A geometric analysis of the SIR, SIRS and SIRWS epidemiological models

We study fast–slow versions of the SIR, SIRS, and SIRWS epidemiological models. The multiple time scale behaviour is introduced to account for large differences between some of the rates of the epidemiological pathways. Our main purpose is to show that the fast–slow models, even though in nonstandar...

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Bibliographic Details
Published inNonlinear analysis: real world applications Vol. 58; p. 103220
Main Authors Jardón-Kojakhmetov, Hildeberto, Kuehn, Christian, Pugliese, Andrea, Sensi, Mattia
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.04.2021
Subjects
Bifurcation analysis
Entry–exit function
Epidemic model
Fast–slow system
Non-standard form
Numerical continuation
Entry–exit function
Fast–slow system
Epidemic model
Numerical continuation
Non-standard form
Bifurcation analysis
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Summary:We study fast–slow versions of the SIR, SIRS, and SIRWS epidemiological models. The multiple time scale behaviour is introduced to account for large differences between some of the rates of the epidemiological pathways. Our main purpose is to show that the fast–slow models, even though in nonstandard form, can be studied by means of Geometric Singular Perturbation Theory (GSPT). In particular, without using Lyapunov’s method, we are able to not only analyse the stability of the endemic equilibria but also to show that in some of the models limit cycles arise. We show that the proposed approach is particularly useful in more complicated (higher dimensional) models such as the SIRWS model, for which we provide a detailed description of its dynamics by combining analytic and numerical techniques.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2020.103220