Modeling the Transmission and Dynamics of COVID-19 Using Self-protection and Isolation as Control Measures

Demsis Dejene; Tesfaye Worku; Purnachandra Rao Koya

doi:doi:10.11648/j.mma.20200503.18

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Modeling the Transmission and Dynamics of COVID-19 Using Self-protection and Isolation as Control Measures

Demsis Dejene, Tesfaye Worku, Purnachandra Rao Koya

Published in Mathematical Modelling and Applications (Volume 5, Issue 3)

Received: 8 June 2020 Accepted: 28 June 2020 Published: 16 September 2020

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Abstract

In this paper, a deterministic five compartmental mathematical model is developed and conducted simulations to study the dynamics of COVID-19 with the inclusion of self-protection and isolation as control measures. The model is shown mathematically and biologically valid by verifying that the solutions are both positive and bounded. Using next generation matrix method, the reproduction number is formulated. The disease free equilibrium point is found and shown that it is conditionally locally and globally asymptotically stable. Further, following Lyapunov function method Endemic equilibrium point is found and shown that it is conditionally globally asymptotically stable. Numerical simulation study is conducted by assigning reasonable values to the parameters. It is concluded that the spread of the disease can be brought under control if the control measures like Self-protection including social distancing and Isolation are implemented affectively. The results and the discussion are presented in the body of the paper lucidly.

Published in	Mathematical Modelling and Applications (Volume 5, Issue 3)
DOI	10.11648/j.mma.20200503.18
Page(s)	191-201
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

Keywords

COVID-19, Self-Protection, Isolation, Equilibria, Stability, Numerical Simulations

References

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APA Style

Demsis Dejene, Tesfaye Worku, Purnachandra Rao Koya. (2020). Modeling the Transmission and Dynamics of COVID-19 Using Self-protection and Isolation as Control Measures. Mathematical Modelling and Applications, 5(3), 191-201. https://doi.org/10.11648/j.mma.20200503.18

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ACS Style

Demsis Dejene; Tesfaye Worku; Purnachandra Rao Koya. Modeling the Transmission and Dynamics of COVID-19 Using Self-protection and Isolation as Control Measures. Math. Model. Appl. 2020, 5(3), 191-201. doi: 10.11648/j.mma.20200503.18

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AMA Style

Demsis Dejene, Tesfaye Worku, Purnachandra Rao Koya. Modeling the Transmission and Dynamics of COVID-19 Using Self-protection and Isolation as Control Measures. Math Model Appl. 2020;5(3):191-201. doi: 10.11648/j.mma.20200503.18

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@article{10.11648/j.mma.20200503.18,
  author = {Demsis Dejene and Tesfaye Worku and Purnachandra Rao Koya},
  title = {Modeling the Transmission and Dynamics of COVID-19 Using Self-protection and Isolation as Control Measures},
  journal = {Mathematical Modelling and Applications},
  volume = {5},
  number = {3},
  pages = {191-201},
  doi = {10.11648/j.mma.20200503.18},
  url = {https://doi.org/10.11648/j.mma.20200503.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20200503.18},
  abstract = {In this paper, a deterministic five compartmental mathematical model is developed and conducted simulations to study the dynamics of COVID-19 with the inclusion of self-protection and isolation as control measures. The model is shown mathematically and biologically valid by verifying that the solutions are both positive and bounded. Using next generation matrix method, the reproduction number is formulated. The disease free equilibrium point is found and shown that it is conditionally locally and globally asymptotically stable. Further, following Lyapunov function method Endemic equilibrium point is found and shown that it is conditionally globally asymptotically stable. Numerical simulation study is conducted by assigning reasonable values to the parameters. It is concluded that the spread of the disease can be brought under control if the control measures like Self-protection including social distancing and Isolation are implemented affectively. The results and the discussion are presented in the body of the paper lucidly.},
 year = {2020}
}

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TY  - JOUR
T1  - Modeling the Transmission and Dynamics of COVID-19 Using Self-protection and Isolation as Control Measures
AU  - Demsis Dejene
AU  - Tesfaye Worku
AU  - Purnachandra Rao Koya
Y1  - 2020/09/16
PY  - 2020
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DO  - 10.11648/j.mma.20200503.18
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 191
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PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20200503.18
AB  - In this paper, a deterministic five compartmental mathematical model is developed and conducted simulations to study the dynamics of COVID-19 with the inclusion of self-protection and isolation as control measures. The model is shown mathematically and biologically valid by verifying that the solutions are both positive and bounded. Using next generation matrix method, the reproduction number is formulated. The disease free equilibrium point is found and shown that it is conditionally locally and globally asymptotically stable. Further, following Lyapunov function method Endemic equilibrium point is found and shown that it is conditionally globally asymptotically stable. Numerical simulation study is conducted by assigning reasonable values to the parameters. It is concluded that the spread of the disease can be brought under control if the control measures like Self-protection including social distancing and Isolation are implemented affectively. The results and the discussion are presented in the body of the paper lucidly.
VL  - 5
IS  - 3
ER  -

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Author Information

Demsis Dejene

Department of Mathematics, Wollega University, Nekemte, Ethiopia
Tesfaye Worku

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

Department of Mathematics, Wollega University, Nekemte, Ethiopia

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Plain Text BibTeX RIS

APA Style

Demsis Dejene, Tesfaye Worku, Purnachandra Rao Koya. (2020). Modeling the Transmission and Dynamics of COVID-19 Using Self-protection and Isolation as Control Measures. Mathematical Modelling and Applications, 5(3), 191-201. https://doi.org/10.11648/j.mma.20200503.18

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ACS Style

Demsis Dejene; Tesfaye Worku; Purnachandra Rao Koya. Modeling the Transmission and Dynamics of COVID-19 Using Self-protection and Isolation as Control Measures. Math. Model. Appl. 2020, 5(3), 191-201. doi: 10.11648/j.mma.20200503.18

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AMA Style

Demsis Dejene, Tesfaye Worku, Purnachandra Rao Koya. Modeling the Transmission and Dynamics of COVID-19 Using Self-protection and Isolation as Control Measures. Math Model Appl. 2020;5(3):191-201. doi: 10.11648/j.mma.20200503.18

Copy | Download

@article{10.11648/j.mma.20200503.18,
  author = {Demsis Dejene and Tesfaye Worku and Purnachandra Rao Koya},
  title = {Modeling the Transmission and Dynamics of COVID-19 Using Self-protection and Isolation as Control Measures},
  journal = {Mathematical Modelling and Applications},
  volume = {5},
  number = {3},
  pages = {191-201},
  doi = {10.11648/j.mma.20200503.18},
  url = {https://doi.org/10.11648/j.mma.20200503.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20200503.18},
  abstract = {In this paper, a deterministic five compartmental mathematical model is developed and conducted simulations to study the dynamics of COVID-19 with the inclusion of self-protection and isolation as control measures. The model is shown mathematically and biologically valid by verifying that the solutions are both positive and bounded. Using next generation matrix method, the reproduction number is formulated. The disease free equilibrium point is found and shown that it is conditionally locally and globally asymptotically stable. Further, following Lyapunov function method Endemic equilibrium point is found and shown that it is conditionally globally asymptotically stable. Numerical simulation study is conducted by assigning reasonable values to the parameters. It is concluded that the spread of the disease can be brought under control if the control measures like Self-protection including social distancing and Isolation are implemented affectively. The results and the discussion are presented in the body of the paper lucidly.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Modeling the Transmission and Dynamics of COVID-19 Using Self-protection and Isolation as Control Measures
AU  - Demsis Dejene
AU  - Tesfaye Worku
AU  - Purnachandra Rao Koya
Y1  - 2020/09/16
PY  - 2020
N1  - https://doi.org/10.11648/j.mma.20200503.18
DO  - 10.11648/j.mma.20200503.18
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 191
EP  - 201
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20200503.18
AB  - In this paper, a deterministic five compartmental mathematical model is developed and conducted simulations to study the dynamics of COVID-19 with the inclusion of self-protection and isolation as control measures. The model is shown mathematically and biologically valid by verifying that the solutions are both positive and bounded. Using next generation matrix method, the reproduction number is formulated. The disease free equilibrium point is found and shown that it is conditionally locally and globally asymptotically stable. Further, following Lyapunov function method Endemic equilibrium point is found and shown that it is conditionally globally asymptotically stable. Numerical simulation study is conducted by assigning reasonable values to the parameters. It is concluded that the spread of the disease can be brought under control if the control measures like Self-protection including social distancing and Isolation are implemented affectively. The results and the discussion are presented in the body of the paper lucidly.
VL  - 5
IS  - 3
ER  -

Copy | Download