Bifurcations analysis of a discrete time SIR epidemic model with nonlinear incidence function

Reny George; Nadia Gul; Anwar Zeb; Zakieh Avazzadeh; Salih Djilali; Shahram Rezapour

doi:10.1016/j.rinp.2022.105580

Bifurcations analysis of a discrete time SIR epidemic model with nonlinear incidence function

Reny George, Nadia Gul, Anwar Zeb, Zakieh Avazzadeh, Salih Djilali, Shahram Rezapour^*

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

In this paper, we present a discrete-time SIR epidemic model and investigate the stability of its fixed points, as well as the bifurcations of the one and two parameters. The numerical normal form is used to analyze bifurcations. This model exhibits Neimark–Sacker transcritical, flip, and strong resonance bifurcations. Using the critical coefficients, a scenario is identified for each bifurcation. We verify analytical results using the MATLAB package MatContM, which employs the numerical continuation method.

Original language	English
Article number	105580
Journal	Results in Physics
Volume	38
DOIs	https://doi.org/10.1016/j.rinp.2022.105580
Publication status	Published - Jul 2022

Keywords

Bifurcation
Normal form
Numerical continuation method
One parameter bifurcation
SIR epidemic model
Stability

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10.1016/j.rinp.2022.105580

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title = "Bifurcations analysis of a discrete time SIR epidemic model with nonlinear incidence function",

abstract = "In this paper, we present a discrete-time SIR epidemic model and investigate the stability of its fixed points, as well as the bifurcations of the one and two parameters. The numerical normal form is used to analyze bifurcations. This model exhibits Neimark–Sacker transcritical, flip, and strong resonance bifurcations. Using the critical coefficients, a scenario is identified for each bifurcation. We verify analytical results using the MATLAB package MatContM, which employs the numerical continuation method.",

keywords = "Bifurcation, Normal form, Numerical continuation method, One parameter bifurcation, SIR epidemic model, Stability",

author = "Reny George and Nadia Gul and Anwar Zeb and Zakieh Avazzadeh and Salih Djilali and Shahram Rezapour",

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T1 - Bifurcations analysis of a discrete time SIR epidemic model with nonlinear incidence function

AU - George, Reny

AU - Gul, Nadia

AU - Zeb, Anwar

AU - Avazzadeh, Zakieh

AU - Djilali, Salih

AU - Rezapour, Shahram

PY - 2022/7

Y1 - 2022/7

N2 - In this paper, we present a discrete-time SIR epidemic model and investigate the stability of its fixed points, as well as the bifurcations of the one and two parameters. The numerical normal form is used to analyze bifurcations. This model exhibits Neimark–Sacker transcritical, flip, and strong resonance bifurcations. Using the critical coefficients, a scenario is identified for each bifurcation. We verify analytical results using the MATLAB package MatContM, which employs the numerical continuation method.

AB - In this paper, we present a discrete-time SIR epidemic model and investigate the stability of its fixed points, as well as the bifurcations of the one and two parameters. The numerical normal form is used to analyze bifurcations. This model exhibits Neimark–Sacker transcritical, flip, and strong resonance bifurcations. Using the critical coefficients, a scenario is identified for each bifurcation. We verify analytical results using the MATLAB package MatContM, which employs the numerical continuation method.

KW - Bifurcation

KW - Normal form

KW - Numerical continuation method

KW - One parameter bifurcation

KW - SIR epidemic model

KW - Stability

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SN - 2211-3797

VL - 38

JO - Results in Physics

JF - Results in Physics

M1 - 105580

ER -

Bifurcations analysis of a discrete time SIR epidemic model with nonlinear incidence function

Abstract

Keywords

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