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A black swan and canard cascades in an SIR infectious disease model

1 Centre de Recerca Matemática, Campus de Bellaterra, 08193 Bellaterra, Barcelona, Spain
2 Samara National Research University, 34 Moskovskoye shosse, Samara, 443086, Russia

Special Issues: Advances in Mathematical Modelling and Analysis of Bioprocesses

Models of the spread of infectious diseases commonly have to deal with the problem of multiple timescales which naturally occur in the epidemic models. In the most cases, this problem is implicitly avoided with the use of the so-called “constant population size” assumption. However, applicability of this assumption can require a justification (which is typically omitted).
In this paper we consider some multiscale phenomena that arise in a reasonably simple SusceptibleInfected-Removed (SIR) model with variable population size. In particular, we discuss examples of the canard cascades and a black swan that arise in this model.
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Keywords singular perturbations; invariant manifold; stability; canards; canard cascades; black swan; model order reduction; infectious disease model

Citation: Andrei Korobeinikov, Elena Shchepakina, Vladimir Sobolev. A black swan and canard cascades in an SIR infectious disease model. Mathematical Biosciences and Engineering, 2020, 17(1): 725-736. doi: 10.3934/mbe.2020037

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