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

Andrei Korobeinikov; Elena Shchepakina; Vladimir Sobolev; Andrei Korobeinikov; Elena Shchepakina; Vladimir Sobolev

doi:10.3934/mbe.2020037

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 1: 725-736. doi: 10.3934/mbe.2020037

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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

Received: 20 June 2019 Accepted: 15 October 2019 Published: 25 October 2019

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.
- 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[J]. Mathematical Biosciences and Engineering, 2020, 17(1): 725-736. doi: 10.3934/mbe.2020037

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Abstract

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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