Combining models to generate consensus medium-term projections of hospital admissions, occupancy and deaths relating to COVID-19 in England (preprint)

Mathematical modelling has played an important role in offering informed advice during the COVID-19 pandemic. In England, a cross government and academia collaboration generated Medium-Term Projections (MTPs) of possible epidemic trajectories over the future 4-6 weeks from a collection of epidemiological models.In this paper we outline this collaborative modelling approach and evaluate the accuracy of the combined and individual model projections against the data over the period November 2021-December 2022 when various Omicron subvariants were spreading across England. Using a number of statistical methods, we quantify the predictive performance of the model projections for both the combined and individual MTPs, by evaluating the point and probabilistic accuracy. Our results illustrate that the combined MTPs, produced from an ensemble of heterogeneous epidemiological models, were a closer fit to the data than the individual models during the periods of epidemic growth or decline, with the 90% confidence intervals widest around the epidemic peaks. We also show that the combined MTPs increase the robustness and reduce the biases associated with a single model projection. Learning from our experience of ensemble modelling during the COVID-19 epidemic, our findings highlight the importance of developing cross-institutional multi-model infectious disease hubs for future outbreak control.

Viral burdens are associated with age and viral variant in a population-representative study of SARS-CoV-2 that accounts for time-since-infection related sampling bias. (preprint)

In this study, we evaluated the impact of viral variant, in addition to other variables, on within-host viral burdens, by analysing cycle threshold (Ct) values derived from nose and throat swabs, collected as part of the UK COVID-19 Infection Survey. Because viral burden distributions determined from community survey data can be biased due to the impact of variant epidemiology on the time-since-infection of samples, we developed a method to explicitly adjust observed Ct value distributions to account for the expected bias. Analysing the adjusted Ct values using partial least squares regression, we found that among unvaccinated individuals with no known prior infection, the average Ct value was 0.94 lower among Alpha variant infections, compared those with the predecessor strain, B.1.177. However, among vaccinated individuals, it was 0.34 lower among Delta variant infections, compared to those with the Alpha variant. In addition, the average Ct value decreased by 0.20 for every 10 year age increment of the infected individual. In summary, within-host viral burdens are associated with age, in addition to the interplay of vaccination status and viral variant.

Analysis and comprehensive lineage identification for SARS-CoV-2 genomes through scalable learning methods (preprint)

Since its emergence in late 2019, SARS-CoV-2 has diversified into a large number of lineages and globally caused multiple waves of infection. Lineages have the potential to spread rapidly and internationally if they have higher intrinsic transmissibility and/or can evade host immune responses, as has been seen with the Alpha, Delta, and Omicron variants of concern (VoCs). Phylogenetic methods provide the gold standard for representing the global diversity of SARS-CoV-2 and to identify newly emerging lineages. However, these methods are computationally expensive, struggle when datasets get too large, and require manual curation to designate new lineages. These issues will only intensify as the vast number of SARS-CoV-2 genomes already available continues to grow. It will therefore be beneficial to develop complementary methods that can incorporate all of the genetic data available, without down sampling, to extract meaningful information rapidly and with minimal curation. Here, we demonstrate the utility of using algorithmic approaches based on word-statistics to represent whole sequences, bringing speed, scalability, and interpretability to the construction of genetic topologies, and that can be used to augment traditional classification practice based on phylogeny.

Association between household composition and severe COVID-19 outcomes in older people by ethnicity: an observational cohort study using the OpenSAFELY platform (preprint)

Background Ethnic differences in the risk of severe COVID-19 may be linked to household composition. We quantified the association between household composition and risk of severe COVID-19 by ethnicity for older individuals. Methods With the approval of NHS England, we analysed ethnic differences in the association between household composition and severe COVID-19 in people aged 67 or over in England. We defined households by number of generations living together, and used multivariable Cox regression stratified by location and wave of the pandemic and accounted for age, sex, comorbidities, smoking, obesity, housing density and deprivation. We included 2 692 223 people over 67 years in wave 1 (01/02/2020-31/08/2020) and 2 731 427 in wave 2 (01/09/2020-31/01/2021). Findings Multigenerational living was associated with increased risk of severe COVID-19 for White and South Asian older people in both waves (e.g. wave 2, 67+ living with 3 other generations vs 67+ year olds only: White HR 1.61 95% CI 1.38-1.87, South Asian HR 1.76 95% CI 1.48-2.10), with a trend for increased risks of severe COVID-19 with increasing generations in wave 2. Interpretation Multigenerational living was associated with severe COVID-19 in older adults. Older South Asian people are over-represented within multigenerational households in England, especially in the most deprived settings. The number of generations in a household, number of occupants, ethnicity and deprivation status are important considerations in the continued roll-out of COVID-19 vaccination and targeting of interventions for future pandemics. Funding This research was funded in part, by the Wellcome Trust. For the purpose of open access, the author has applied a CC-BY public copyright licence to any Author Accepted Manuscript version arising from this submission.

Modelling the impact of non-pharmaceutical interventions on workplace transmission of SARS-CoV-2 in the home-delivery sector (preprint)

Objective: We aimed to use mathematical models of SARS-COV-2 to assess the potential efficacy of non-pharmaceutical interventions on transmission in the parcel delivery and logistics sector. Methods: We developed a network-based model of workplace contacts based on data and consultations from companies in the parcel delivery and logistics sectors. We used these in stochastic simulations of disease transmission to predict the probability of workplace outbreaks in this settings. Individuals in the model have different viral load trajectories based on SARS-CoV-2 in-host dynamics, which couple to their infectiousness and test positive probability over time, in order to determine the impact of testing and isolation measures. Results: The baseline model (without any interventions) showed different workplace infection rates for staff in different job roles. Based on our assumptions of contact patterns in the parcel delivery work setting we found that when a delivery driver was the index case, on average they infect only 0.18 other employees , while for warehouse and office workers this went up to 0.93 and 2.58 respectively. In the large-item delivery setting this was predicted to be 0.83, 0.94, and 1.61 respectively. Nonetheless, the vast majority of simulations resulted in $0$ secondary cases among customers (even without contact-free delivery). Our results showed that a combination of social distancing, office staff working from home, and fixed driver pairings (all interventions carried out by the companies we consulted) reduce the risk of workplace outbreaks by 3-4 times. Conclusion: This work suggests that, without interventions, significant transmission could occur in these workplaces, but that these pose minimal risk to customers. We found that identifying and isolating regular close-contacts of infectious individuals (i.e. house-share, carpools, or delivery pairs) is an efficient measure for stopping workplace outbreaks. Regular testing can make these isolation measures even more effective but also increases the number of staff isolating at one time. It is therefore more efficient to combine these measures with social distancing and contact reduction interventions, as these reduce both transmission and the number of people needing to isolate.

Novel methods for estimating the instantaneous and overall COVID-19 case fatality risk among care home residents in England (preprint)

The COVID-19 pandemic has had high mortality rates in the elderly and frail worldwide, particularly in care homes. This is driven by the difficulty of isolating care homes from the wider community, the large population sizes within care facilities (relative to typical households), and the age/frailty of the residents. To quantify the mortality risk posed by disease, the case fatality risk (CFR) is an important tool. This quantifies the proportion of cases that result in death. Throughout the pandemic, CFR amongst care home residents in England has been monitored closely. To estimate CFR, we apply both novel and existing methods to data on deaths in care homes, collected by Public Health England and the Care Quality Commission. We compare these different methods, evaluating their relative strengths and weaknesses. Using these methods, we estimate temporal trends in the instantaneous CFR (at both daily and weekly resolutions) and the overall CFR across the whole of England, and dis-aggregated at regional level. We also investigate how the CFR varies based on age and on the type of care required, dis-aggregating by whether care homes include nursing staff and by age of residents. This work has contributed to the summary of measures used for monitoring the UK epidemic.

Impact of voluntary risk-mitigation behaviour on transmission of the Omicron SARS-CoV-2 variant in England (preprint)

Abstract Background The Omicron variant of SARS-CoV-2 infection poses substantial challenges to public health. In England, "plan B" mitigation measures were introduced in December 2021 including increased home working and face coverings in shops, but stopped short of restrictions on social contacts. The impact of voluntary risk mitigation behaviours on future SARS-CoV-2 burden is unknown. Methods We developed a rapid online survey of risk mitigation behaviours during the winter 2021 festive period and deployed in two longitudinal cohort studies in the UK (Avon Longitudinal Study of Parents and Children (ALSPAC) and TwinsUK/Covid Symptom Study (CSS) Biobank) in December 2021. Using an individual-based, probabilistic model of COVID-19 transmission between social contacts with SARS-CoV-2 Omicron variant parameters and realistic vaccine coverage in England, we describe the potential impact of the SARS-CoV-2 Omicron wave in England in terms of the effective reproduction number and cumulative infections, hospital admissions and deaths. Using survey results, we estimated in real-time the impact of voluntary risk mitigation behaviours on the Omicron wave in England, if implemented for the entire epidemic wave. Results Over 95% of survey respondents (N_ALSPAC=2,686 and N_Twins=6,155) reported some risk mitigation behaviours, with being fully vaccinated and using home testing kits the most frequently reported behaviours. Less than half of those respondents reported that their behaviour was due to "plan B". We estimate that without risk mitigation behaviours, the Omicron variant is consistent with an effective reproduction number between 2.5 and 3.5. Due to the reduced vaccine effectiveness against infection with the Omicron variant, our modelled estimates suggest that between 55% and 60% of the English population could be infected during the current wave, translating into between 15,000 and 46,000 cumulative deaths, depending on assumptions about vaccine effectiveness. We estimate that voluntary risk reduction measures could reduce the effective reproduction number to between 1.8 and 2.2 and reduce the cumulative number of deaths by up to 24%. Conclusions We conclude that voluntary measures substantially reduce the projected impact of the SARS-CoV-2 Omicron variant, but that voluntary measures alone would be unlikely to completely control transmission.

A computational framework for modelling infectious disease policy based on age and household structure with applications to the COVID-19 pandemic (preprint)

The widespread, and in many countries unprecedented, use of non-pharmaceutical interventions (NPIs) during the COVID-19 pandemic has highlighted the need for mathematical models which can estimate the impact of these measures while accounting for the highly heterogeneous risk profile of COVID-19. Models accounting either for age structure or the household structure necessary to explicitly model many NPIs are commonly used in infectious disease modelling, but models incorporating both levels of structure present substantial computational and mathematical challenges due to their high dimensionality. Here we present a modelling framework for the spread of an epidemic that includes explicit representation of age structure and household structure. Our model is formulated in terms of tractable systems of ordinary differential equations for which we provide an open-source Python implementation. Such tractability leads to significant benefits for model calibration, exhaustive evaluation of possible parameter values, and interpretability of results. We demonstrate the flexibility of our model through four policy case studies, where we quantify the likely benefits of the following measures which were either considered or implemented in the UK during the current COVID-19 pandemic: control of within- and between-household mixing through NPIs; formation of support bubbles during lockdown periods; out-of-household isolation (OOHI); and temporary relaxation of NPIs during holiday periods. Our ordinary differential equation formulation and associated analysis demonstrate that multiple dimensions of risk stratification and social structure can be incorporated into infectious disease models without sacrificing mathematical tractability. This model and its software implementation expand the range of tools available to infectious disease policy analysts.

Short-term Projections based on Early Omicron Variant Dynamics in England (preprint)

Throughout the ongoing COVID-19 pandemic, the worldwide transmission and replication of SARS-COV-2, the causative agent of COVID-19 disease, has resulted in the opportunity for multiple mutations to occur that may alter the virus transmission characteristics, the effectiveness of vaccines and the severity of disease upon infection. The Omicron variant (B.1.1.529) was first reported to the WHO by South Africa on 24 November 2021 and was declared a variant of concern by the WHO on 26 November 2021. The variant was first detected in the UK on 27 November 2021 and has since been reported in a number of countries globally where it is frequently associated with rapid increase in cases. Here we present analyses of UK data showing the earliest signatures of the Omicron variant and mathematical modelling that uses the UK data to simulate the potential impact of this variant in the UK. In order to account for the uncertainty in transmission advantage, vaccine escape and severity at the time of writing, we carry out a sensitivity analysis to assess the impact of these variant characteristics on future risk.

Early signals of Omicron severity in sentinel UK hospitals (preprint)

On 26th November 2021, a novel SARS-CoV-2 variant B.1.1.529 (Omicron variant) was designated as a variant of concern by the World Health Organisation. Using data from the Virology laboratory at the Manchester Medical Microbiology Partnership (MMMP, a partnership between UKHSA and the Manchester Foundation Trust), we have extracted a real-time feed of Omicron samples from hospitals across Greater Manchester, an area of the United Kingdom with a population size of approximately three million individuals. Omicron hospital samples are growing exponentially across Greater Manchester (doubling time 2.7 days (95% CI: 2.1, 3.7)). The proportion of Omicron in hospital samples follows a similar trajectory to the SGTF proportion in cases, but with a two-day offset. This is consistent with the delay from testing positive to hospital admission, implying a similar proportion of Omicron cases are converting to hospital admissions as for Delta cases. Comparing the Greater Manchester data to national hospitalisation data, similar tends are observed. Therefore, there is no signal of a substantial reduction in hospital admission risk with Omicron, and Omicron epidemics are likely to place a substantial burden on public health infrastructure.

Transmission dynamics of SARS-CoV-2 in a strictly-Orthodox Jewish community in the UK (preprint)

Some social settings such as households and workplaces, have been identified as high risk for SARS-CoV-2 transmission. Identifying and quantifying the importance of these settings is critical for designing interventions. A tightly-knit religious community in the UK experienced a very large COVID-19 epidemic in 2020, reaching 64.3% seroprevalence within 10 months, and we surveyed this community both for serological status and individual-level attendance at particular settings. Using these data, and a network model of people and places represented as a stochastic graph rewriting system, we estimated the relative contribution of transmission in households, schools and religious institutions to the epidemic, and the relative risk of infection in each of these settings. All congregate settings were important for transmission, with some such as primary schools and places of worship having a higher share of transmission than others. We found that the model needed a higher general-community transmission rate for women (3.3-fold), and lower susceptibility to infection in children to recreate the observed serological data. The precise share of transmission in each place was related to assumptions about the internal structure of those places. Identification of key settings of transmission can allow public health interventions to be targeted at these locations.

EpiBeds: Data informed modelling of the COVID-19 hospital burden in England (preprint)

The first year of the COVID-19 pandemic put considerable strain on the national healthcare system in England. In order to predict the effect of the local epidemic on hospital capacity in England, we used a variety of data streams to inform the construction and parameterisation of a hospital progression model, which was coupled to a model of the generalised epidemic. We named this model EpiBeds. Data from a partially complete patient-pathway line-list was used to provide initial estimates of the mean duration that individuals spend in the different hospital compartments. We then fitted EpiBeds using complete data on hospital occupancy and hospital deaths, enabling estimation of the proportion of individuals that follow different clinical pathways, and the reproduction number of the generalised epidemic. The construction of EpiBeds makes it straightforward to adapt to different patient pathways and settings beyond England. As part of the UK response to the pandemic, EpiBeds has provided weekly forecasts to the NHS for hospital bed occupancy and admissions in England, Wales, Scotland, and Northern Ireland.

Total Effect Analysis of Vaccination on Household Transmission in the Office for National Statistics COVID-19 Infection Survey (preprint)

We investigate the distribution of numbers of secondary cases in households in the Office for National Statistics COVID-19 Infection Survey (ONS CIS), stratified by timing of vaccination and infection in the households. This shows a total effect of a statistically significant approximate halving of the secondary attack rate in households following vaccination.

Possible future waves of SARS-CoV-2 infection generated by variants of concern with a range of characteristics (preprint)

Ongoing infection with, and associated viral reproduction of, SARS-CoV-2 provides opportunities for the virus to acquire advantageous mutations, which may alter viral transmissibility and disease severity, and allow escape from natural or vaccine-derived immunity. The number of countries reporting Variants of Concern (VOCs) with such mutations continues to rise. Here, we investigate two scenarios for third waves of the COVID pandemic: one driven by increased transmissibility, and another driven by immune escape. We do this using three mathematical models: a parsimonious susceptible-latent-infectious-recovered (SEIR) deterministic model with homogeneous mixing, an age-structured SARS-CoV-2 transmission model and a stochastic importation model. We calibrated our models to the situation in England in May 2021, although the insights will generalise to other contexts. We therefore accurately captured infection dynamics and vaccination rates, and also used these to explore the potential impact of a putative new VOC-targeted vaccine. Epidemiological trajectories for putative VOCs are wide-ranging and heavily dependent on their transmissibility, immune escape capability, and the time at which a postulated VOC-targeted vaccine may be introduced. We demonstrate that a VOC with either a substantial transmission advantage over resident variants, or the ability to evade vaccine-derived and prior immunity, is expected to generate a wave of infections and hospitalisations comparable to those seen in the winter 2020-21 wave. Moreover, a variant that is less transmissible, but shows partial immune-escape could provoke a wave of infection that would not be revealed until control measures are further relaxed.

Early epidemiological signatures of novel SARS-CoV-2 variants: establishment of B.1.617.2 in England (preprint)

The rapid emergence of SARS-CoV-2 mutants with new phenotypic properties is a critical challenge to the control of the ongoing pandemic. B.1.1.7 was monitored in the UK through routine testing and S-gene target failures (SGTF), comprising over 90% of cases by March 2021. Now, the reverse is occurring: SGTF cases are being replaced by an S-gene positive variant, which we associate with B.1.617.2. Evidence from the characteristics of S-gene positive cases demonstrates that, following importation, B.1.617.2 is transmitted locally, growing at a rate higher than B.1.1.7 and a doubling time between 5-14 days. S-gene positive cases should be prioritised for sequencing and aggressive control in any countries in which this variant is newly detected.

Inferring Risks of Coronavirus Transmission from Community Household Data (preprint)

The response of many governments to the COVID-19 pandemic has involved measures to control within- and between-household transmission, providing motivation to improve understanding of the absolute and relative risks in these contexts. Here, we perform exploratory, residual-based, and transmission-dynamic household analysis of the Office for National Statistics (ONS) COVID-19 Infection Survey (CIS) data from 26 April 2020 to 15 July 2021 in England. This provides evidence for: (i) temporally varying rates of introduction of infection into households broadly following the trajectory of the overall epidemic and vaccination programme; (ii) Susceptible-Infectious Transmission Probabilities (SITPs) of within-household transmission in the 15-35% range; (iii) the emergence of the Alpha and Delta variants, with the former being around 50% more infectious than wildtype and 35% less infectious than Delta within households; (iv) significantly (in the range 25-300%) more risk of bringing infection into the household for workers in patient-facing roles pre-vaccine; (v) increased risk for secondary school-age children of bringing the infection into the household when schools are open; (vi) increased risk for primary school-age children of bringing the infection into the household when schools were open since the emergence of new variants.

Using a household structured branching process to analyse contact tracing in the SARS-CoV-2 pandemic (preprint)

We explore strategies of contact tracing, case isolation and quarantine of exposed contacts to control the SARS-CoV-2 epidemic using a branching process model with household structure. This structure reflects higher transmission risks among household members than among non-household members, and is also the level at which physical distancing policies have been applied. We explore implementation choices that make use of household structure, and investigate strategies including two-step tracing, backwards tracing, smartphone tracing and tracing upon symptom report rather than test results. The primary model outcome is the effect on the growth rate of the epidemic under contact tracing in combination with different levels of physical distancing, and we investigate epidemic extinction times to indicate the time period over which interventions must be sustained. We consider effects of non-uptake of isolation/quarantine, non-adherence, and declining recall of contacts over time. We find that compared to self-isolation of cases but no contact tracing, a household-based contact tracing strategy allows for some relaxation of physical distancing measures; however, it is unable to completely control the epidemic in the absence of other measures. Even assuming no imported cases and sustainment of moderate distancing, testing and tracing efforts, the time to bring the epidemic to extinction could be in the order of months to years.

A renewal equation model to assess roles andlimitations of contact tracing for diseaseoutbreak control (preprint)

We propose a deterministic model capturing essential features of contact tracing as part of public health non-pharmaceutical interventions to mitigate an outbreak of an infectious disease. By incorporating a mechanistic formulation of the processes at the individual level, we obtain an integral equation (delayed in calendar time and advanced in time since infection) for the probability that an infected individual is detected and isolated at any point in time. This is then coupled with a renewal equation for the total incidence to form a closed system describing the transmission dynamics involving contact tracing. We define and calculate basic and effective reproduction numbers in terms of pathogen characteristics and contact tracing implementation constraints. When applied to the case of SARS-CoV-2, our results show that only combinations of diagnosis of symptomatic infections and contact tracing that are almost perfect in terms of speed and coverage can attain control, unless additional measures to reduce overall community transmission are in place. Under constraints on the testing or tracing capacity, a temporary interruption of contact tracing may, depending on the overall growth rate and prevalence of the infection, lead to an irreversible loss of control even when the epidemic was previously contained.

Short-term forecasts to inform the response to the COVID-19 epidemic in the UK (preprint)

Background: Short-term forecasts of infectious disease can create situational awareness and inform planning for outbreak response. Here, we report on multi-model forecasts of Covid-19 in the UK that were generated at regular intervals starting at the end of March 2020, in order to monitor expected healthcare utilisation and population impacts in real time. Methods: We evaluated the performance of individual model forecasts generated between 24 March and 14 July 2020, using a variety of metrics including the weighted interval score as well as metrics that assess the calibration, sharpness, bias and absolute error of forecasts separately. We further combined the predictions from individual models to ensemble forecasts using a simple mean as well as a quantile regression average that aimed to maximise performance. We further compared model performance to a null model of no change. Results: In most cases, individual models performed better than the null model, and ensembles models were well calibrated and performed comparatively to the best individual models. The quantile regression average did not noticeably outperform the mean ensemble. Conclusions: Ensembles of multi-model forecasts can inform the policy response to the Covid-19 pandemic by assessing future resource needs and expected population impact of morbidity and mortality.