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Journal of Mathematical Biology

, Volume 69, Issue 6–7, pp 1431–1459 | Cite as

Analysis of symmetries in models of multi-strain infections

  • Konstantin B. BlyussEmail author
Article

Abstract

In mathematical studies of the dynamics of multi-strain diseases caused by antigenically diverse pathogens, there is a substantial interest in analytical insights. Using the example of a generic model of multi-strain diseases with cross-immunity between strains, we show that a significant understanding of the stability of steady states and possible dynamical behaviours can be achieved when the symmetry of interactions between strains is taken into account. Techniques of equivariant bifurcation theory allow one to identify the type of possible symmetry-breaking Hopf bifurcation, as well as to classify different periodic solutions in terms of their spatial and temporal symmetries. The approach is also illustrated on other models of multi-strain diseases, where the same methodology provides a systematic understanding of bifurcation scenarios and periodic behaviours. The results of the analysis are quite generic, and have wider implications for understanding the dynamics of a large class of models of multi-strain diseases.

Keywords

Multi-strain diseases Symmetry Equivariant Bifurcation Theory 

Mathematics Subject Classification (2000)

92D30 37G40 

Notes

Acknowledgments

The author would like to thank Jon Dawes for useful discussions and anonymous referees for their helpful comments and suggestions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of SussexBrighton UK

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