Symmetry breaking in a model of antigenic variation with immune delay

Blyuss, Konstantin B and Kyrychko, Yuliya N (2012) Symmetry breaking in a model of antigenic variation with immune delay. Bulletin of Mathematical Biology, 74 (10). pp. 2488-2509. ISSN 1522-9602

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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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: Konstantin Blyuss
Date Deposited: 08 Nov 2012 12:28
Last Modified: 08 Nov 2012 12:28
URI: http://sro.sussex.ac.uk/id/eprint/41429
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