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Analysis of symmetries in models of multi-strain infections
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.
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Publication status
- Published
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- Accepted version
Journal
Journal of Mathematical BiologyISSN
0303-6812Publisher
Springer VerlagExternal DOI
Issue
6-7Volume
69Page range
1431-1459Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2015-07-24First Open Access (FOA) Date
2015-12-02First Compliant Deposit (FCD) Date
2015-07-24Usage metrics
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