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.
| Published in | American Journal of Applied Mathematics (Volume 8, Issue 5) |
| DOI | 10.11648/j.ajam.20200805.12 |
| Page(s) | 247-256 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
COVID-19 Pandemic, Stability Analysis, Next Generation Matrix, Basic Reproduction Number, Simulation
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APA Style
Abayneh Fentie Bezabih, Geremew Kenassa Edessa, Purnachandra Rao Koya. (2020). Mathematical Epidemiology Model Analysis on the Dynamics of COVID-19 Pandemic. American Journal of Applied Mathematics, 8(5), 247-256. https://doi.org/10.11648/j.ajam.20200805.12
ACS Style
Abayneh Fentie Bezabih; Geremew Kenassa Edessa; Purnachandra Rao Koya. Mathematical Epidemiology Model Analysis on the Dynamics of COVID-19 Pandemic. Am. J. Appl. Math. 2020, 8(5), 247-256. doi: 10.11648/j.ajam.20200805.12
AMA Style
Abayneh Fentie Bezabih, Geremew Kenassa Edessa, Purnachandra Rao Koya. Mathematical Epidemiology Model Analysis on the Dynamics of COVID-19 Pandemic. Am J Appl Math. 2020;8(5):247-256. doi: 10.11648/j.ajam.20200805.12
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Download@article{10.11648/j.ajam.20200805.12,
author = {Abayneh Fentie Bezabih and Geremew Kenassa Edessa and Purnachandra Rao Koya},
title = {Mathematical Epidemiology Model Analysis on the Dynamics of COVID-19 Pandemic},
journal = {American Journal of Applied Mathematics},
volume = {8},
number = {5},
pages = {247-256},
doi = {10.11648/j.ajam.20200805.12},
url = {https://doi.org/10.11648/j.ajam.20200805.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20200805.12},
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.},
year = {2020}
}
TY - JOUR T1 - Mathematical Epidemiology Model Analysis on the Dynamics of COVID-19 Pandemic AU - Abayneh Fentie Bezabih AU - Geremew Kenassa Edessa AU - Purnachandra Rao Koya Y1 - 2020/09/08 PY - 2020 N1 - https://doi.org/10.11648/j.ajam.20200805.12 DO - 10.11648/j.ajam.20200805.12 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 247 EP - 256 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20200805.12 AB - 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. VL - 8 IS - 5 ER -
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