  • Reuben Iortyer Gweryina Department of Mathematics/Statistics/Computer Science, Federal University of Agriculture, PMB 2373, Makurdi, Nigeria, 970101
  • Emilian Chinwendu Madubueze Department of Mathematics/Statistics/Computer Science, Federal University of Agriculture, PMB 2373, Makurdi, Nigeria, 970101
  • Simon James Ogaji Department of Mathematics/Statistics/Computer Science, Federal University of Agriculture, PMB 2373, Makurdi, Nigeria, 970101



Boundedness, Global stability, Local bifurcation, Xenophobes, Xenophobic-mathematical model


In this study, we applied the principle of a competitive predator-prey system to propose a prey-predator-like model of xenophobia in Africa. The boundedness of the solution, the existence and stability of equilibrium states of the xenophobic model are discussed accordingly. As a special case, the coexistence state was found to be locally and globally stable based on the parametric conditions of effective group defense and anti-xenophobic policy implementation. The system was further analyzed by Sotomayor?s theory to show that each equilibrium point bifurcates transcritically. However, numerical proof showed period-doubling bifurcation, which makes the xenophobic situation more chaotic in Africa. Further numerical simulations support the analytical results with the view that tolerance, group defense and anti-xenophobic policies are critical parameters for the coexistence of foreigners and xenophobes.


Crush, J. & Ramachandran, S., Xenophobic Violence in South Africa: Denialism, Minimalism and Realism, Migration Policy Series, 66, pp. 1-49, 2014.

Ogunnoiki, A.O. & Adeyemi, A.A., The Impact of Xenophobic Attacks on Nigeria-South Africa Relations, African Journal of Social Sciences and Humanities Research, 22, pp. 1-18, 2019.

Solomon, H. & Kosaka, H., Xenophobia in South Africa: Reflection, Narratives and Recommendations, Southern African Peace and Security Studies, 22, pp. 5-30, 2013.

Whitaker, B.E., Citizens and Foreigners: Democratization and the Politics of Exclusion in Africa, African Studies Review 481, pp. 109-126, 2005.

Soyombo, O.T., Xenophobia in Contemporary Society: A Sociological Analysis, IFE PsychologIA, 163, pp. 85-104, 2008.

Nkwede, J.O., Xenophobic Violence, and Economic Development in South Africa, International Journal of Innovative Legal and Political Studies, 7(3), pp. 20-28, 2019.

Wimmer, A., Explaining Xenophobia and Racism: A Critical Review of Current Research Approaches, Ethnic and Racial Studies, 20(1), pp. 17-41, 1997.

Human Right Watch, There Will Be Blood: Xenophobia in South Africa Routine and Lethal, https: 24 Reuben Iortyer Gweryina, et al. news/2020/9/17. (Retrieved on October 11, 2020)

Big-Alabo, S. & Big-Alabo, T., Xenophobic Attacks on Nigerians in South Africa: Ethical Implications and Responses of the Nigerian Government, International Journal of Multidisciplinary Research and Development, 73, pp. 30-41, 2020.

Misago, J.P., Landau, L.B. & Monson, T., Towards Tolerance, Law and Dignity: Addressing Violence Against Foreign Nationals in South Africa, International Organization for Migration, 1, pp. 1-67, 2009.

Crawly, K, Developing and Validating A Social Model for Xenophobic Violence In South Africa, M.Sc Thesis, Department of Public and Development Management, University of Witwaterrand, Johannesburg, 2011.

Holder, E., Mapping Xenophobic Violence in South Africa: Modelling Spatial Relationships Between Group Grievances and Opportunities to Measure the Propensity for Xenophobic Violence, MSc Thesis 622. Department of Geography, University of Arkansas, Fayetteville, 2012.

Zhang, H., Cai, Y., Fu, S. & Wang, W., Impact of the Fear Effect in

A Prey-Predator Model Incorporating a Prey Refuge, Applied Mathematics and Computations, 356, pp. 328-337, 2019.

Huang, Y., Zhu, Z. & Li, Z., Modelling the Allee Effect and Fear Effect

in Predator-Prey System Incorporating a Prey Refuge, Advances in Difference Equations, 321, 2020. DOI: 10.1186/s13662-020-02727-5

Samadar, S., Dhar, M. & Bhattacharya, P., Effect of Fear on Prey-Predator Dynamics Exploring the Role of Prey Refuge and Additional Food, Chaos, 30 063129, 2020. DOI: 10.1063/5.0006968

Sasmal, S.K. & Takeuchi, Y., Dynamics of Predator-Prey System with Fear and Group Defense, Journal of Mathematical Analysis and Applications, 481(123471), pp. 1-23, 2020.

Martcheva, M., An Introduction to Mathematical Epidemiology, 61, Springer Science and Business Media, 4, 2015.

Lelu, F. & Jiao, Y., Stability and Hopf Bifurcation of a Predator-Prey Model, Boundary Problems, 129, pp. 1-11, 2019.

Dubey, B., A Prey-Predator Model with a Reserved Area, Non-linear

Analysis: Modelling and Control, 124, pp. 479-494, 2007.

Osuna, O., Rodriguez-Ceballos, J., Vargas-De-Leon, C. & Villasenor- Aguilar, G., A Note on the Existence and Construction of Dulac Functions, Nonlinear Analysis: Modelling and Control, 22(4), pp. 431-440, 2017.

Liu, Y., Zhao, L., Huang, X. & Deng, H., Stability and Bifurcation Analysis of Two Species Amensalism Model with Michalis-Menten Type Harvesting Modelling the Phenomenon of Xenophobia in Africa 25

and a Cover for the First Species, Advances in Difference Equations, 295, 2018. DOI: 10.1186/s13662-018-1752-2

Das, K., Srinivas, M.N., Madhusudanan, V. & Pinelas, S., Mathematical

Analysis of a Prey-Predator System: An Adaptive Back-Stepping Control and Stochastic Approach, Mathematical and Computational Applications, 2422, pp. 1-20, 2019.