Analyses of the SIR Epidemic Model Including Treatment and Immigration

Özlem Ak Gümüş; George Maria Selvam; Narin Kılınç; Janagaraj Rajendran

doi:10.33187/jmsm.1341741

EN

Analyses of the SIR Epidemic Model Including Treatment and Immigration

Abstract

This paper aims to examine the dynamics of a variation of a nonlinear SIR epidemic model. We analyze the complex dynamic nature of the discrete-time SIR epidemic model by discretizing a continuous SIR epidemic model subject to treatment and immigration effects with the Euler method. First of all, we show the existence of equilibrium points in the model by reducing the three-dimensional system to the two-dimensional system. Next, we show the stability conditions of the obtained positive equilibrium point and the visibility of flip bifurcation. A feedback control strategy is applied to control the chaos occurring in the system after a certain period of time. We also perform numerical simulations to support analytical results. We do all these analyses for models with and without immigration and show the effect of immigration on dynamics.

Keywords

Flip bifurcation, Immigration, SIR model, Stability

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Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Özlem Ak Gümüş ^*
0000-0003-2610-8565
Türkiye

George Maria Selvam
0000-0003-2004-3537
India

Narin Kılınç
0000-0002-3564-651X
Türkiye

Janagaraj Rajendran
0000-0002-9811-078X
India

Early Pub Date

February 5, 2024

Publication Date

May 8, 2024

Submission Date

August 11, 2023

Acceptance Date

December 12, 2023

Published in Issue

Year 2024 Volume: 7 Number: 1

DOI

https://doi.org/10.33187/jmsm.1341741

IZ

https://izlik.org/JA78TZ27UA

APA

Ak Gümüş, Ö., Selvam, G. M., Kılınç, N., & Rajendran, J. (2024). Analyses of the SIR Epidemic Model Including Treatment and Immigration. Journal of Mathematical Sciences and Modelling, 7(1), 1-13. https://doi.org/10.33187/jmsm.1341741

AMA

1.Ak Gümüş Ö, Selvam GM, Kılınç N, Rajendran J. Analyses of the SIR Epidemic Model Including Treatment and Immigration. Journal of Mathematical Sciences and Modelling. 2024;7(1):1-13. doi:10.33187/jmsm.1341741

Chicago

Ak Gümüş, Özlem, George Maria Selvam, Narin Kılınç, and Janagaraj Rajendran. 2024. “Analyses of the SIR Epidemic Model Including Treatment and Immigration”. Journal of Mathematical Sciences and Modelling 7 (1): 1-13. https://doi.org/10.33187/jmsm.1341741.

EndNote

Ak Gümüş Ö, Selvam GM, Kılınç N, Rajendran J (May 1, 2024) Analyses of the SIR Epidemic Model Including Treatment and Immigration. Journal of Mathematical Sciences and Modelling 7 1 1–13.

IEEE

[1]Ö. Ak Gümüş, G. M. Selvam, N. Kılınç, and J. Rajendran, “Analyses of the SIR Epidemic Model Including Treatment and Immigration”, Journal of Mathematical Sciences and Modelling, vol. 7, no. 1, pp. 1–13, May 2024, doi: 10.33187/jmsm.1341741.

ISNAD

Ak Gümüş, Özlem - Selvam, George Maria - Kılınç, Narin - Rajendran, Janagaraj. “Analyses of the SIR Epidemic Model Including Treatment and Immigration”. Journal of Mathematical Sciences and Modelling 7/1 (May 1, 2024): 1-13. https://doi.org/10.33187/jmsm.1341741.

JAMA

1.Ak Gümüş Ö, Selvam GM, Kılınç N, Rajendran J. Analyses of the SIR Epidemic Model Including Treatment and Immigration. Journal of Mathematical Sciences and Modelling. 2024;7:1–13.

MLA

Ak Gümüş, Özlem, et al. “Analyses of the SIR Epidemic Model Including Treatment and Immigration”. Journal of Mathematical Sciences and Modelling, vol. 7, no. 1, May 2024, pp. 1-13, doi:10.33187/jmsm.1341741.

Vancouver

1.Özlem Ak Gümüş, George Maria Selvam, Narin Kılınç, Janagaraj Rajendran. Analyses of the SIR Epidemic Model Including Treatment and Immigration. Journal of Mathematical Sciences and Modelling. 2024 May 1;7(1):1-13. doi:10.33187/jmsm.1341741