Low thrust propulsion in a coplanar circular restricted four body problem

This paper formulates a circular restricted four body problem (CRFBP), where the three primaries are set in the stable Lagrangian equilateral triangle configuration and the fourth body is massless. The analysis of this autonomous coplanar CRFBP is undertaken, which identies eight natural equilibria; four of which are close to the smaller body, two stable and two unstable, when considering the primaries to be the Sun and two smaller bodies of the solar system. Following this, the model incorporates `near term' low-thrust propulsion capabilities to generate surfaces of articial equilibrium points close to the smaller primary, both in and out of the plane containing the celestial bodies. A stability analysis of these points is carried out and a stable subset of them is identied. Throughout the analysis the Sun-Jupiter-Asteroid-Spacecraft system is used, for conceivable masses of a hypothetical asteroid set at the libration point L4. It is shown that eight bounded orbits exist, which can be maintained with a constant thrust less than 1:5 10􀀀4N for a 1000kg spacecraft. This illustrates that, by exploiting low-thrust technologies, it would be possible to maintain an observation point more than 66% closer to the asteroid than that of a stable natural equilibrium point. The analysis then focusses on a major Jupiter Trojan: the 624-Hektor asteroid. The thrust required to enable close asteroid observation is determined in the simplied CRFBP model. Finally, a numerical simulation of the real Sun-Jupiter-624 Hektor-Spacecraft is undertaken, which tests the validity of the stability analysis of the simplied model

Signatures of early frailty in the gut microbiota

Background: Frailty is arguably the biggest problem associated with population ageing, and associates with gut microbiome composition in elderly and care-dependent individuals. Here we characterize frailty associations with the gut microbiota in a younger community dwelling population, to identify targets for intervention to encourage healthy ageing. Method: We analysed 16S rRNA gene sequence data derived from faecal samples obtained from 728 female twins. Frailty was quantified using a frailty index (FI). Mixed effects models were used to identify associations with diversity, operational taxonomic units (OTUs) and taxa. OTU associations were replicated in the Eldermet cohort. Phenotypes were correlated with modules of OTUs collapsed by co-occurrence. Results: Frailty negatively associated with alpha diversity of the gut microbiota. Models considering a number of covariates identified 637 OTUs associated with FI. Twenty-two OTU associations were significant independent of alpha diversity. Species more abundant with frailty included Eubacterium dolichum and Eggerthella lenta. A Faecalibacterium prausnitzii OTU was less abundant in frailer individuals, and retained significance in discordant twin analysis. Sixty OTU associations were replicated in the Eldermet cohort. OTU co-occurrence modules had mutually exclusive associations between frailty and alpha diversity. Conclusions: There was a striking negative association between frailty and gut microbiota diversity, underpinned by specific taxonomic associations. Whether these relationships are causal or consequential is unknown. Nevertheless, they represent targets for diagnostic surveillance, or for intervention studies to improve vitality in ageing

SARS-CoV-2 infection following booster vaccination: Illness and symptom profile in a prospective, observational community-based case-control study

BACKGROUND: Booster COVID-19 vaccines have shown efficacy in clinical trials and effectiveness in real-world data against symptomatic and severe illness. However, some people still become infected with SARS-CoV-2 following a third (booster) vaccination. This study describes the characteristics of SARS-CoV-2 illness following a third vaccination and assesses the risk of progression to symptomatic disease in SARS-CoV-2 infected individuals with time since vaccination. METHODS: This prospective, community-based, case-control study used data from UK-based, adult (≥18 years) users of the COVID Symptom Study mobile application, self-reporting a first positive COVID-19 test between June 1, 2021 and April 1, 2022. To describe the characteristics of SARS-CoV-2 illness following a third vaccination, we selected cases and controls who had received a third and second dose of monovalent vaccination against COVID-19, respectively, and reported a first positive SARS-CoV-2 test at least 7 days after most recent vaccination. Cases and controls were matched (1:1) based on age, sex, BMI, time between first vaccination and infection, and week of testing. We used logistic regression models (adjusted for age, sex, BMI, level of social deprivation and frailty) to analyse associations of disease severity, overall disease duration, and individual symptoms with booster vaccination status. To assess for potential waning of vaccine effectiveness, we compared disease severity, duration, and symptom profiles of individuals testing positive within 3 months of most recent vaccination (reference group) to profiles of individuals infected between 3 and 4, 4–5, and 5–6 months, for both third and second dose. All analyses were stratified by time period, based on the predominant SARS-CoV-2 variant at time of infection (Delta: June 1, 2021–27 Nov, 2021; Omicron: 20 Dec, 2021-Apr 1, 2022). FINDINGS: During the study period, 50,162 (Delta period) and 162,041 (Omicron) participants reported a positive SARS-CoV-2 test. During the Delta period, infection following three vaccination doses was associated with lower odds of long COVID (symptoms≥ 4 weeks) (OR=0.83, CI[0.50–1.36], p < 0.0001), hospitalisation (OR=0.55, CI[0.39–0.75], p < 0.0001) and severe symptoms (OR=0.36, CI[0.27–0.49], p < 0.0001), and higher odds of asymptomatic infection (OR=3.45, CI[2.86–4.16], p < 0.0001), compared to infection following only two vaccination doses. During the Omicron period, infection following three vaccination doses was associated with lower odds of severe symptoms (OR=0.48, CI[0.42–0.55], p < 0.0001). During the Delta period, infected individuals were less likely to report almost all individual symptoms after a third vaccination. During the Omicron period, individuals were less likely to report most symptoms after a third vaccination, except for upper respiratory symptoms e.g. sneezing (OR=1.40, CI[1.18–1.35], p < 0.0001), runny nose (OR=1.26, CI[1.18–1.35], p < 0.0001), sore throat (OR=1.17, CI[1.10–1.25], p < 0.0001), and hoarse voice (OR=1.13, CI[1.06–1.21], p < 0.0001), which were more likely to be reported. There was evidence of reduced vaccine effectiveness during both Delta and Omicron periods in those infected more than 3 months after their most recent vaccination, with increased reporting of severe symptoms, long duration illness, and most individual symptoms. INTERPRETATION: This study suggests that a third dose of monovalent vaccine may reduce symptoms, severity and duration of SARS-CoV-2 infection following vaccination. For Omicron variants, the third vaccination appears to reduce overall symptom burden but may increase upper respiratory symptoms, potentially due to immunological priming. There is evidence of waning vaccine effectiveness against progression to symptomatic and severe disease and long COVID after three months. Our findings support ongoing booster vaccination promotion amongst individuals at high risk from COVID-19, to reduce severe symptoms and duration of illness, and health system burden. Disseminating knowledge on expected symptoms following booster vaccination may encourage vaccine uptake

SARS-CoV-2 (COVID-19) infection in pregnant women: characterization of symptoms and syndromes predictive of disease and severity through real-time, remote participatory epidemiology

Objective: To test whether pregnant and non-pregnant women differ in COVID-19 symptom profile and severity. To extend previous investigations on hospitalized pregnant women to those who did not require hospitalization. Design: Observational study prospectively collecting longitudinal (smartphone application interface) and cross-sectional (web-based survey) data. Setting:Community-based self-participatory citizen surveillance in the United Kingdom, Sweden and the United States of America. Population: Two female community-based cohorts aged 18-44 years. The discovery cohort was drawn from 1,170,315 UK, Sweden and USA women (79 pregnant tested positive) who self-reported status and symptoms longitudinally via smartphone. The replication cohort included 1,344,966 USA women (134 pregnant tested positive) who provided cross-sectional self-reports. Methods: Pregnant and non-pregnant were compared for frequencies of symptoms and events, including SARS-CoV-2 testing and hospitalization rates. Multivariable regression was used to investigate symptoms severity and comorbidity effects. Results: Pregnant and non-pregnant women positive for SARS-CoV-2 infection were not different in syndromic severity. Pregnant were more likely to have received testing than non-pregnant, despite reporting fewer symptoms. Pre-existing lung disease was most closely associated with the syndromic severity in pregnant hospitalized women. Heart and kidney diseases and diabetes increased risk. The most frequent symptoms among all non-hospitalized women were anosmia [63% pregnant, 92% non-pregnant] and headache [72%, 62%]. Cardiopulmonary symptoms, including persistent cough [80%] and chest pain [73%], were more frequent among pregnant women who were hospitalized. Conclusions: Symptom characteristics and severity were comparable among pregnant and non-pregnant women, except for gastrointestinal symptoms. Consistent with observations in non-pregnant populations, lung disease and diabetes were associated with increased risk of more severe SARS-CoV-2 infection during pregnancy. Tweetable abstract: Pregnancy with SARS-CoV-2 has no higher risk of severe symptoms. Underlying lung disease or cardiac condition can increase risk. Competing Interest Statement: ATC previously served as an investigator on a clinical trial of diet and lifestyle using a separate mobile application that was supported by Zoe Global Ltd. Clinical Trial -- Funding Statement: This work was supported by Zoe Global. The Department of Twin Research receives grants from the Wellcome Trust (212904/Z/18/Z) and Medical Research Council/British Heart Foundation Ancestry and Biological Informative Markers for Stratification of Hypertension (AIMHY; MR/M016560/1), and support from the European Union, the Chronic Disease Research Foundation, Zoe Global, the NIHR Clinical Research Facility and the Biomedical Research Centre (based at Guys and St Thomas NHS Foundation Trust in partnership with Kings College London). The School of Biomedical Engineering & Imaging Science and Center for Medical Engineering at Kings College London receive grants from the Wellcome/EPSRC Centre for Medical Engineering [WT 203148/Z/16/Z]. E.M. is funded by the Skills Development Scheme of the Medical Research Council UK. C.M.A. is funded by NIDDK K23 DK120899 and the Boston Childrens Hospital Office of Faculty Development Career Development Award. CHS is supported by an Alzheimers Society Junior fellowship (AS-JF-17-011). W.M., J.S.B. and A.T.C. are supported by the Massachusetts Consortium on Pathogen Readiness (MassCPR) and Mark and Lisa Schwartz

Disentangling post-vaccination symptoms from early COVID-19

Background: Identifying and testing individuals likely to have SARS-CoV-2 is critical for infection control, including post-vaccination. Vaccination is a major public health strategy to reduce SARS-CoV-2 infection globally. Some individuals experience systemic symptoms post-vaccination, which overlap with COVID-19 symptoms. This study compared early post-vaccination symptoms in individuals who subsequently tested positive or negative for SARS-CoV-2, using data from the COVID Symptom Study (CSS) app. Methods: We conducted a prospective observational study in 1,072,313 UK CSS participants who were asymptomatic when vaccinated with Pfizer-BioNTech mRNA vaccine (BNT162b2) or Oxford-AstraZeneca adenovirus-vectored vaccine (ChAdOx1 nCoV-19) between 8 December 2020 and 17 May 2021, who subsequently reported symptoms within seven days (N=362,770) (other than local symptoms at injection site) and were tested for SARS-CoV-2 (N=14,842), aiming to differentiate vaccination side-effects per se from superimposed SARS-CoV-2 infection. The post-vaccination symptoms and SARS-CoV-2 test results were contemporaneously logged by participants. Demographic and clinical information (including comorbidities) were recorded. Symptom profiles in individuals testing positive were compared with a 1:1 matched population testing negative, including using machine learning and multiple models considering UK testing criteria. Findings: Differentiating post-vaccination side-effects alone from early COVID-19 was challenging, with a sensitivity in identification of individuals testing positive of 0.6 at best. Most of these individuals did not have fever, persistent cough, or anosmia/dysosmia, requisite symptoms for accessing UK testing; and many only had systemic symptoms commonly seen post-vaccination in individuals negative for SARS-CoV-2 (headache, myalgia, and fatigue). Interpretation: Post-vaccination symptoms per se cannot be differentiated from COVID-19 with clinical robustness, either using symptom profiles or machine-derived models. Individuals presenting with systemic symptoms post-vaccination should be tested for SARS-CoV-2 or quarantining, to prevent community spread. Funding: UK Government Department of Health and Social Care, Wellcome Trust, UK Engineering and Physical Sciences Research Council, UK National Institute for Health Research, UK Medical Research Council and British Heart Foundation, Chronic Disease Research Foundation, Zoe Limited

Profiling post-COVID-19 condition across different variants of SARS-CoV-2: a prospective longitudinal study in unvaccinated wild-type, unvaccinated alpha-variant, and vaccinated delta-variant populations

BACKGROUND: Self-reported symptom studies rapidly increased understanding of SARS-CoV-2 during the COVID-19 pandemic and enabled monitoring of long-term effects of COVID-19 outside hospital settings. Post-COVID-19 condition presents as heterogeneous profiles, which need characterisation to enable personalised patient care. We aimed to describe post-COVID-19 condition profiles by viral variant and vaccination status. METHODS: In this prospective longitudinal cohort study, we analysed data from UK-based adults (aged 18–100 years) who regularly provided health reports via the Covid Symptom Study smartphone app between March 24, 2020, and Dec 8, 2021. We included participants who reported feeling physically normal for at least 30 days before testing positive for SARS-CoV-2 who subsequently developed long COVID (ie, symptoms lasting longer than 28 days from the date of the initial positive test). We separately defined post-COVID-19 condition as symptoms that persisted for at least 84 days after the initial positive test. We did unsupervised clustering analysis of time-series data to identify distinct symptom profiles for vaccinated and unvaccinated people with post-COVID-19 condition after infection with the wild-type, alpha (B.1.1.7), or delta (B.1.617.2 and AY.x) variants of SARS-CoV-2. Clusters were then characterised on the basis of symptom prevalence, duration, demography, and previous comorbidities. We also used an additional testing sample with additional data from the Covid Symptom Study Biobank (collected between October, 2020, and April, 2021) to investigate the effects of the identified symptom clusters of post-COVID-19 condition on the lives of affected people. FINDINGS: We included 9804 people from the COVID Symptom Study with long COVID, 1513 (15%) of whom developed post-COVID-19 condition. Sample sizes were sufficient only for analyses of the unvaccinated wild-type, unvaccinated alpha variant, and vaccinated delta variant groups. We identified distinct profiles of symptoms for post-COVID-19 condition within and across variants: four endotypes were identified for infections due to the wild-type variant (in unvaccinated people), seven for the alpha variant (in unvaccinated people), and five for the delta variant (in vaccinated people). Across all variants, we identified a cardiorespiratory cluster of symptoms, a central neurological cluster, and a multi-organ systemic inflammatory cluster. These three main clusers were confirmed in a testing sample. Gastrointestinal symptoms clustered in no more than two specific phenotypes per viral variant. INTERPRETATION: Our unsupervised analysis identified different profiles of post-COVID-19 condition, characterised by differing symptom combinations, durations, and functional outcomes. Our classification could be useful for understanding the distinct mechanisms of post-COVID-19 condition, as well as for identification of subgroups of individuals who might be at risk of prolonged debilitation. FUNDING: UK Government Department of Health and Social Care, Chronic Disease Research Foundation, The Wellcome Trust, UK Engineering and Physical Sciences Research Council, UK Research and Innovation London Medical Imaging & Artificial Intelligence Centre for Value-Based Healthcare, UK National Institute for Health Research, UK Medical Research Council, British Heart Foundation, UK Alzheimer's Society, and ZOE

Anxiety and depression symptoms after COVID-19 infection: results from the COVID Symptom Study app

Background: Mental health issues have been reported after SARS-CoV-2 infection. However, comparison to prevalence in uninfected individuals and contribution from common risk factors (eg, obesity and comorbidities) have not been examined. We identified how COVID-19 relates to mental health in the large community-based COVID Symptom Study. // Methods: We assessed anxiety and depression symptoms using two validated questionnaires in 413148 individuals between February and April 2021; 26998 had tested positive for SARS-CoV-2. We adjusted for physical and mental prepandemic comorbidities, body mass index (BMI), age and sex. // Findings: Overall, 26.4% of participants met screening criteria for general anxiety and depression. Anxiety and depression were slightly more prevalent in previously SARS-CoV-2-positive (30.4%) vs SARS-CoV-2-negative (26.1%) individuals. This association was small compared with the effect of an unhealthy BMI and the presence of other comorbidities, and not evident in younger participants (≤40 years). Findings were robust to multiple sensitivity analyses. Association between SARS-CoV-2 infection and anxiety and depression was stronger in individuals with recent (120 days) infection, suggesting a short-term effect. // Interpretation: A small association was identified between SARS-CoV-2 infection and anxiety and depression symptoms. The proportion meeting criteria for self-reported anxiety and depression disorders is only slightly higher than prepandemic

Probable delirium is a presenting symptom of COVID-19 in frail, older adults: a cohort study of 322 hospitalised and 535 community-based older adults

BACKGROUND: Frailty, increased vulnerability to physiological stressors, is associated with adverse outcomes. COVID-19 exhibits a more severe disease course in older, comorbid adults. Awareness of atypical presentations is critical to facilitate early identification. OBJECTIVE: To assess how frailty affects presenting COVID-19 symptoms in older adults. DESIGN: Observational cohort study of hospitalised older patients and self-report data for community-based older adults. SETTINGS: Admissions to St Thomas’ Hospital, London with laboratory-confirmed COVID-19. Community-based data for older adults using the COVID Symptom Study mobile application. SUBJECTS: Hospital cohort: patients aged 65 and over (n = 322); unscheduled hospital admission between 1 March 2020 and 5 May 2020; COVID-19 confirmed by RT-PCR of nasopharyngeal swab. Community-based cohort: participants aged 65 and over enrolled in the COVID Symptom Study (n = 535); reported test-positive for COVID-19 from 24 March (application launch) to 8 May 2020. METHODS: Multivariable logistic regression analysis performed on age-matched samples from hospital and community-based cohorts to ascertain association of frailty with symptoms of confirmed COVID-19. RESULTS: Hospital cohort: significantly higher prevalence of probable delirium in the frail sample, with no difference in fever or cough. Community-based cohort: significantly higher prevalence of possible delirium in frailer, older adults and fatigue and shortness of breath. CONCLUSIONS: This is the first study demonstrating higher prevalence of probable delirium as a COVID-19 symptom in older adults with frailty compared to other older adults. This emphasises need for systematic frailty assessment and screening for delirium in acutely ill older patients in hospital and community settings. Clinicians should suspect COVID-19 in frail adults with delirium