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      New insights on novel coronavirus 2019-nCoV/SARS-CoV-2 modelling in the aspect of fractional derivatives and fixed points

      , , , Department of Mathematics, GMR Institute of Technology, Rajam-532127, Andhra Pradesh, India, Institute for Groundwater Studies, University of the Free State, Bloemfontein 9300, South Africa, Department of Medical Research, China Medical University Hospital, Taichung, Taiwan, Institute of Mathematics, University of Santiago de Compostela, Santiago de Compostela 15782, Spain
      Mathematical Biosciences and Engineering
      American Institute of Mathematical Sciences (AIMS)

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          Abstract

          <abstract><p>Extended orthogonal spaces are introduced and proved pertinent fixed point results. Thereafter, we present an analysis of the existence and unique solutions of the novel coronavirus 2019-nCoV/SARS-CoV-2 model via fractional derivatives. To strengthen our paper, we apply an efficient numerical scheme to solve the coronavirus 2019-nCoV/SARS-CoV-2 model with different types of differential operators.</p></abstract>

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          Aerosol and Surface Stability of SARS-CoV-2 as Compared with SARS-CoV-1

          To the Editor: A novel human coronavirus that is now named severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) (formerly called HCoV-19) emerged in Wuhan, China, in late 2019 and is now causing a pandemic. 1 We analyzed the aerosol and surface stability of SARS-CoV-2 and compared it with SARS-CoV-1, the most closely related human coronavirus. 2 We evaluated the stability of SARS-CoV-2 and SARS-CoV-1 in aerosols and on various surfaces and estimated their decay rates using a Bayesian regression model (see the Methods section in the Supplementary Appendix, available with the full text of this letter at NEJM.org). SARS-CoV-2 nCoV-WA1-2020 (MN985325.1) and SARS-CoV-1 Tor2 (AY274119.3) were the strains used. Aerosols (<5 μm) containing SARS-CoV-2 (105.25 50% tissue-culture infectious dose [TCID50] per milliliter) or SARS-CoV-1 (106.75-7.00 TCID50 per milliliter) were generated with the use of a three-jet Collison nebulizer and fed into a Goldberg drum to create an aerosolized environment. The inoculum resulted in cycle-threshold values between 20 and 22, similar to those observed in samples obtained from the upper and lower respiratory tract in humans. Our data consisted of 10 experimental conditions involving two viruses (SARS-CoV-2 and SARS-CoV-1) in five environmental conditions (aerosols, plastic, stainless steel, copper, and cardboard). All experimental measurements are reported as means across three replicates. SARS-CoV-2 remained viable in aerosols throughout the duration of our experiment (3 hours), with a reduction in infectious titer from 103.5 to 102.7 TCID50 per liter of air. This reduction was similar to that observed with SARS-CoV-1, from 104.3 to 103.5 TCID50 per milliliter (Figure 1A). SARS-CoV-2 was more stable on plastic and stainless steel than on copper and cardboard, and viable virus was detected up to 72 hours after application to these surfaces (Figure 1A), although the virus titer was greatly reduced (from 103.7 to 100.6 TCID50 per milliliter of medium after 72 hours on plastic and from 103.7 to 100.6 TCID50 per milliliter after 48 hours on stainless steel). The stability kinetics of SARS-CoV-1 were similar (from 103.4 to 100.7 TCID50 per milliliter after 72 hours on plastic and from 103.6 to 100.6 TCID50 per milliliter after 48 hours on stainless steel). On copper, no viable SARS-CoV-2 was measured after 4 hours and no viable SARS-CoV-1 was measured after 8 hours. On cardboard, no viable SARS-CoV-2 was measured after 24 hours and no viable SARS-CoV-1 was measured after 8 hours (Figure 1A). Both viruses had an exponential decay in virus titer across all experimental conditions, as indicated by a linear decrease in the log10TCID50 per liter of air or milliliter of medium over time (Figure 1B). The half-lives of SARS-CoV-2 and SARS-CoV-1 were similar in aerosols, with median estimates of approximately 1.1 to 1.2 hours and 95% credible intervals of 0.64 to 2.64 for SARS-CoV-2 and 0.78 to 2.43 for SARS-CoV-1 (Figure 1C, and Table S1 in the Supplementary Appendix). The half-lives of the two viruses were also similar on copper. On cardboard, the half-life of SARS-CoV-2 was longer than that of SARS-CoV-1. The longest viability of both viruses was on stainless steel and plastic; the estimated median half-life of SARS-CoV-2 was approximately 5.6 hours on stainless steel and 6.8 hours on plastic (Figure 1C). Estimated differences in the half-lives of the two viruses were small except for those on cardboard (Figure 1C). Individual replicate data were noticeably “noisier” (i.e., there was more variation in the experiment, resulting in a larger standard error) for cardboard than for other surfaces (Fig. S1 through S5), so we advise caution in interpreting this result. We found that the stability of SARS-CoV-2 was similar to that of SARS-CoV-1 under the experimental circumstances tested. This indicates that differences in the epidemiologic characteristics of these viruses probably arise from other factors, including high viral loads in the upper respiratory tract and the potential for persons infected with SARS-CoV-2 to shed and transmit the virus while asymptomatic. 3,4 Our results indicate that aerosol and fomite transmission of SARS-CoV-2 is plausible, since the virus can remain viable and infectious in aerosols for hours and on surfaces up to days (depending on the inoculum shed). These findings echo those with SARS-CoV-1, in which these forms of transmission were associated with nosocomial spread and super-spreading events, 5 and they provide information for pandemic mitigation efforts.
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            Network-based drug repurposing for novel coronavirus 2019-nCoV/SARS-CoV-2

            Human coronaviruses (HCoVs), including severe acute respiratory syndrome coronavirus (SARS-CoV) and 2019 novel coronavirus (2019-nCoV, also known as SARS-CoV-2), lead global epidemics with high morbidity and mortality. However, there are currently no effective drugs targeting 2019-nCoV/SARS-CoV-2. Drug repurposing, representing as an effective drug discovery strategy from existing drugs, could shorten the time and reduce the cost compared to de novo drug discovery. In this study, we present an integrative, antiviral drug repurposing methodology implementing a systems pharmacology-based network medicine platform, quantifying the interplay between the HCoV–host interactome and drug targets in the human protein–protein interaction network. Phylogenetic analyses of 15 HCoV whole genomes reveal that 2019-nCoV/SARS-CoV-2 shares the highest nucleotide sequence identity with SARS-CoV (79.7%). Specifically, the envelope and nucleocapsid proteins of 2019-nCoV/SARS-CoV-2 are two evolutionarily conserved regions, having the sequence identities of 96% and 89.6%, respectively, compared to SARS-CoV. Using network proximity analyses of drug targets and HCoV–host interactions in the human interactome, we prioritize 16 potential anti-HCoV repurposable drugs (e.g., melatonin, mercaptopurine, and sirolimus) that are further validated by enrichment analyses of drug-gene signatures and HCoV-induced transcriptomics data in human cell lines. We further identify three potential drug combinations (e.g., sirolimus plus dactinomycin, mercaptopurine plus melatonin, and toremifene plus emodin) captured by the “Complementary Exposure” pattern: the targets of the drugs both hit the HCoV–host subnetwork, but target separate neighborhoods in the human interactome network. In summary, this study offers powerful network-based methodologies for rapid identification of candidate repurposable drugs and potential drug combinations targeting 2019-nCoV/SARS-CoV-2.
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              New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model

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                Author and article information

                Journal
                Mathematical Biosciences and Engineering
                MBE
                American Institute of Mathematical Sciences (AIMS)
                1551-0018
                2021
                2021
                : 18
                : 6
                : 8683-8726
                Article
                10.3934/mbe.2021430
                c145514c-6124-48d1-a007-25b7c09b884c
                © 2021
                History

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