A fractional differential equation model for the COVID-19 transmission by using the Caputo\u2013Fabrizio derivative

Dumitru Baleanu,Hakimeh Mohammadi,Shahram Rezapour

doi:10.1186/s13662-020-02762-2

Abstract

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.

Highlights

Corona viruses are a large family of viruses that have a distinctive corona or ‘crown’ of sugary-proteins, and because of their appearance, they were called corona viruses in 1960
Detailed investigations found that corona viruses are transmitted between animals and people, for instance, SARS-CoV and MERS-CoV were transmitted from civet cats and dromedary camels to humans, respectively
6 Numerical results we present a numerical simulation for the transmission model of COVID19 (1) by using the homotopy analysis transform method (HATM)

Summary

Introduction

Corona viruses are a large family of viruses that have a distinctive corona or ‘crown’ of sugary-proteins, and because of their appearance, they were called corona viruses in 1960. We investigate this model by using the Caputo–Fabrizio fractional derivative. Let F be a function such that its Caputo–Fabrizio fractional derivation exists.

Results

Conclusion