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International Journal of Differential Equations
Volume 2016 (2016), Article ID 5915768, 12 pages
http://dx.doi.org/10.1155/2016/5915768
Research Article

Equivariant Hopf Bifurcation in a Time-Delayed Ring of Antigenic Variants

College of Engineering, Technology, and Physical Sciences, Department of Mathematics, Alabama A & M University, 4900 Meridian Street North, Huntsville, AL 35762, USA

Received 4 July 2015; Revised 26 November 2015; Accepted 1 December 2015

Academic Editor: Salim Messaoudi

Copyright © 2016 Israel Ncube. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider an intrahost malaria model allowing for antigenic variation within a single species. The host’s immune response is compartmentalised into reactions to major and minor epitopes. We investigate the dynamics of the model, paying particular attention to bifurcation and stability of the uniform nonzero endemic equilibrium. We establish conditions for the existence of an equivariant Hopf bifurcation in a ring of antigenic variants, characterised by time delay.