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Numerical simulation of a Caputo fractional epidemic model for the novel coronavirus with the impact of environmental transmission


[ 1 ] Instytut Analizy Konstrukcji, Wydział Inżynierii Lądowej i Transportu, Politechnika Poznańska | [ P ] employee

Scientific discipline (Law 2.0)

[2.6] Civil engineering and transport

Year of publication


Published in

Alexandria Engineering Journal

Journal year: 2022 | Journal volume: vol. 61 | Journal number: iss. 7

Article type

scientific article

Publication language


  • Caputo fractional derivative
  • Adams–Bashforth method
  • COVID-19
  • Stability

EN The coronavirus infectious disease (COVID-19) is a novel respiratory disease reported in 2019 in China. The infection is very destructive to human lives and caused millions of deaths. Various approaches have been made recently to understand the complex dynamics of COVID-19. The mathematical modeling approach is one of the considerable tools to study the disease spreading pattern. In this article, we develop a fractional order epidemic model for COVID-19 in the sense of Caputo operator. The model is based on the effective contacts among the population and environmental impact to analyze the disease dynamics. The fractional models are comparatively better in understanding the disease outbreak and providing deeper insights into the infectious disease dynamics. We first consider the classical integer model studied in recent literature and then we generalize it by introducing the Caputo fractional derivative. Furthermore, we explore some fundamental mathematical analysis of the fractional model, including the basic reproductive number R0 and equilibria stability utilizing the Routh-Hurwitz and the Lyapunov function approaches. Besides theoretical analysis, we also focused on the numerical solution. To simulate the model, we use the well-known generalized Adams–Bashforth Moulton Scheme. Finally, the influence of some of the model essential parameters on the dynamics of the disease is demonstrated graphically.

Date of online publication


Pages (from - to)

5083 - 5095




License type

CC BY-NC-ND (attribution - noncommercial - no derivatives)

Open Access Mode

open journal

Open Access Text Version

final published version

Date of Open Access to the publication

in press

Points of MNiSW / journal


Impact Factor

3.732 [List 2020]

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