A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative

We present a fractional-order model for the COVID-19 transmission with Caputo–Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We pr...

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Bibliographic Details
Published in:Advances in difference equations 2020-06, Vol.2020 (1), p.299-299, Article 299
Main Authors: Baleanu, Dumitru, Mohammadi, Hakimeh, Rezapour, Shahram
Format: Article
Language:English
Subjects:
Analysis
Caputo–Fabrizio derivative
Computer simulation
Coronaviruses
COVID-19
Difference and Functional Equations
Differential equations
Disease transmission
Fixed point
Functional Analysis
Homotopy analysis method
Iterative methods
Laplace transforms
Mathematical model
Mathematics
Mathematics and Statistics
Numerical simulation
Ordinary Differential Equations
Partial Differential Equations
Viruses
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Summary:We present a fractional-order model for the COVID-19 transmission with Caputo–Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We prove the existence of a unique solution and the stability of the iteration approach by using fixed point theory. We also present numerical results to simulate virus transmission and compare the results with those of the Caputo derivative.
ISSN:1687-1839
1687-1847
1687-1847
DOI:10.1186/s13662-020-02762-2