Epidemiological Modelling and Analysis of COVID-19 Pandemic with Treatment

Abayneh Fentie Bezabih; Geremew Kenassa Edessa; Koya Purnachandra Rao

doi:doi:10.11648/j.mma.20210601.11

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Epidemiological Modelling and Analysis of COVID-19 Pandemic with Treatment

Abayneh Fentie Bezabih, Geremew Kenassa Edessa, Koya Purnachandra Rao

Published in Mathematical Modelling and Applications (Volume 6, Issue 1)

Received: 10 November 2020 Accepted: 25 November 2020 Published: 12 January 2021

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Abstract

In this paper, Mathematical Model of COVID-19 Pandemic is formulated and discussed. The positivity, boundedness, and existence of the solutions of the model equations are stated and proved. The Disease-free equilibrium point & endemic equilibrium points are identified. Stability Analysis of the model is done with the concept of Next generation matrix. we have investigated that Disease-free equilibrium point (DFEP) of the model is locally asymptotically stable if α≤β+δ+μ & unstable if α>β+δ+μ, The basic reproduction number (threshold value) R₀ is the largest eigen value in spectral radius matrix ρ. Thus, eigen values of spectral radius Matrix ρ are determined from the roots of characteristic polynomial equation, det[ρ-λI]=0, Hence, the basic reproduction number is R₀=α / β. It is shown that if reproduction number is less than one, then COVID-19 cases will be reduced in the community. However, if reproduction number is greater than one, then covid-19 continue to persist in the Community. Lastly, numerical simulations are done with DEDiscover 2.6.4. Software. It is observed that with Constant treatment, increase or decrease contact rate among persons leads great variation on the basic reproduction number which is directly implies that infection rate plays a vital role on decline or persistence of COVID-19 pandemic.

Published in	Mathematical Modelling and Applications (Volume 6, Issue 1)
DOI	10.11648/j.mma.20210601.11
Page(s)	1-9
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), 2021. Published by Science Publishing Group

Keywords

COVID-19, PANDEMIC, Model, Stability, Next Generation Matrix, Reproduction Number, Simulation

References

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[2]	Chayu, Yang and Jin Wang, March 2020. A mathematical model for the novel corona virus epidemic in Wuhan, China. Mathematical biosciences and engineering 17 (3): March (2020) 2708–2724.
[3]	Alexander, Okhuese Victor. mathematical predictions for covid-19 as a global pandemic. Research Gate. march 2020.
[4]	Jyoti Bhola, Vandana Revathi Venkateswaran and Monika Koul. Corona Epidemic in Indian context: Predictive Mathematical Modeling, med Rxiv preprint doi: https://doi.org/10.1101/2020.04.03.20047175.
[5]	Binti Hamzah FA, Lau C, Nazri H, Ligot DV, Lee G, Tan CL, etal. Corona Tracker: World-wideCOVID-19 Outbreak Data Analysis and Prediction. Bull World Health Organ. E-pub: 19 March 2020. doi: http://dx.doi.org/10.2471/BLT.20.255695.
[6]	Website: https://www. who. int› health-topics› corona virus.
[7]	Website: https:/www.who.int›docs›default-source›who-china-joint.
[8]	P. Zhou, X. L. Yang, X. G. Wang, B. Hu, L. Zhang, W. Zhang, et al., Discovery of a novel corona virus associated with the recent pneumonia outbreak in humans and its potential bat origin, bioRxiv, 2020.
[9]	Abayneh Fentie Bezabih, Geremew Kenassa Edessa, Koya Purnachandra Rao "Mathematical Eco-Epidemic Model on Prey-Predator System. IOSR Journal of Mathematics (IOSR-JM), 16 (1), (2020): pp. 22-34.
[10]	Alfred Hugo, Estomih S. Massawe, and Oluwole Daniel Makinde. An Eco-Epidemiological Mathematical Model with Treatment and Disease Infection in both Prey and Predator Population. Journal of Ecology and natural environment Vol. 4 (10), July 2012, pp. 266-273.
[11]	Tadele Tesfa Tegegne, Purnachandra Rao Koya and Temesgen Tibebu Mekonnen. Impact of Heterosexuality & Homosexuality on the transmission and dynamics of HIV/AIDS, IOSR Journal of Mathematics (IOSR-JM), Volume 12, Issue 6 Ver, 2016, PP 38-49.
[12]	P. van den Driessche and James Watmough. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences 180 (2002) 29–48.
[13]	Abayneh Fentie Bezabih, Geremew Kenassa Edessa, Purnachandra Rao Koya. Mathematical Eco-Epidemiological Model on Prey-Predator System. Mathematical Modeling and Applications. Vol. 5, No. 3, 2020, pp. 183-190. doi: http://10.11648/j.mma.20200503.17.
[14]	Selam Nigusie Mitku, Purnachandra Rao Koya. Mathematical Modeling and Simulation Study for the Control and Transmission Dynamics of Measles. American Journal of Applied Mathematics. Vol. 5, No. 4, 2017, pp. 99-107. doi: http://10.11648/j.ajam.20170504.
[15]	Sachin Kumar and Harsha Kharbanda. Stability Analysis of Prey-Predator Model with Infection, Migration and Vaccination In Prey, arXiv: 1709. 10319vl [math. DS], 29 Sep 2017.
[16]	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: http://10.11648/j.ajam.20200805.12.

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APA Style

Abayneh Fentie Bezabih, Geremew Kenassa Edessa, Koya Purnachandra Rao. (2021). Epidemiological Modelling and Analysis of COVID-19 Pandemic with Treatment. Mathematical Modelling and Applications, 6(1), 1-9. https://doi.org/10.11648/j.mma.20210601.11

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ACS Style

Abayneh Fentie Bezabih; Geremew Kenassa Edessa; Koya Purnachandra Rao. Epidemiological Modelling and Analysis of COVID-19 Pandemic with Treatment. Math. Model. Appl. 2021, 6(1), 1-9. doi: 10.11648/j.mma.20210601.11

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AMA Style

Abayneh Fentie Bezabih, Geremew Kenassa Edessa, Koya Purnachandra Rao. Epidemiological Modelling and Analysis of COVID-19 Pandemic with Treatment. Math Model Appl. 2021;6(1):1-9. doi: 10.11648/j.mma.20210601.11

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@article{10.11648/j.mma.20210601.11,
  author = {Abayneh Fentie Bezabih and Geremew Kenassa Edessa and Koya Purnachandra Rao},
  title = {Epidemiological Modelling and Analysis of COVID-19 Pandemic with Treatment},
  journal = {Mathematical Modelling and Applications},
  volume = {6},
  number = {1},
  pages = {1-9},
  doi = {10.11648/j.mma.20210601.11},
  url = {https://doi.org/10.11648/j.mma.20210601.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20210601.11},
  abstract = {In this paper, Mathematical Model of COVID-19 Pandemic is formulated and discussed. The positivity, boundedness, and existence of the solutions of the model equations are stated and proved. The Disease-free equilibrium point & endemic equilibrium points are identified. Stability Analysis of the model is done with the concept of Next generation matrix. we have investigated that Disease-free equilibrium point (DFEP) of the model is locally asymptotically stable if α≤β+δ+μ & unstable if α>β+δ+μ, The basic reproduction number (threshold value) R0 is the largest eigen value in spectral radius matrix ρ. Thus, eigen values of spectral radius Matrix ρ are determined from the roots of characteristic polynomial equation, det[ρ-λI]=0, Hence, the basic reproduction number is R0=α / β. It is shown that if reproduction number is less than one, then COVID-19 cases will be reduced in the community. However, if reproduction number is greater than one, then covid-19 continue to persist in the Community. Lastly, numerical simulations are done with DEDiscover 2.6.4. Software. It is observed that with Constant treatment, increase or decrease contact rate among persons leads great variation on the basic reproduction number which is directly implies that infection rate plays a vital role on decline or persistence of COVID-19 pandemic.},
 year = {2021}
}

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TY - JOUR
T1 - Epidemiological Modelling and Analysis of COVID-19 Pandemic with Treatment
AU - Abayneh Fentie Bezabih
AU - Geremew Kenassa Edessa
AU - Koya Purnachandra Rao
Y1 - 2021/01/12
PY - 2021
N1 - https://doi.org/10.11648/j.mma.20210601.11
DO - 10.11648/j.mma.20210601.11
T2 - Mathematical Modelling and Applications
JF - Mathematical Modelling and Applications
JO - Mathematical Modelling and Applications
SP - 1
EP - 9
PB - Science Publishing Group
SN - 2575-1794
UR - https://doi.org/10.11648/j.mma.20210601.11
AB - In this paper, Mathematical Model of COVID-19 Pandemic is formulated and discussed. The positivity, boundedness, and existence of the solutions of the model equations are stated and proved. The Disease-free equilibrium point & endemic equilibrium points are identified. Stability Analysis of the model is done with the concept of Next generation matrix. we have investigated that Disease-free equilibrium point (DFEP) of the model is locally asymptotically stable if α≤β+δ+μ & unstable if α>β+δ+μ, The basic reproduction number (threshold value) R0 is the largest eigen value in spectral radius matrix ρ. Thus, eigen values of spectral radius Matrix ρ are determined from the roots of characteristic polynomial equation, det[ρ-λI]=0, Hence, the basic reproduction number is R0=α / β. It is shown that if reproduction number is less than one, then COVID-19 cases will be reduced in the community. However, if reproduction number is greater than one, then covid-19 continue to persist in the Community. Lastly, numerical simulations are done with DEDiscover 2.6.4. Software. It is observed that with Constant treatment, increase or decrease contact rate among persons leads great variation on the basic reproduction number which is directly implies that infection rate plays a vital role on decline or persistence of COVID-19 pandemic.
VL - 6
IS - 1
ER -

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Author Information

Abayneh Fentie Bezabih

Department of Mathematics, Wollega University, Nekemte, Ethiopia
Geremew Kenassa Edessa

Department of Mathematics, Wollega University, Nekemte, Ethiopia
Koya Purnachandra Rao

Department of Mathematics, Wollega University, Nekemte, Ethiopia

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APA Style

Abayneh Fentie Bezabih, Geremew Kenassa Edessa, Koya Purnachandra Rao. (2021). Epidemiological Modelling and Analysis of COVID-19 Pandemic with Treatment. Mathematical Modelling and Applications, 6(1), 1-9. https://doi.org/10.11648/j.mma.20210601.11

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ACS Style

Abayneh Fentie Bezabih; Geremew Kenassa Edessa; Koya Purnachandra Rao. Epidemiological Modelling and Analysis of COVID-19 Pandemic with Treatment. Math. Model. Appl. 2021, 6(1), 1-9. doi: 10.11648/j.mma.20210601.11

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AMA Style

Abayneh Fentie Bezabih, Geremew Kenassa Edessa, Koya Purnachandra Rao. Epidemiological Modelling and Analysis of COVID-19 Pandemic with Treatment. Math Model Appl. 2021;6(1):1-9. doi: 10.11648/j.mma.20210601.11

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@article{10.11648/j.mma.20210601.11,
  author = {Abayneh Fentie Bezabih and Geremew Kenassa Edessa and Koya Purnachandra Rao},
  title = {Epidemiological Modelling and Analysis of COVID-19 Pandemic with Treatment},
  journal = {Mathematical Modelling and Applications},
  volume = {6},
  number = {1},
  pages = {1-9},
  doi = {10.11648/j.mma.20210601.11},
  url = {https://doi.org/10.11648/j.mma.20210601.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20210601.11},
  abstract = {In this paper, Mathematical Model of COVID-19 Pandemic is formulated and discussed. The positivity, boundedness, and existence of the solutions of the model equations are stated and proved. The Disease-free equilibrium point & endemic equilibrium points are identified. Stability Analysis of the model is done with the concept of Next generation matrix. we have investigated that Disease-free equilibrium point (DFEP) of the model is locally asymptotically stable if α≤β+δ+μ & unstable if α>β+δ+μ, The basic reproduction number (threshold value) R0 is the largest eigen value in spectral radius matrix ρ. Thus, eigen values of spectral radius Matrix ρ are determined from the roots of characteristic polynomial equation, det[ρ-λI]=0, Hence, the basic reproduction number is R0=α / β. It is shown that if reproduction number is less than one, then COVID-19 cases will be reduced in the community. However, if reproduction number is greater than one, then covid-19 continue to persist in the Community. Lastly, numerical simulations are done with DEDiscover 2.6.4. Software. It is observed that with Constant treatment, increase or decrease contact rate among persons leads great variation on the basic reproduction number which is directly implies that infection rate plays a vital role on decline or persistence of COVID-19 pandemic.},
 year = {2021}
}

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