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

Xijuan Liu; Peng Liu; Yun Liu; Xijuan Liu; Peng Liu; Yun Liu

doi:10.3934/math.2022187

AIMS Mathematics

2022, Volume 7, Issue 3: 3360-3378. doi: 10.3934/math.2022187

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Research article

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

1.
College of Information Engineering, Tarim University, Alar, China
2.
College of Geo-Exploration Science and Technology, Jilin University, Jilin, China

Received: 27 September 2021 Accepted: 17 November 2021 Published: 30 November 2021
MSC : 92B05, 37G05, 37G15, 39A28

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.
- SIR epidemic model,
- two-dimensional parameter space,
- chaos,
- codimension-two bifurcation
Citation: Xijuan Liu, Peng Liu, Yun Liu. The existence of codimension-two bifurcations in a discrete-time SIR epidemic model[J]. AIMS Mathematics, 2022, 7(3): 3360-3378. doi: 10.3934/math.2022187

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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.

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