Topics in Graph Theory: Extremal Intersecting Systems, Perfect Graphs, and Bireflexive Graphs

In this thesis we investigate three different aspects of graph theory. Firstly, we consider interesecting systems of independent sets in graphs, and the extension of the classical theorem of Erdos, Ko and Rado to graphs. Our main results are a proof of an Erdos-Ko-Rado type theorem for a class of trees, and a class of trees which form counterexamples to a conjecture of Hurlberg and Kamat, in such a way that extends the previous counterexamples given by Baber. Secondly, we investigate perfect graphs - specifically, edge modification aspects of perfect graphs and their subclasses. We give some alternative characterisations of perfect graphs in terms of edge modification, as well as considering the possible connection of the critically perfect graphs - previously studied by Wagler - to the Strong Perfect Graph Theorem. We prove that the situation where critically perfect graphs arise has no analogue in seven different subclasses of perfect graphs (e.g. chordal, comparability graphs), and consider the connectivity of a bipartite reconfiguration-type graph associated to each of these subclasses. Thirdly, we consider a graph theoretic structure called a bireflexive graph where every vertex is both adjacent and nonadjacent to itself, and use this to characterise modular decompositions as the surjective homomorphisms of these structures. We examine some analogues of some graph theoretic notions and define a “dual” version of the reconstruction conjecture

Social capital and geographical variation in the incidence of COVID-19: an ecological study

BACKGROUND: The new behavioural norms needed to reduce the spread of COVID-19 are likely scaffolded by social capital. Research on social capital and COVID-19 has yielded mixed results, with some studies finding it to be protective while others identifying it as a risk factor. We examined the association between social capital and COVID-19 at a finer spatial scale than previous research, and examined changes in the relationship over the course of the pandemic. METHODS: Routine COVID-19 surveillance data from Wales were linked to estimates of social capital at a small area level. Generalised linear mixed effects models predicting COVID-19 case rates across areas using social capital estimates and possible confounding variables were fitted to the data. A moving window version of the analysis explored whether this relationship varied across time. RESULTS: Areas with higher levels of social capital had lower rates of COVID-19 (rate ratio for trust=0.94, 95% CI 0.92 to 0.96; rate ratio for belonging=0.94, 95% CI 0.92 to 0.96). These associations were strongest during periods of lockdown, with evidence that social capital was less protective, and potentially even a risk factor, during periods when restrictions were eased. Trust, but not belonging, remained protective after adjusting for deprivation, population density, ethnicity and proportion population aged over 65 years. CONCLUSIONS: Social capital is an important public health resource, which should be considered in future pandemic preparedness. Its importance may be greatest during times when social activity is most restricted

Covid and the common good: In-group out-group dynamics and Covid-19 vaccination in Wales and the United States

Vaccination is a social act, where benefits spill-over to third parties. How we approach such social decisions is influenced by whether likely beneficiaries share salient social identities with us. This study explores these dynamics using representative survey data from two contexts: national identity groups in Wales (N=4187) and political partisans in America (N=4864). In both cases, those in the minority in their local area were less likely to be vaccinated. In Wales, respondents who did not identify as Welsh were less likely to be vaccinated the greater the proportion of residents of their local area identified as Welsh. In America, the vaccination rate of Biden voters fell off more steeply than that of Trump voters as the proportion of Trump voters in their county increased. Results are robust to controlling for likely confounds and sensitivity analyses. In-group out-group dynamics help to shape important health decisions

large decrease in clinical notifications and epidemiological investigation questionnaires for laboratory-confirmed cases after the 2nd epidemic wave, Portugal March 2020–July 2021

Funding Information: The present publication was funded by Fundação Ciência e Tecnologia, IP national support through CHRC (UIDP/04923/2020). Publisher Copyright: Copyright © 2023 Ricoca Peixoto, Vieira, Aguiar, Sentis, Carvalho, Rhys Thomas, Abrantes and Nunes.Introduction: In Portugal, COVID-19 laboratory notifications, clinical notifications (CNs), and epidemiological investigation questionnaires (EI) were electronically submitted by laboratories, clinicians, and public health professionals, respectively, to the Portuguese National Epidemiological Surveillance System (SINAVE), as mandated by law. We described CN and EI completeness in SINAVE to inform pandemic surveillance efforts. Methods: We calculated the proportion of COVID-19 laboratory-notified cases without CN nor EI, and without EI by region and age group, in each month, from March 2020 to July 2021. We tested the correlation between those proportions and monthly case counts in two epidemic periods and used Poisson regression to identify factors associated with the outcomes. Results: The analysis included 909,720 laboratory-notified cases. After October 2020, an increase in the number of COVID-19 cases was associated with a decrease in the submissions of CN and EI. By July 2021, 68.57% of cases had no associated CN nor EI, and 96.26% had no EI. Until January 2021, there was a positive correlation between monthly case counts and the monthly proportion of cases without CN nor EI and without EI, but not afterward. Cases aged 75 years or older had a lower proportion without CN nor EI (aRR: 0.842 CI95% 0.839–0.845). When compared to the Norte region, cases from Alentejo, Algarve, and Madeira had a lower probability of having no EI (aRR;0.659 CI 95%0.654–0.664; aRR 0.705 CI 95% 0.7–0.711; and aRR 0.363 CI 95% 0.354–0.373, respectively). Discussion: After January 2021, CN and EI were submitted in a small proportion of laboratory-confirmed cases, varying by age and region. Facing the large number of COVID-19 cases, public health services may have adopted other registry strategies including new surveillance and management tools to respond to operational needs. This may have contributed to the abandonment of official CN and EI submission. Useful knowledge on the context of infection, symptom profile, and other knowledge gaps was no longer adequately supported by SINAVE. Regular evaluation of pandemic surveillance systems' completeness is necessary to inform surveillance improvements and procedures considering dynamic objectives, usefulness, acceptability, and simplicity.publishersversionpublishe

Initial assessment of the impact of the emergency state lockdown measures on the 1st wave of the COVID-19 epidemic in Portugal

Introduction: Portugal took early action to control the COVID-19 epidemic, initiating lockdown measures on March 16th when it recorded only 62 cases of COVID-19 per million inhabitants and reported no deaths. The Portuguese public complied quickly, reducing their overall mobility by 80%. The aim of this study was to estimate the initial impact of the lockdown in Portugal in terms of the reduction of the burden on the healthcare system. Material and Methods: We forecasted epidemic curves for: Cases, hospital inpatients (overall and in intensive care), and deaths without lockdown, assuming that the impact of containment measures would start 14 days after initial lockdown was implemented. We used exponential smoothing models for deaths, intensive care and hospitalizations and an ARIMA model for number of cases. Models were selected considering fitness to the observed data up to the 31st March 2020. We then compared observed (with intervention) and forecasted curves (without intervention). Results: Between April 1st and April 15th, there were 146 fewer deaths (-25%), 5568 fewer cases (-23%) and, as of April 15th, there were 519 fewer intensive care inpatients (-69%) than forecasted without the lockdown. On April 15th, the number of intensive care inpatients could have reached 748, three times higher than the observed value (229) if the intervention had been delayed. Discussion: If the lockdown had not been implemented in mid-March, Portugal intensive care capacity (528 beds) would have likely been breached during the first half of April. The lockdown seems to have been effective in reducing transmission of SARS-CoV-2, serious COVID-19 disease, and associated mortality, thus decreasing demand on health services. Conclusion: An early lockdown allowed time for the National Health Service to mobilize resources and acquire personal protective equipment, increase testing, contact tracing and hospital and intensive care capacity and to promote broad prevention and control measures. When lifting more stringent measures, strong surveillance and communication strategies that mobilize individual prevention efforts are necessary.publishe

Developing a population data science approach to assess increased risk of COVID-19 associated with attending large sporting events.

Objectives To design and test a method to assess whether test events were associated with an increase in risk of confirmed COVID-19, in order to inform policy on the safe re-introduction of spectator events following decreasing incidence of COVID-19 and relaxing of restrictions. Approach We designed a cohort study to measure relative risk of confirmed COVID-19 in those attending two large sporting events in South Wales during May-June 2021. First, we linked ticketing information to records on the Welsh Demographic Service (WDS) and identified NHS numbers for attendees. We then linked attendees to routine SARS-CoV-2 test data to calculate incidence rates in people attending each event for a fourteen days period following the event.  We selected a comparison cohort from WDS for each event, individually matched by age band, gender and locality of residence. Risk ratios were then computed for the two events. Results We successfully assigned NHS numbers to 91% and 84% of people attending the two events, respectively. Other identifiers were available for the remainder. Only a small number of attendees (1) than event 2 (<1), which did include pre-event testing. Conclusions We demonstrate the potential for data linkage to inform COVID-19 policy regarding sporting events. At that point in the epidemic, there was no evidence that attending large sporting events increased risk of COVID-19. However, these events took place between epidemic waves when background incidence and testing rate was low

Defining causality in COVID-19 and neurological disorders.

When faced with acute neurological presentations in a patient with COVID-19, how confident can one be that SARS-CoV2 is causal

Utilising accessible and reproducible neurological assessments in clinical studies: Insights from use of the Neurological Impairment Scale in the multi-centre COVID-CNS study

Reproducible and standardised neurological assessment scales are important in quantifying research outcomes. These scales are often performed by non-neurologists and/or non-clinicians and must be robust, quantifiable, reproducible and comparable to a neurologist's assessment. COVID-CNS is a multi-centre study which utilised the Neurological Impairment Scale (NIS) as a core assessment tool in studying neurological outcomes following COVID-19 infection. We investigated the strengths and weaknesses of the NIS when used by non-neurology clinicians and non-clinicians, and compared performance to a structured neurological examination performed by a neurology clinician. Through our findings, we provide practical advice on how non-clinicians can be readily trained in conducting reproducible and standardised neurological assessments in a multi-centre study, as well as illustrating potential pitfalls of these tools