Mathematical analysis of SIRD model of COVID-19 with Caputo fractional derivative based on real data

Kottakkaran Sooppy Nisar; Shabir Ahmad; Aman Ullah; Kamal Shah; Hussam Alrabaiah; Muhammad Arfan

doi:10.1016/j.rinp.2020.103772

Mathematical analysis of SIRD model of COVID-19 with Caputo fractional derivative based on real data

Kottakkaran Sooppy Nisar
, Shabir Ahmad
, Aman Ullah
, Kamal Shah
, Hussam Alrabaiah
, Muhammad Arfan

Mathematics

University of Malakand
Tafila Technical University
Prince Sattam Bin Abdulaziz University

Research output: Contribution to journal › Article › peer-review

103 Scopus citations

Abstract

We discuss a fractional-order SIRD mathematical model of the COVID-19 disease in the sense of Caputo in this article. We compute the basic reproduction number through the next-generation matrix. We derive the stability results based on the basic reproduction number. We prove the results of the solution existence and uniqueness via fixed point theory. We utilize the fractional Adams–Bashforth method for obtaining the approximate solution of the proposed model. We illustrate the obtained numerical results in plots to show the COVID-19 transmission dynamics. Further, we compare our results with some reported real data against confirmed infected and death cases per day for the initial 67 days in Wuhan city.

Original language	English
Article number	103772
Journal	Results in Physics
Volume	21
DOIs	https://doi.org/10.1016/j.rinp.2020.103772
State	Published - Feb 2021

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Keywords

Approximate solution
Fixed point theory
Fractional derivative
Numerical simulations
SIRD mathematical model

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10.1016/j.rinp.2020.103772

Cite this

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title = "Mathematical analysis of SIRD model of COVID-19 with Caputo fractional derivative based on real data",

abstract = "We discuss a fractional-order SIRD mathematical model of the COVID-19 disease in the sense of Caputo in this article. We compute the basic reproduction number through the next-generation matrix. We derive the stability results based on the basic reproduction number. We prove the results of the solution existence and uniqueness via fixed point theory. We utilize the fractional Adams–Bashforth method for obtaining the approximate solution of the proposed model. We illustrate the obtained numerical results in plots to show the COVID-19 transmission dynamics. Further, we compare our results with some reported real data against confirmed infected and death cases per day for the initial 67 days in Wuhan city.",

keywords = "Approximate solution, Fixed point theory, Fractional derivative, Numerical simulations, SIRD mathematical model",

author = "Nisar, \{Kottakkaran Sooppy\} and Shabir Ahmad and Aman Ullah and Kamal Shah and Hussam Alrabaiah and Muhammad Arfan",

note = "Publisher Copyright: {\textcopyright} 2020 The Author(s)",

year = "2021",

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doi = "10.1016/j.rinp.2020.103772",

language = "English",

volume = "21",

journal = "Results in Physics",

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T1 - Mathematical analysis of SIRD model of COVID-19 with Caputo fractional derivative based on real data

AU - Nisar, Kottakkaran Sooppy

AU - Ahmad, Shabir

AU - Ullah, Aman

AU - Shah, Kamal

AU - Alrabaiah, Hussam

AU - Arfan, Muhammad

PY - 2021/2

Y1 - 2021/2

N2 - We discuss a fractional-order SIRD mathematical model of the COVID-19 disease in the sense of Caputo in this article. We compute the basic reproduction number through the next-generation matrix. We derive the stability results based on the basic reproduction number. We prove the results of the solution existence and uniqueness via fixed point theory. We utilize the fractional Adams–Bashforth method for obtaining the approximate solution of the proposed model. We illustrate the obtained numerical results in plots to show the COVID-19 transmission dynamics. Further, we compare our results with some reported real data against confirmed infected and death cases per day for the initial 67 days in Wuhan city.

AB - We discuss a fractional-order SIRD mathematical model of the COVID-19 disease in the sense of Caputo in this article. We compute the basic reproduction number through the next-generation matrix. We derive the stability results based on the basic reproduction number. We prove the results of the solution existence and uniqueness via fixed point theory. We utilize the fractional Adams–Bashforth method for obtaining the approximate solution of the proposed model. We illustrate the obtained numerical results in plots to show the COVID-19 transmission dynamics. Further, we compare our results with some reported real data against confirmed infected and death cases per day for the initial 67 days in Wuhan city.

KW - Approximate solution

KW - Fixed point theory

KW - Fractional derivative

KW - Numerical simulations

KW - SIRD mathematical model

UR - https://www.scopus.com/pages/publications/85098947196

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DO - 10.1016/j.rinp.2020.103772

M3 - Article

AN - SCOPUS:85098947196

SN - 2211-3797

VL - 21

JO - Results in Physics

JF - Results in Physics

M1 - 103772

ER -

Mathematical analysis of SIRD model of COVID-19 with Caputo fractional derivative based on real data

Abstract

UN SDGs

Keywords

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