23
views
0
recommends
+1 Recommend
2 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: not found

      Modeling and analysis of COVID-19 epidemics with treatment in fractional derivatives using real data from Pakistan

      research-article

      Read this article at

      ScienceOpenPublisherPMC
      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          Coronaviruses are a large family of viruses that cause different symptoms, from mild cold to severe respiratory distress, and they can be seen in different types of animals such as camels, cattle, cats and bats. Novel coronavirus called COVID-19 is a newly emerged virus that appeared in many countries of the world, but the actual source of the virus is not yet known. The outbreak has caused pandemic with 26,622,706 confirmed infections and 874,708 reported deaths worldwide till August 31, 2020, with 17,717,911 recovered cases. Currently, there exist no vaccines officially approved for the prevention or management of the disease, but alternative drugs meant for HIV, HBV, malaria and some other flus are used to treat this virus. In the present paper, a fractional-order epidemic model with two different operators called the classical Caputo operator and the Atangana–Baleanu–Caputo operator for the transmission of COVID-19 epidemic is proposed and analyzed. The reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {R}}}_0$$\end{document} is obtained for the prediction and persistence of the disease. The dynamic behavior of the equilibria is studied by using fractional Routh–Hurwitz stability criterion and fractional La Salle invariant principle. Special attention is given to the global dynamics of the equilibria. Moreover, the fitting of parameters through least squares curve fitting technique is performed, and the average absolute relative error between COVID-19 actual cases and the model’s solution for the infectious class is tried to be reduced and the best fitted values of the relevant parameters are achieved. The numerical solution of the proposed COVID-19 fractional-order model under the Caputo operator is obtained by using generalized Adams–Bashforth–Moulton method, whereas for the Atangana–Baleanu–Caputo operator, we have used a new numerical scheme. Also, the treatment compartment is included in the population which determines the impact of alternative drugs applied for treating the infected individuals. Furthermore, numerical simulations of the model and their graphical presentations are performed to visualize the effectiveness of our theoretical results and to monitor the effect of arbitrary-order derivative.

          Related collections

          Most cited references72

          • Record: found
          • Abstract: found
          • Article: found
          Is Open Access

          Detection of 2019 novel coronavirus (2019-nCoV) by real-time RT-PCR

          Background The ongoing outbreak of the recently emerged novel coronavirus (2019-nCoV) poses a challenge for public health laboratories as virus isolates are unavailable while there is growing evidence that the outbreak is more widespread than initially thought, and international spread through travellers does already occur. Aim We aimed to develop and deploy robust diagnostic methodology for use in public health laboratory settings without having virus material available. Methods Here we present a validated diagnostic workflow for 2019-nCoV, its design relying on close genetic relatedness of 2019-nCoV with SARS coronavirus, making use of synthetic nucleic acid technology. Results The workflow reliably detects 2019-nCoV, and further discriminates 2019-nCoV from SARS-CoV. Through coordination between academic and public laboratories, we confirmed assay exclusivity based on 297 original clinical specimens containing a full spectrum of human respiratory viruses. Control material is made available through European Virus Archive – Global (EVAg), a European Union infrastructure project. Conclusion The present study demonstrates the enormous response capacity achieved through coordination of academic and public laboratories in national and European research networks.
            Bookmark
            • Record: found
            • Abstract: found
            • Article: not found

            First Case of 2019 Novel Coronavirus in the United States

            Summary An outbreak of novel coronavirus (2019-nCoV) that began in Wuhan, China, has spread rapidly, with cases now confirmed in multiple countries. We report the first case of 2019-nCoV infection confirmed in the United States and describe the identification, diagnosis, clinical course, and management of the case, including the patient’s initial mild symptoms at presentation with progression to pneumonia on day 9 of illness. This case highlights the importance of close coordination between clinicians and public health authorities at the local, state, and federal levels, as well as the need for rapid dissemination of clinical information related to the care of patients with this emerging infection.
              Bookmark
              • Record: found
              • Abstract: found
              • Article: not found

              Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study

              Summary Background Since Dec 31, 2019, the Chinese city of Wuhan has reported an outbreak of atypical pneumonia caused by the 2019 novel coronavirus (2019-nCoV). Cases have been exported to other Chinese cities, as well as internationally, threatening to trigger a global outbreak. Here, we provide an estimate of the size of the epidemic in Wuhan on the basis of the number of cases exported from Wuhan to cities outside mainland China and forecast the extent of the domestic and global public health risks of epidemics, accounting for social and non-pharmaceutical prevention interventions. Methods We used data from Dec 31, 2019, to Jan 28, 2020, on the number of cases exported from Wuhan internationally (known days of symptom onset from Dec 25, 2019, to Jan 19, 2020) to infer the number of infections in Wuhan from Dec 1, 2019, to Jan 25, 2020. Cases exported domestically were then estimated. We forecasted the national and global spread of 2019-nCoV, accounting for the effect of the metropolitan-wide quarantine of Wuhan and surrounding cities, which began Jan 23–24, 2020. We used data on monthly flight bookings from the Official Aviation Guide and data on human mobility across more than 300 prefecture-level cities in mainland China from the Tencent database. Data on confirmed cases were obtained from the reports published by the Chinese Center for Disease Control and Prevention. Serial interval estimates were based on previous studies of severe acute respiratory syndrome coronavirus (SARS-CoV). A susceptible-exposed-infectious-recovered metapopulation model was used to simulate the epidemics across all major cities in China. The basic reproductive number was estimated using Markov Chain Monte Carlo methods and presented using the resulting posterior mean and 95% credibile interval (CrI). Findings In our baseline scenario, we estimated that the basic reproductive number for 2019-nCoV was 2·68 (95% CrI 2·47–2·86) and that 75 815 individuals (95% CrI 37 304–130 330) have been infected in Wuhan as of Jan 25, 2020. The epidemic doubling time was 6·4 days (95% CrI 5·8–7·1). We estimated that in the baseline scenario, Chongqing, Beijing, Shanghai, Guangzhou, and Shenzhen had imported 461 (95% CrI 227–805), 113 (57–193), 98 (49–168), 111 (56–191), and 80 (40–139) infections from Wuhan, respectively. If the transmissibility of 2019-nCoV were similar everywhere domestically and over time, we inferred that epidemics are already growing exponentially in multiple major cities of China with a lag time behind the Wuhan outbreak of about 1–2 weeks. Interpretation Given that 2019-nCoV is no longer contained within Wuhan, other major Chinese cities are probably sustaining localised outbreaks. Large cities overseas with close transport links to China could also become outbreak epicentres, unless substantial public health interventions at both the population and personal levels are implemented immediately. Independent self-sustaining outbreaks in major cities globally could become inevitable because of substantial exportation of presymptomatic cases and in the absence of large-scale public health interventions. Preparedness plans and mitigation interventions should be readied for quick deployment globally. Funding Health and Medical Research Fund (Hong Kong, China).
                Bookmark

                Author and article information

                Contributors
                naik.parvaiz@xjtu.edu.cn
                mehmetyavuz@erbakan.edu.tr
                sania.qureshi@faculty.muet.edu.pk
                jianzu@xjtu.edu.cn
                S.B.Townley@exeter.ac.uk
                Journal
                Eur Phys J Plus
                Eur Phys J Plus
                European Physical Journal plus
                Springer Berlin Heidelberg (Berlin/Heidelberg )
                2190-5444
                8 October 2020
                2020
                : 135
                : 10
                : 795
                Affiliations
                [1 ]GRID grid.43169.39, ISNI 0000 0001 0599 1243, School of Mathematics and Statistics, , Xi’an Jiaotong University, ; Xi’an, 710049 Shaanxi People’s Republic of China
                [2 ]GRID grid.411124.3, ISNI 0000 0004 1769 6008, Department of Mathematics and Computer Sciences, Faculty of Science, , Necmettin Erbakan University, ; 42090 Konya, Turkey
                [3 ]GRID grid.8391.3, ISNI 0000 0004 1936 8024, Department of Mathematics, College of Engineering, Mathematics and Physical Sciences, , University of Exeter, ; TR10, Cornwall, UK
                [4 ]GRID grid.444814.9, ISNI 0000 0001 0376 1014, Department of Basic Sciences and Related Studies, , Mehran University of Engineering and Technology, ; Jamshoro, 76062 Pakistan
                Article
                819
                10.1140/epjp/s13360-020-00819-5
                7594999
                33145145
                c077942c-d6da-47bd-8506-e3e529da5a17
                © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020

                This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.

                History
                : 27 May 2020
                : 29 September 2020
                Funding
                Funded by: FundRef http://dx.doi.org/10.13039/501100001809, National Natural Science Foundation of China;
                Award ID: 11971375
                Award ID: 11571272
                Award Recipient :
                Funded by: FundRef http://dx.doi.org/10.13039/501100001809, National Natural Science Foundation of China;
                Award ID: 11201368
                Award ID: 11631012
                Award Recipient :
                Funded by: National Science and Technology major project of China
                Award ID: 2018ZX10721202
                Award Recipient :
                Funded by: China Postdoctoral Science Foundation
                Award ID: 2014M560755
                Award ID: 2019M663653
                Award Recipient :
                Funded by: FundRef http://dx.doi.org/10.13039/501100007128, Natural Science Foundation of Shaanxi Province;
                Award ID: 2019JM-273
                Award Recipient :
                Categories
                Regular Article
                Custom metadata
                © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020

                Comments

                Comment on this article