Application of an Epidemic Model to Turkey Data and Stability Analysis for the COVID-19 Pandemic

Year 2021, Volume: 25 Issue: 6, 1438 - 1445, 31.12.2021

Ömer Faruk Gözükızıl , Nejdet Köker

https://doi.org/10.16984/saufenbilder.980797

Cited By: 1

Abstract

An epidemic disease caused by a new coronavirus has spread all over the world with a high rate of transmission. The main purpose of this article is to define an epidemic model for the Covid-19 pandemic, to apply it to Turkey's data and to interpret it. Accordingly, a SEIR model was created to calculate the infected population and the number of deaths caused by this epidemic, and the stability of the model was examined. Since all the parameters affecting the stability cannot be calculated clearly, it cannot be expected to reach a realistic result. For this reason, a model was created with accessible parameters. Later, the diseased and non diseased equilibrium points of the model were discussed. The Hurwitz theorem is used to find the local stability of the model, while the Lyaponov function theory is used to investigate its global stability. Finally, some numerical results are given with the help of MATLAB program.

Keywords

SEIR Model, Covid-19 Pandemic, Stability.

References

• [1] Lyapunov, A.M., The General Problem of the Stability of Motion, Üniv. Kharkov, PhD thesis, 1892.
• [2] Carcione José M. ve diğ., A Simulation of a COVID-19 Epidemic Based on a Deterministic SEIR Model, Frontiers in Public Health, 2020.
• [3] Edwards C.M. ve Penney D.E., Differential Equations and Boundary Value Problems (Translation Prof. Dr. Ömer Akın), Palme Publishing, Ankara, 366-434, 2005.
• [4] Boyce W. E. ve DiPrima R. C., Elementary Differential Equations and Boundary Value Problems (Translation Uğuz M. ve Ürtiş Ç.), Palme Publishing, Ankara, 495-527, 2016.
• [5] Haran M., An introduction to models for disease Dynamics, SAMSI, 5-25, 2009.
• [6] Van den Driessche P., Watmough J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, 2002.
• [7] Alzahrani E., Zeb A., Stability analysis and prevention strategies of tobacco smoking model, 2020.
• [8] https://corona.cbddo.gov.tr/Home/DeathConfirmedRatio, Access Date: 04.07.2021.
• [9] https://data.tuik.gov.tr/Bulten/Index?p=Dogum-Istatistikleri-2020-33706, Access Date: 04.07.2021.
• [10] https://www.nufusu.com/turkiye-nufusu-yas-gruplari, Access Date: 04.07.2021.
• [11] https://data.tuik.gov.tr/Bulten/Index?p=Olum-ve-Olum-Nedeni-Istatistikleri-2019-33710, Access Date: 04.07.2021.