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

Hildeberto Jardon Kojakhmetov, Christian Kuehn, Andrea Pugliese, Mattia Sensi*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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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.
Original languageEnglish
Article number103220
JournalNonlinear Analysis: Real World Applications
Early online date28-Sep-2020
Publication statusPublished - Apr-2021
Externally publishedYes

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