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      A mathematical model for COVID-19 transmission by using the Caputo fractional derivative

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          Highlights

          • •

            COVID-19 is transmitted from asymptomatic individuals to susceptible individuals.

          • •

            COVID-19 is transmitted from symptomatic individuals to susceptible individuals.

          • •

            Since R0=1.6 is greater than 1, the COVID-19 will spread exponentially.

          • •

            If COVID-19 is not controlled, it is estimated that about 20 million people will become infected in the next three years.

          Abstract

          We present a mathematical model for the transmission of COVID-19 by the Caputo fractional-order derivative. We calculate the equilibrium points and the reproduction number for the model and obtain the region of the feasibility of system. By fixed point theory, we prove the existence of a unique solution. Using the generalized Adams-Bashforth-Moulton method, we solve the system and obtain the approximate solutions. We present a numerical simulation for the transmission of COVID-19 in the world, and in this simulation, the reproduction number is obtained as R 0 = 1 : 610007996 , which shows that the epidemic continues.

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          Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission.

          P van den Driessche, James Watmough (2002)
          A precise definition of the basic reproduction number, R0, is presented for a general compartmental disease transmission model based on a system of ordinary differential equations. It is shown that, if R0 1, then it is unstable. Thus, R0 is a threshold parameter for the model. An analysis of the local centre manifold yields a simple criterion for the existence and stability of super- and sub-threshold endemic equilibria for R0 near one. This criterion, together with the definition of R0, is illustrated by treatment, multigroup, staged progression, multistrain and vector-host models and can be applied to more complex models. The results are significant for disease control.
          Article 0 comments Cited 625 times – based on 0 reviews     Review now
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            A new definition of fractional derivative without singular kernel

            M. CAPUTO, M Fabrizio, M.A. Fabrizio … (2015)
            Article 0 comments Cited 322 times – based on 0 reviews     Review now
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              Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative

              Muhammad Khan, Abdon Atangana (2020)
              The present paper describes the mathematical modeling and dynamics of a novel corona virus (2019-nCoV). We describe the brief details of interaction among the bats and unknown hosts, then among the peoples and the infections reservoir (seafood market). The seafood marked are considered the main source of infection when the bats and the unknown hosts (may be wild animals) leaves the infection there. The purchasing of items from the seafood market by peoples have the ability to infect either asymptomatically or symptomatically. We reduced the model with the assumptions that the seafood market has enough source of infection that can be effective to infect people. We present the mathematical results of the model and then formulate a fractional model. We consider the available infection cases for January 21, 2020, till January 28, 2020 and parameterized the model. We compute the basic reproduction number for the data is R 0 ≈ 2.4829 . The fractional model is then solved numerically by presenting many graphical results, which can be helpful for the infection minimization.
              Article 0 comments Cited 300 times – based on 0 reviews     Review now
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                Author and article information

                Journal
                Journal ID (nlm-ta): Chaos Solitons Fractals
                Journal ID (iso-abbrev): Chaos Solitons Fractals
                Title: Chaos, Solitons, and Fractals
                Publisher: Elsevier Ltd.
                ISSN (Print): 0960-0779
                ISSN (Electronic): 0960-0779
                Publication date PMC-release: 11 July 2020
                Publication date (Print): November 2020
                Publication date (Electronic): 11 July 2020
                Volume: 140
                Page: 110107
                Affiliations
                [a ]Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam
                [b ]Department of Mathematics, Miandoab Branch, Islamic Azad University, Miandoab, Iran
                [c ]Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam
                [d ]Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
                [e ]Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
                Author notes
                [* ]Corresponding author at: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
                Article
                Publisher Item ID: S0960-0779(20)30504-X Publisher ID: 110107
                DOI: 10.1016/j.chaos.2020.110107
                PMC ID: 7836840
                PubMed ID: 33519107
                SO-VID: cfac4586-e742-42fb-8f0c-8bb59c696c4c
                Copyright © © 2020 Elsevier Ltd. All rights reserved.
                License:

                Since January 2020 Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID-19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website. Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre - including this research content - immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active.

                History
                Date received : 19 May 2020
                Date revision received : 1 July 2020
                Date accepted : 9 July 2020
                Categories
                Subject: Article

                Keywords: covid-19,equilibrium point,fixed point,fractional mathematical model,numerical result,34a08,65p99
                Data availability:
                Keywords: covid-19, equilibrium point, fixed point, fractional mathematical model, numerical result, 34a08, 65p99

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