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Symmetry breaking in a model of antigenic variation with immune delay

journal contribution
posted on 2023-06-08, 12:46 authored by Konstantin BlyussKonstantin Blyuss, Yuliya KyrychkoYuliya Kyrychko
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.

History

Publication status

  • Published

Journal

Bulletin of Mathematical Biology

ISSN

1522-9602

Publisher

Springer Verlag

Issue

10

Volume

74

Page range

2488-2509

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-11-08

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