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Dynamics of an SEIRS COVID-19 Epidemic Model with Saturated Incidence and Saturated Treatment Response: Bifurcation Analysis and Simulations

David A. Oluyori
Department of Mathematics, School of Physical Science, Ahmadu Bello University, Zaria, Kaduna State, Nigeria

Angel G. C. Perez
Facultad de Matematicas, Universidad Autonoma de Yucatan, Merida, Yucatan, Mexico

Victor A. Okhuese
Department of Mathematics, Nasarawa State University, Keffi, Nigeria

Muhammad Akram
Department of Eastern Medicine, Government College University, Faisalabad, Pakistan


DOI: https://doi.org/10.52542/tjdu.1.1.39-56

Keywords: COVID-19, epidemic model, bifurcation, saturated treatment, stability

Abstract

In this work, we study the dynamics of the Coronavirus Disease 2019 pandemic using an SEIRS model with saturated incidence and treatment rates. We derive the basic reproduction number R_0 and study the local stability of the disease-free and endemic states. Since the condition R_0<1 for our model does not determine if the disease will die out, we study the backward bifurcation and Hopf bifurcation to understand the dynamics of the disease at the occurrence of a second wave and the kind of treatment measures needed to curtail it. We present some numerical simulations considering the symptomatic and asymptomatic infections and make a comparison with the reported COVID-19 data for Nigeria. Our results show that the limited availability of medical resources favours the emergence of complex dynamics that complicates the control of the outbreak.



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Published
2021-05-21

How to Cite
David A. Oluyori, Angel G. C. Perez, Victor A. Okhuese, Muhammad Akram, “ Dynamics of an SEIRS COVID-19 epidemic model with saturated incidence and saturated treatment response: bifurcation analysis and simulations”, Technical Journal of Daukeyev University, Vol. 1, Issue 1, 2021, pp. 39-65.

Issue
Volume 1, Issue 1 (2021)

Section
Article

Copyright © 2021 David A. Oluyori, Angel G. C. Perez, Victor A. Okhuese, Muhammad Akram

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Copyright © 2021 David A. Oluyori, Angel G. C. Perez, Victor A. Okhuese, Muhammad Akram
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