American Journal of Mathematical and Computer Modelling

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An SEIRD Epidemic Model for Predicting the Spread of COVID-19 over a Period of One Year: A Case of the United States

Received: 26 June 2020    Accepted: 16 July 2020    Published: 28 July 2020
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Abstract

COVID-19 is currently a perilous disease that has an incubation period of between 4 and 6 days. The United States Disease Control and Prevention Centers posited that in certain cases, coronaviruses are zoonotic, which means that they have been responsible for moving from animals to humans. The outbreak of the new coronavirus (COVID-19) disease has had an enormous impact globally. The World Health Organization (WHO) has put in place various safety measures that will help alleviate the spread of the epidemic. This paper presents an SEIRD epidemic model with government policy to predict the spread of COVID-19. Through mathematical analysis, the essence of the model is investigated. The basic reproductive number of the envisaged model is computed and decides whether or not the disease is present in the population. Disease-free and symptomatic equilibria are studied for their existence and stability via the Lyapunov function. It is established from our numerical simulations that the introduction of government policy helps to alleviate the spread of the disease, where the basic reproductive number takes part in sustaining their stability. In the prediction of infected and death cases that were very similar to real-life data, it was established that the model was effective.

DOI 10.11648/j.ajmcm.20200503.12
Published in American Journal of Mathematical and Computer Modelling (Volume 5, Issue 3, September 2020)
Page(s) 70-76
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, SEIRD, Basic Reproduction Number, Disease-free Equilibrium, Routh-Herwitz Criterion, Global Stability, Lyapunov Function, LaSalle’s Invariance Principle

References
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[2] M. M. Ojo, and F. O. Akinpelu, “Lyapunov Functions and Global Properties of SEIR Epidemic Model,” International journal of Chemistry, Mathematics and Physics, vol 1 (1), 2017.
[3] C. Wang, P. W. Horby, F. G. Hayden, and G. F. Gao, “A novel coronavirus outbreak of global health concern”, The Lancet, vol 395 (10223), pp. 470-473, 2020.
[4] R. M. May, and R. M. Anderson, “Population biology of infectious diseases: Part II”, Nature, vol 280 (5722), pp. 455-461, 1979.
[5] B. Ivorra, B. Martínez-López, J. M. Sánchez-Vizcaíno, and Á. M. Ramos, “Mathematical formulation and validation of the Be-FAST model for Classical Swine Fever Virus spread between and within farms”, Annals of operations research, vol 219 (1), pp. 25-47, 2014.
[6] B. Martínez-López, B. Ivorra, Á. M. Ramos, and J. M. Sánchez-Vizcaíno, “A novel spatial and stochastic model to evaluate the within-and between-farm transmission of classical swine fever virus. I. General concepts and description of the model”, Veterinary microbiology, vol 147 (3-4), pp 300-309, 2011.
[7] H. R. Thieme, Mathematics in population biology, vol. 12, Princeton University Press, 2018.
[8] F. Brauer, and C. Castillo-Chavez, Mathematical models in population biology and epidemiology, vol. 2, New York: Springer, 2012.
[9] D. Yan, and H. Cao, “The global dynamics for an age-structured tuberculosis transmission model with the exponential progression rate”, Applied Mathematical Modelling, vol 75, pp. 769-786, 2019.
[10] K. Roosa, Y. Lee, R. Luo, A. Kirpich, R. Rothenberg, J. M. Hyman,... and G. Chowell, “Real-time forecasts of the COVID-19 epidemic in China from February 5th to February 24th, 2020”, Infectious Disease Modelling, vol 5, pp. 256-263, 2020.
[11] A. J. Kucharski, T. W. Russell, C Diamond, Y. Liu, J. Edmunds, S. Funk,... and N. Davies, “Early dynamics of transmission and control of COVID-19: a mathematical modelling study”, The lancet infectious diseases, 2020.
[12] S. A. Al-Sheikh, “Modeling and analysis of an SEIR epidemic model with a limited resource for treatment”, Global Journal of Science Frontier Research Mathematics and Decision Sciences, vol 12 (14), pp. 56-66, 2012.
[13] C. Fraser, C. A. Donnelly, S. Cauchemez, W. P. Hanage, M. D. Van Kerkhove, T. D. Hollingsworth,... and T. Jombart, “Pandemic potential of a strain of influenza A (H1N1)”, Early findings science, vol 324 (5934), 1557-1561, 2009.
[14] G. N. Milligan, and A. D. Barrett, Vaccinology: An Essential Guide, Wiley Blackwell, February, 2015.
[15] M. Martcheva, An introduction to mathematical epidemiology, vol. 61. New York: Springer, 2015.
[16] Worldometers, COVID-19 Coronavirus Pandemic. Dover, Delaware, U.S.A, June, 2020. http://www.worldometers.info/c-oronavirus.
Author Information
  • School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China

  • School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China

  • School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu, China

  • School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China

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    Joseph Roger Arhin, Francis Sam, Kenneth Coker, Ernest Owusu Ansah. (2020). An SEIRD Epidemic Model for Predicting the Spread of COVID-19 over a Period of One Year: A Case of the United States. American Journal of Mathematical and Computer Modelling, 5(3), 70-76. https://doi.org/10.11648/j.ajmcm.20200503.12

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    ACS Style

    Joseph Roger Arhin; Francis Sam; Kenneth Coker; Ernest Owusu Ansah. An SEIRD Epidemic Model for Predicting the Spread of COVID-19 over a Period of One Year: A Case of the United States. Am. J. Math. Comput. Model. 2020, 5(3), 70-76. doi: 10.11648/j.ajmcm.20200503.12

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    AMA Style

    Joseph Roger Arhin, Francis Sam, Kenneth Coker, Ernest Owusu Ansah. An SEIRD Epidemic Model for Predicting the Spread of COVID-19 over a Period of One Year: A Case of the United States. Am J Math Comput Model. 2020;5(3):70-76. doi: 10.11648/j.ajmcm.20200503.12

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  • @article{10.11648/j.ajmcm.20200503.12,
      author = {Joseph Roger Arhin and Francis Sam and Kenneth Coker and Ernest Owusu Ansah},
      title = {An SEIRD Epidemic Model for Predicting the Spread of COVID-19 over a Period of One Year: A Case of the United States},
      journal = {American Journal of Mathematical and Computer Modelling},
      volume = {5},
      number = {3},
      pages = {70-76},
      doi = {10.11648/j.ajmcm.20200503.12},
      url = {https://doi.org/10.11648/j.ajmcm.20200503.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajmcm.20200503.12},
      abstract = {COVID-19 is currently a perilous disease that has an incubation period of between 4 and 6 days. The United States Disease Control and Prevention Centers posited that in certain cases, coronaviruses are zoonotic, which means that they have been responsible for moving from animals to humans. The outbreak of the new coronavirus (COVID-19) disease has had an enormous impact globally. The World Health Organization (WHO) has put in place various safety measures that will help alleviate the spread of the epidemic. This paper presents an SEIRD epidemic model with government policy to predict the spread of COVID-19. Through mathematical analysis, the essence of the model is investigated. The basic reproductive number of the envisaged model is computed and decides whether or not the disease is present in the population. Disease-free and symptomatic equilibria are studied for their existence and stability via the Lyapunov function. It is established from our numerical simulations that the introduction of government policy helps to alleviate the spread of the disease, where the basic reproductive number takes part in sustaining their stability. In the prediction of infected and death cases that were very similar to real-life data, it was established that the model was effective.},
     year = {2020}
    }
    

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    AB  - COVID-19 is currently a perilous disease that has an incubation period of between 4 and 6 days. The United States Disease Control and Prevention Centers posited that in certain cases, coronaviruses are zoonotic, which means that they have been responsible for moving from animals to humans. The outbreak of the new coronavirus (COVID-19) disease has had an enormous impact globally. The World Health Organization (WHO) has put in place various safety measures that will help alleviate the spread of the epidemic. This paper presents an SEIRD epidemic model with government policy to predict the spread of COVID-19. Through mathematical analysis, the essence of the model is investigated. The basic reproductive number of the envisaged model is computed and decides whether or not the disease is present in the population. Disease-free and symptomatic equilibria are studied for their existence and stability via the Lyapunov function. It is established from our numerical simulations that the introduction of government policy helps to alleviate the spread of the disease, where the basic reproductive number takes part in sustaining their stability. In the prediction of infected and death cases that were very similar to real-life data, it was established that the model was effective.
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