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Stability and bifurcations in a model of antigenic variation in malaria

journal contribution
posted on 2023-06-07, 23:33 authored by Konstantin BlyussKonstantin Blyuss, Sunetra Gupta
We examine the properties of a recently proposed model for antigenic variation in malaria which incorporates multiple epitopes and both long-lasting and transient immune responses. We show that in the case of a vanishing decay rate for the long-lasting immune response, the system exhibits the so-called "bifurcations without parameters" due to the existence of a hypersurface of equilibria in the phase space. When the decay rate of the long-lasting immune response is different from zero, the hypersurface of equilibria degenerates, and a multitude of other steady states are born, many of which are related by a permutation symmetry of the system. The robustness of the fully symmetric state of the system was investigated by means of numerical computation of transverse Lyapunov exponents. The results of this exercise indicate that for a vanishing decay of long-lasting immune response, the fully symmetric state is not robust in the substantial part of the parameter space, and instead all variants develop their own temporal dynamics contributing to the overall time evolution. At the same time, if the decay rate of the long-lasting immune response is increased, the fully symmetric state can become robust provided the growth rate of the long-lasting immune response is rapid.

History

Publication status

  • Published

Journal

Journal of Mathematical Biology

ISSN

0303-6812

Issue

6

Volume

58

Page range

923-937

Pages

15.0

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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