Analysis of symmetries in models of multi-strain infections

Blyuss, Konstantin B (2014) Analysis of symmetries in models of multi-strain infections. Journal of Mathematical Biology, 69 (6-7). pp. 1431-1459. ISSN 0303-6812

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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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: T Technology > T Technology (General) > T0055.4 Industrial engineering. Management engineering > T0057 Applied mathematics. Quantitative methods
Depositing User: Konstantin Blyuss
Date Deposited: 24 Jul 2015 12:55
Last Modified: 11 Sep 2017 08:47
URI: http://sro.sussex.ac.uk/id/eprint/55738

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