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), 2020. Published by Science Publishing Group

Keywords

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

References

[1]	Tweeten L., Barone E. and Wolfson E. “A Timeline of How the Wuhan Coronavirus Has Spread—And How the World Has Reacted”. Time, 30 January 2020. Retrieved 08 February 2020 from https://time.com/5774366/how-coronavirus-spread-china.
[2]	World Health Organization. 2020a. “Novel Coronavirus (2019-nCoV) Situation Report – 10”. World Health Organization, 30 January 2020. Retrieved 08 February 2020 from https://www.who.int/docs/defaultsource/coronaviruse/situation-reports/20200130-sitrep10-ncov.pdf?sfvrsn=d0-b2e480_2.
[3]	European Centre for Disease Prevention and Control. “Disease background of 2019nCoV”. European Centre for Disease Prevention and Control. Retrieved 08 February 2020 from https://www.ecdc.europa.eu/en/2019-ncov-background-disease.2020.
[4]	Cui, J. et al. Origin and evolution of pathogenic coronaviruses. Nat. Rev. Microbiol. 17, 181–192 2019.
[5]	Su, S. et al. Epidemiology, genetic recombination, and pathogenesis of coronaviruses. Trends Microbiol. 24, 490–502 (2016).
[6]	Xia S, Liu Q, Wang Q, Sun ZW, Su S, Du LY, et al. Middle East respiratory syndrome coronavirus (MERS-CoV) entry inhibitors targeting spike protein. Virus research. 2014; 194: 200–210. doi: 10.1016/j.virusres.2014.10.007PMID:2545106.
[7]	Memish Z A, Al-Tawfiq J A, Alhakeem R F, Assiri A, Alharby K D, Almahallawi M S, et al. Middle East respiratory syndrome coronavirus (MERS-CoV): A cluster analysis with implications for global management of suspected cases. Travel medicine and infectious disease. 2015; 13 (4): 311–314. doi: 10.1016/j.tmaid.2015.06.012 PMID: 26211569.
[8]	Zhang RH. MERS-CoV: current research progress and prospect. Journal of Applied Virology. 2015; 4 (2): 30–36.
[9]	Ferguson N M, Van Kerkhove M D. Identification of MERS-CoV in dromedary camels. The Lancet infectious diseases. 2014; 14 (2): 93–94. doi: 10.1016/S1473-3099(13)70691-1 PMID: 24355867.
[10]	Chowell G, Blumberg S, Simonsen L, Miller M A, Viboud C. Synthesizing data and models for the spread of MERS-CoV, 2013: Key role of index cases and hospital transmission. Epidemics. 2014; 9: 40–51. doi: 10.1016/j.epidem.2014.09.011 PMID: 25480133.
[11]	Khan A, Farooqui A, Guan Y, Kelvin D J. Lessons to learn from MERS-CoV outbreak in South Korea. The Journal of Infection in Developing Countries. 2015; 9 (06): 543–546. doi: 10.3855/jidc.7278 PMID:26142661.
[12]	Cauchemez S, Van Kerkhove MD, Riley S, Donnelly CA, Fraser C, Ferguso NM, et al. Transmission scenarios for Middle East Respiratory Syndrome Coronavirus (MERS-CoV) and how to tell them apart. Euro surveillance: bulletin Europeen sur les maladies transmissibles, European communicable disease bulletin. 2013; 18 (24).
[13]	Lee SS, Wong NS. Probable transmission chains of Middle East respiratory syndrome coronavirus and the multiple generations of secondary infection in South Korea. International Journal of Infectious Diseases. 2015; 38: 65–67. doi: 10.1016/j.ijid.2015.07.014 PMID: 26216766.
[14]	Sharif-Yakan A, Kanj S S. Emergence of MERS-CoV in the Middle East: origins, transmission, treatment, and perspectives. PLoS pathogens. 2014; 10 (12): e1004457. doi: 10.1371/journal.ppat.1004457 PMID: 25474536.
[15]	Coronaviridae Study Group of the International Committee on Taxonomy of Viruses. The species Severe Acute Respiratory Syndrome-related coronavirus: classifying 2019-nCoV and naming it SARS-CoV-2. Nat Microbiol. 2020 Mar 2. [Epubahead of print].
[16]	World Health Organization (WHO). Responding to community spread of COVID-19 interim guidance. 2020 Mar 7. Accessed 2020 Mar 24. https://www.who.int/docs/default source/coronaviruse/20200307-responding-to-COVID-19- communitytransmission-final.pdf.
[17]	Assiri, Abdullah; et al. “Epidemiological, demographic, and clinical characteristics of 47 cases of Middle East respiratory syndrome coronavirus disease from Saudi Arabia: a descriptive study”. The Lancet Infectious Diseases. 13: 752–761. doi: 10.1016/S1473-3099(13)70204-4. 9 September 2013.
[18]	Assiri, A.; et al. “Hospital Outbreak of Middle East Respiratory Syndrome Coronavirus”. NEJM. 369: 407–416. doi: 10.1056/NEJMoa1306742. Retrieved 20 May 2014.
[19]	“Interim Guidance - Clinical management of severe acute respiratory infections when novel coronavirus is suspected: What to do and what not to do” (PDF). WHO. 2 November 2013. Retrieved 21 May 2014.
[20]	The Health Protection Agency (HPA) UK Novel Coronavirus Investigation team “State of Knowledge and Data Gaps of Middle East Respiratory Syndrome Coronavirus (MERS-CoV) in Humans”. Eurosurveillance. 14 March 2013.
[21]	WHO Coronavirus disease (COVID-19) technical guidance: Laboratory testing for 2019-nCoV in humans. https://www. who.int/emergencies/diseases/novel-coronavirus 2019/technic al-guidance/laboratory-guidance.
[22]	”See Also”. ProMED-mail. 20 September 2012. Retrieved 31 May 2013.
[23]	Zhi-Qiang Xia, Juan Zhang, Ya-Kui Xue, Gui-Quan Sun, Zhen Jin Modeling the Transmission of Middle East Respirator Syndrome Corona Virus in the Republic of Korea. Article in PLoS ONE DOI: 10.1371/journal.pone.0144778.2015.
[24]	Diekmann, O. and J. A. P. Heesterbeek. Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Integration. Wiley: New York, NY. 2000.
[25]	Heesterbeek H. et al. “Modeling infectious disease dynamics in the complex landscape of global health”. Science, 347: aaa4339. 2015.
[26]	Siettos C. I. and Russo L. “Mathematical modeling of infectious disease dynamics”. Virulence, 4: 295-306.; 2013.
[27]	Tuite A. R. and Fisman D. N. “Reporting, Epidemic Growth, and Reproduction Numbers for the 2019 Novel Coronavirus (2019-nCoV) Epidemic”. Annals of Internal Medicine, 10.7326/M20-0358.; 2020.
[28]	Lim P L. Middle East respiratory syndrome (MERS) in Asia: lessons gleaned from the South Korean outbreak. Transactions of the Royal Society of Tropical Medicine and Hygiene. 2015; 109 (9): 541–542. doi: 10.1093/trstmh/trv064 PMID: 26286944.
[29]	Demsis Dejene, Purnachandra Rao Koya. Population Dynamics of Dogs Subjected To Rabies Disease. IOSR Journal of Mathematics IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 12, Issue 3 Ver. IV (May. - Jun. 2016), PP 110-120 www.iosrjournals.org DOI: 10.9790/5728-120304110120.
[30]	LaSalle, J. P. “The Stability of Dynamical Systems”. Regional Conference Series in Applied Mathematics, SIAM: Philadelphia, PA. 1976.
[31]	The government of Wuhan homepage. Available from: http://english.wh.gov.cn/.
[32]	J. A. Spencer, D. P. Shutt, S. K. Moser, H. Clegg, H. J. Wearing, H. Mukundan, et al., Epidemiological parameter review and comparative dynamics of influenza, respiratory syncytial virus, rhinovirus, human coronvirus, and adenovirus, medRxiv, 2020.

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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