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Research Article | Open Access

The existence of codimension-two bifurcations in a discrete-time SIR epidemic model

Xijuan Liu1, Peng Liu2, Yun Liu1( )
College of Information Engineering, Tarim University, Alar, China
College of Geo-Exploration Science and Technology, Jilin University, Jilin, China
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Abstract

In this paper, we consider a discrete-time SIR epidemic model. Codimension-two bifurcations associated with 1:2, 1:3 and 1:4 strong resonances are analyzed by using a series of affine transformations and bifurcation theory. Numerical simulations are carried out to verify and illustrate these theoretical results. More precisely, two kinds of high-resolution stability phase diagrams are exhibited to describe how the system's complexity unfolds with control parameters varying.

Keywords

SIR epidemic modeltwo-dimensional parameter spacechaoscodimension-two bifurcation
CLC number: 92B05, 37G05, 37G15, 39A28

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AIMS Mathematics
Volume 7 Issue 3,
March 2022
Pages 3360-3378
DOI: 10.3934/math.2022187

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Cite this article:
Liu X, Liu P, Liu Y. The existence of codimension-two bifurcations in a discrete-time SIR epidemic model. AIMS Mathematics, 2022, 7(3): 3360-3378. https://doi.org/10.3934/math.2022187

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Received: 27 September 2021
Accepted: 17 November 2021
Published: 15 March 2021
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)