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      Numerical treatment on the new fractional-order SIDARTHE COVID-19 pandemic differential model via neural networks

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          Abstract

          In this study, modeling the COVID-19 pandemic via a novel fractional-order SIDARTHE (FO-SIDARTHE) differential system is presented. The purpose of this research seemed to be to show the consequences and relevance of the fractional-order (FO) COVID-19 SIDARTHE differential system, as well as FO required conditions underlying four control measures, called SI,  SD,  SA, and SR. The FO-SIDARTHE system incorporates eight phases of infection: susceptible (S), infected (I), diagnosed (D), ailing (A), recognized (R), threatening (T), healed (H), and extinct (E). Our objective of all these investigations is to use fractional derivatives to increase the accuracy of the SIDARTHE system. A FO-SIDARTHE system has yet to be disclosed, nor has it yet been treated using the strength of stochastic solvers. Stochastic solvers based on the Levenberg–Marquardt backpropagation methodology (L-MB) and neural networks (NNs), specifically L-MBNNs, are being used to analyze a FO-SIDARTHE problem. Three cases having varied values under the same fractional order are being presented to resolve the FO-SIDARTHE system. The statistics employed to provide numerical solutions toward the FO-SIDARTHE system are classified as obeys: 72% toward training, 18% in testing, and 10% for authorization. To establish the accuracy of such L-MBNNs utilizing Adams–Bashforth–Moulton, the numerical findings were compared with the reference solutions.

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          Clinical Characteristics of Coronavirus Disease 2019 in China

          Wei-jie Guan, Zheng-yi Ni, Yu Hu … (2020)
          Abstract Background Since December 2019, when coronavirus disease 2019 (Covid-19) emerged in Wuhan city and rapidly spread throughout China, data have been needed on the clinical characteristics of the affected patients. Methods We extracted data regarding 1099 patients with laboratory-confirmed Covid-19 from 552 hospitals in 30 provinces, autonomous regions, and municipalities in mainland China through January 29, 2020. The primary composite end point was admission to an intensive care unit (ICU), the use of mechanical ventilation, or death. Results The median age of the patients was 47 years; 41.9% of the patients were female. The primary composite end point occurred in 67 patients (6.1%), including 5.0% who were admitted to the ICU, 2.3% who underwent invasive mechanical ventilation, and 1.4% who died. Only 1.9% of the patients had a history of direct contact with wildlife. Among nonresidents of Wuhan, 72.3% had contact with residents of Wuhan, including 31.3% who had visited the city. The most common symptoms were fever (43.8% on admission and 88.7% during hospitalization) and cough (67.8%). Diarrhea was uncommon (3.8%). The median incubation period was 4 days (interquartile range, 2 to 7). On admission, ground-glass opacity was the most common radiologic finding on chest computed tomography (CT) (56.4%). No radiographic or CT abnormality was found in 157 of 877 patients (17.9%) with nonsevere disease and in 5 of 173 patients (2.9%) with severe disease. Lymphocytopenia was present in 83.2% of the patients on admission. Conclusions During the first 2 months of the current outbreak, Covid-19 spread rapidly throughout China and caused varying degrees of illness. Patients often presented without fever, and many did not have abnormal radiologic findings. (Funded by the National Health Commission of China and others.)
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            Characteristics of and Important Lessons From the Coronavirus Disease 2019 (COVID-19) Outbreak in China: Summary of a Report of 72 314 Cases From the Chinese Center for Disease Control and Prevention

            Zunyou Wu, Jennifer M. McGoogan (2020)
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              Is Open Access

              Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts

              Joel Hellewell, Sam Abbott, Amy Gimma … (2020)
              Summary Background Isolation of cases and contact tracing is used to control outbreaks of infectious diseases, and has been used for coronavirus disease 2019 (COVID-19). Whether this strategy will achieve control depends on characteristics of both the pathogen and the response. Here we use a mathematical model to assess if isolation and contact tracing are able to control onwards transmission from imported cases of COVID-19. Methods We developed a stochastic transmission model, parameterised to the COVID-19 outbreak. We used the model to quantify the potential effectiveness of contact tracing and isolation of cases at controlling a severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)-like pathogen. We considered scenarios that varied in the number of initial cases, the basic reproduction number (R 0), the delay from symptom onset to isolation, the probability that contacts were traced, the proportion of transmission that occurred before symptom onset, and the proportion of subclinical infections. We assumed isolation prevented all further transmission in the model. Outbreaks were deemed controlled if transmission ended within 12 weeks or before 5000 cases in total. We measured the success of controlling outbreaks using isolation and contact tracing, and quantified the weekly maximum number of cases traced to measure feasibility of public health effort. Findings Simulated outbreaks starting with five initial cases, an R 0 of 1·5, and 0% transmission before symptom onset could be controlled even with low contact tracing probability; however, the probability of controlling an outbreak decreased with the number of initial cases, when R 0 was 2·5 or 3·5 and with more transmission before symptom onset. Across different initial numbers of cases, the majority of scenarios with an R 0 of 1·5 were controllable with less than 50% of contacts successfully traced. To control the majority of outbreaks, for R 0 of 2·5 more than 70% of contacts had to be traced, and for an R 0 of 3·5 more than 90% of contacts had to be traced. The delay between symptom onset and isolation had the largest role in determining whether an outbreak was controllable when R 0 was 1·5. For R 0 values of 2·5 or 3·5, if there were 40 initial cases, contact tracing and isolation were only potentially feasible when less than 1% of transmission occurred before symptom onset. Interpretation In most scenarios, highly effective contact tracing and case isolation is enough to control a new outbreak of COVID-19 within 3 months. The probability of control decreases with long delays from symptom onset to isolation, fewer cases ascertained by contact tracing, and increasing transmission before symptoms. This model can be modified to reflect updated transmission characteristics and more specific definitions of outbreak control to assess the potential success of local response efforts. Funding Wellcome Trust, Global Challenges Research Fund, and Health Data Research UK.
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                Author and article information

                Contributors
                Zulqurnain Sabir: zulqurnain-maths@hu.edu.pk
                Muhammad Asif Zahoor Raja: rajamaz@yuntect.edu.tw
                Hasan Bulut: hbulut@firat.edu.tr
                Journal
                Journal ID (nlm-ta): Eur Phys J Plus
                Journal ID (iso-abbrev): Eur Phys J Plus
                Title: European Physical Journal plus
                Publisher: Springer Berlin Heidelberg (Berlin/Heidelberg )
                ISSN (Electronic): 2190-5444
                Publication date (Electronic): 11 March 2022
                Publication date (Print): 2022
                Volume: 137
                Issue: 3
                Electronic Location Identifier: 334
                Affiliations
                [1 ]GRID grid.411320.5, ISNI 0000 0004 0574 1529, Department of Mathematics, , Firat University, ; Elazig, Turkey
                [2 ]GRID grid.440530.6, ISNI 0000 0004 0609 1900, Department of Mathematics and Statistics, , Hazara University, ; Mansehra, Pakistan
                [3 ]GRID grid.412127.3, ISNI 0000 0004 0532 0820, Future Technology Research Center, , National Yunlin University of Science and Technology, ; 123 University Road, Section 3, Yunlin, Douliou, 64002 Taiwan, ROC
                Author information
                http://orcid.org/0000-0003-0071-871X
                Article
                Publisher ID: 2525
                DOI: 10.1140/epjp/s13360-022-02525-w
                PMC ID: 8916505
                SO-VID: a8653624-d9b9-4b1a-a362-9a77808913b9
                Copyright © © The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
                License:

                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
                Date received : 14 January 2022
                Date accepted : 22 February 2022
                Categories
                Subject: Regular Article
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                issue-copyright-statement © The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022

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