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Nonlinear Sciences > Chaotic Dynamics

arXiv:1209.4475 (nlin)
[Submitted on 20 Sep 2012]

Title:Symmetry breaking in a model of antigenic variation with immune delay

Authors:K.B. Blyuss, Y.N. Kyrychko
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Abstract:Effects of immune delay on symmetric dynamics are investigated within a model of antigenic variation in malaria. Using isotypic decomposition of the phase space, stability problem is reduced to the analysis of a cubic transcendental equation for the eigenvalues. This allows one to identify periodic solutions with different symmetries arising at a Hopf bifurcation. In the case of small immune delay, the boundary of the Hopf bifurcation is found in a closed form in terms of system parameters. For arbitrary values of the time delay, general expressions for the critical time delay are found, which indicate bifurcation to an odd or even periodic solution. Numerical simulations of the full system are performed to illustrate different types of dynamical behaviour. The results of this analysis are quite generic and can be used to study within-host dynamics of many infectious diseases.
Comments: 21 page, 4 figures. arXiv admin note: substantial text overlap with arXiv:1202.4290
Subjects: Chaotic Dynamics (nlin.CD); Dynamical Systems (math.DS); Quantitative Methods (q-bio.QM)
Cite as: arXiv:1209.4475 [nlin.CD]
  (or arXiv:1209.4475v1 [nlin.CD] for this version)
  https://doi.org/10.48550/arXiv.1209.4475
Journal reference: Bull. Math. Biol. 74, 2488-2509 (2012)

Submission history

From: Konstantin Blyuss [view email]
[v1] Thu, 20 Sep 2012 09:37:10 UTC (57 KB)
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