Complex solutions of the Dean equations and non-uniqueness at all Reynolds numbers

Steady, incompressible flow down a slowly-curving circular pipe is considered, analyti- cally and numerically. Both real and complex solutions are investigated. Using high-order Hermite–Pad ́e approximants, the Dean series solution is analytically continued outside its circle of convergence where it predicts a complex solution branch for real, positive Dean number, K . This is confirmed by numerical solution. It is shown that other previously unknown solution branches exist for all K > 0, which are related to an unforced com- plex eigensolution. This non-uniqueness is believed to be generic to the Navier–Stokes equations in most geometries. By means of path continuation, numerical solutions are followed around the complex K -plane. The standard Dean two-vortex solution is shown to lie on the same hypersurface as the eigensolution and the four-vortex solutions found in the literature. Elliptic pipes are considered and shown to exhibit similar behaviour to the circular case. There is an imaginary singularity limiting convergence of the Dean series, an unforced solution at K = 0 and nonuniqueness for K > 0, culminating in a real bifurcation

Post-vaccination COVID-19: A case-control study and genomic analysis of 119 breakthrough infections in partially vaccinated individuals

BACKGROUND: Post-vaccination infections challenge the control of the COVID-19 pandemic. METHODS: We matched 119 cases of post-vaccination SARS-CoV-2 infection with BNT162b2 mRNA, or ChAdOx1 nCOV-19, to 476 unvaccinated patients with COVID-19 (Sept 2020-March 2021), according to age and sex. Differences in 60-day all-cause mortality, hospital admission, and hospital length of stay were evaluated. Phylogenetic, single nucleotide polymorphism (SNP) and minority variant allele (MVA) full genome sequencing analysis was performed. RESULTS: 116/119 cases developed COVID-19 post first vaccination dose (median 14 days, IQR 9 - 24 days). Overall, 13/119 (10∙9%) cases and 158/476 (33∙2%) controls died (p<0.001), corresponding to 4∙5 number needed to treat (NNT). Multivariably, vaccination was associated with 69∙3% (95%CI 45∙8 - 82∙6) relative risk (RR) reduction in mortality. Similar results were seen in subgroup analysis for patients with infection onset ≥14 days after first vaccination (RR reduction 65∙1%, 95%CI 27∙2 - 83∙2, NNT 4∙5), and across vaccine subgroups (BNT162b2: RR reduction 66%, 95%CI 34∙9 - 82∙2, NNT 4∙7, ChAdOx1: RR reduction 78∙4%, 95%CI 30∙4 - 93∙3, NNT 4∙1). Hospital admissions (OR 0∙80, 95%CI 0∙51 - 1∙28), and length of stay (-1∙89 days, 95%CI -4∙57 - 0∙78) were lower for cases, while Ct values were higher (30∙8 versus 28∙8, p = 0.053). B.1.1.7 was the predominant lineage in cases (100/108, 92.6%) and controls (341/446, 76.5%). Genomic analysis identified one post-vaccination case harboring the E484K vaccine escape mutation (B.1.525 lineage). CONCLUSIONS: Previous vaccination reduces mortality when B.1.1.7 is the predominant lineage. No significant lineage-specific genomic changes during phylogenetic, SNP and MVA analysis were detected

Systematic Review and Patient-Level Meta-Analysis of SARS-CoV-2 Viral Dynamics to Model Response to Antiviral Therapies

Severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2) viral loads change rapidly following symptom onset, so to assess antivirals it is important to understand the natural history and patient factors influencing this. We undertook an individual patient-level meta-analysis of SARS-CoV-2 viral dynamics in humans to describe viral dynamics and estimate the effects of antivirals used to date. This systematic review identified case reports, case series, and clinical trial data from publications between January 1, 2020, and May 31, 2020, following Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines. A multivariable Cox proportional hazards (Cox-PH) regression model of time to viral clearance was fitted to respiratory and stool samples. A simplified four parameter nonlinear mixed-effects (NLME) model was fitted to viral load trajectories in all sampling sites and covariate modeling of respiratory viral dynamics was performed to quantify time-dependent drug effects. Patient-level data from 645 individuals (age 1 month to 100 years) with 6,316 viral loads were extracted. Model-based simulations of viral load trajectories in samples from the upper and lower respiratory tract, stool, blood, urine, ocular secretions, and breast milk were generated. Cox-PH modeling showed longer time to viral clearance in older patients, men, and those with more severe disease. Remdesivir was associated with faster viral clearance (adjusted hazard ratio (AHR) = 9.19, P < 0.001), as well as interferon, particularly when combined with ribavirin (AHR = 2.2, P = 0.015; AHR = 6.04, P = 0.006). Combination therapy should be further investigated. A viral dynamic dataset and NLME model for designing and analyzing antiviral trials has been established

Evolution of viral variants in remdesivir-treated and untreated SARS-CoV-2-infected pediatrics patients

Detailed information on intrahost viral evolution in SARS-CoV-2 with and without treatment is limited. Sequential viral loads and deep sequencing of SARS-CoV-2 from the upper respiratory tract of nine hospitalized children, three of whom were treated with remdesivir, revealed that remdesivir treatment suppressed viral load in one patient but not in a second infected with an identical strain without any evidence of drug resistance found. Reduced levels of subgenomic RNA during treatment of the second patient, suggest an additional effect of remdesivir on viral replication. Haplotype reconstruction uncovered persistent SARS-CoV-2 variant genotypes in four patients. These likely arose from within-host evolution, although superinfection cannot be excluded in one case. Although our dataset is small, observed sample-to-sample heterogeneity in variant frequencies across four of nine patients suggests the presence of discrete viral populations in the lung with incomplete population sampling in diagnostic swabs. Such compartmentalization could compromise the penetration of remdesivir into the lung, limiting the drugs in vivo efficacy, as has been observed in other lung infections

Emergence of genomic diversity and recurrent mutations in SARS-CoV-2

SARS-CoV-2 is a SARS-like coronavirus of likely zoonotic origin first identified in December 2019 in Wuhan, the capital of China's Hubei province. The virus has since spread globally, resulting in the currently ongoing COVID-19 pandemic. The first whole genome sequence was published on January 52,020, and thousands of genomes have been sequenced since this date. This resource allows unprecedented insights into the past demography of SARS-CoV-2 but also monitoring of how the virus is adapting to its novel human host, providing information to direct drug and vaccine design. We curated a dataset of 7666 public genome assemblies and analysed the emergence of genomic diversity over time. Our results are in line with previous estimates and point to all sequences sharing a common ancestor towards the end of 2019, supporting this as the period when SARS-CoV-2 jumped into its human host. Due to extensive transmission, the genetic diversity of the virus in several countries recapitulates a large fraction of its worldwide genetic diversity. We identify regions of the SARS-CoV-2 genome that have remained largely invariant to date, and others that have already accumulated diversity. By focusing on mutations which have emerged independently multiple times (homoplasies), we identify 198 filtered recurrent mutations in the SARS-CoV-2 genome. Nearly 80% of the recurrent mutations produced non-synonymous changes at the protein level, suggesting possible ongoing adaptation of SARS-CoV-2. Three sites in Orf1ab in the regions encoding Nsp6, Nsp11, Nsp13, and one in the Spike protein are characterised by a particularly large number of recurrent mutations (>15 events) which may signpost convergent evolution and are of particular interest in the context of adaptation of SARS-CoV-2 to the human host. We additionally provide an interactive user-friendly web-application to query the alignment of the 7666 SARS-CoV-2 genomes