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Mathematical Epidemiology Model Analysis on the Dynamics of COVID-19 Pandemic
American Journal of Applied Mathematics
Volume 8, Issue 5, October 2020, Pages: 247-256
Received: Jun. 2, 2020; Accepted: Jun. 28, 2020; Published: Sep. 8, 2020
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Authors
Abayneh Fentie Bezabih, Department of Mathematics, Wollega University, Nekemte, Ethiopia
Geremew Kenassa Edessa, Department of Mathematics, Wollega University, Nekemte, Ethiopia
Purnachandra Rao Koya, Department of Mathematics, Wollega University, Nekemte, Ethiopia
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Abstract
In the present work, Susceptible-Exposed-Infected-Recovered-Susceptible (SEIRS) mathematical model for COVID-19 Pandemic is formulated and analyzed. The positivity, boundedness, and existence of the solutions of the model are proved. The Disease-free equilibrium point and endemic equilibrium points are identified. Local Stability of disease-free Equilibrium point is checked with the help of Next generation matrix. Global stability of endemic equilibrium point is proved using the Concept of Liapunove function. The basic reproduction number for Novel Corona virus pandemic is computed as R0 = (αβΛ) ⁄ [(δ + μ) (β + δ + μ) (γ + δ + μ)] which depend on six different parameters. It is observed that if basic reproduction number is less than one, then number of cases decrease over time and eventually the disease dies out, and if the basic reproduction number is equals to one, then number of cases are stable. On the other hand, if the basic reproduction number is greater than one, then the number of cases increase over time gets worth. Sensitivity analysis of the basic reproduction number is done with respect to each parameter. It is observed that only some parameters Λ, α, β have high impact on the basic reproduction number. Consequently, with real data on the parameter it is helpful to predict the disease persistence or decline in the present situation. Lastly, numerical simulations are given using DEDiscover software to illustrate analytical results.
Keywords
COVID-19 Pandemic, Stability Analysis, Next Generation Matrix, Basic Reproduction Number, Simulation
To cite this article
Abayneh Fentie Bezabih, Geremew Kenassa Edessa, Purnachandra Rao Koya, Mathematical Epidemiology Model Analysis on the Dynamics of COVID-19 Pandemic, American Journal of Applied Mathematics. Vol. 8, No. 5, 2020, pp. 247-256. doi: 10.11648/j.ajam.20200805.12
Copyright
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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