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

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 devloped 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 0.14 other employees, while for warehouse and office workers this went up to 0.65 and 2.24 respectively. In the LIDD setting this was predicted to be 1.40, 0.98, and 1.34 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 have occured in these workplaces, but that these posed 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 use these isolation measures in addition to social distancing and contact reduction interventions, rather than instead of, as these reduce both transmission and the number of people needing to isolate at one time.

Estimation of reproduction numbers in real time: Conceptual and statistical challenges.

The reproduction number R has been a central metric of the COVID-19 pandemic response, published weekly by the UK government and regularly reported in the media. Here, we provide a formal definition and discuss the advantages and most common misconceptions around this quantity. We consider the intuition behind different formulations of R , the complexities in its estimation (including the unavoidable lags involved), and its value compared to other indicators (e.g. the growth rate) that can be directly observed from aggregate surveillance data and react more promptly to changes in epidemic trend. As models become more sophisticated, with age and/or spatial structure, formulating R becomes increasingly complicated and inevitably model-dependent. We present some models currently used in the UK pandemic response as examples. Ultimately, limitations in the available data streams, data quality and time constraints force pragmatic choices to be made on a quantity that is an average across time, space, social structure and settings. Effectively communicating these challenges is important but often difficult in an emergency.

Inferring risks of coronavirus transmission from community household data.

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 COVID-19 Infection Survey 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 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 of 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.

Commentary on the use of the reproduction number R during the COVID-19 pandemic.

Since the beginning of the COVID-19 pandemic, the reproduction number [Formula: see text] has become a popular epidemiological metric used to communicate the state of the epidemic. At its most basic, [Formula: see text] is defined as the average number of secondary infections caused by one primary infected individual. [Formula: see text] seems convenient, because the epidemic is expanding if [Formula: see text] and contracting if [Formula: see text]. The magnitude of [Formula: see text] indicates by how much transmission needs to be reduced to control the epidemic. Using [Formula: see text] in a naïve way can cause new problems. The reasons for this are threefold: (1) There is not just one definition of [Formula: see text] but many, and the precise definition of [Formula: see text] affects both its estimated value and how it should be interpreted. (2) Even with a particular clearly defined [Formula: see text], there may be different statistical methods used to estimate its value, and the choice of method will affect the estimate. (3) The availability and type of data used to estimate [Formula: see text] vary, and it is not always clear what data should be included in the estimation. In this review, we discuss when [Formula: see text] is useful, when it may be of use but needs to be interpreted with care, and when it may be an inappropriate indicator of the progress of the epidemic. We also argue that careful definition of [Formula: see text], and the data and methods used to estimate it, can make [Formula: see text] a more useful metric for future management of the epidemic.

Voluntary risk mitigation behaviour can reduce impact of SARS-CoV-2: a real-time modelling study of the January 2022 Omicron wave in England.

BACKGROUND: Predicting the likely size of future SARS-CoV-2 waves is necessary for public health planning. In England, voluntary "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 ahead of 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 predicted 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 (NALSPAC = 2686 and NTwins = 6155) reported some risk mitigation behaviours, with vaccination and using home testing kits reported most frequently. 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 12,000 and 46,000 cumulative deaths, depending on assumptions about severity and vaccine effectiveness. The actual number of deaths was 15,208 (26 November 2021-1 March 2022). 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: Predicting future infection burden is affected by uncertainty in disease severity and vaccine effectiveness estimates. In addition to biological uncertainty, we show 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.

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

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.

EpiBeds: Data informed modelling of the COVID-19 hospital burden in England.

The first year of the COVID-19 pandemic put considerable strain on healthcare systems worldwide. 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, EpiBeds, which was coupled to a model of the generalised epidemic. In this model, individuals progress through different pathways (e.g. may recover, die, or progress to intensive care and recover or die) and 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 the different clinical pathways, the reproduction number of the generalised epidemic, and to make short-term predictions of hospital bed demand. 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 provided weekly forecasts to the NHS for hospital bed occupancy and admissions in England, Wales, Scotland, and Northern Ireland at national and regional scales.

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

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.

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

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 age-based 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 (1 February 2020-31 August 2020) and 2 731 427 in Wave 2 (1 September 2020-31 January 2021). RESULTS: 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 three other generations vs 67+-year-olds only: White hazard ratio (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. There was also an increased risk of severe COVID-19 in Wave 1 associated with living alone for White (HR 1.35 95% CI 1.30-1.41), South Asian (HR 1.47 95% CI 1.18-1.84) and Other (HR 1.72 95% CI 0.99-2.97) ethnicities, an effect that persisted for White older people in Wave 2. CONCLUSIONS: Both multigenerational living and living alone were 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, whereas a substantial proportion of White older people live alone. 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.

Transmission dynamics of SARS-CoV-2 in a strictly-Orthodox Jewish community in the UK.

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.

The challenges of data in future pandemics.

The use of data has been essential throughout the unfolding COVID-19 pandemic. We have needed it to populate our models, inform our understanding, and shape our responses to the disease. However, data has not always been easy to find and access, it has varied in quality and coverage, been difficult to reuse or repurpose. This paper reviews these and other challenges and recommends steps to develop a data ecosystem better able to deal with future pandemics by better supporting preparedness, prevention, detection and response.

Modelling: Understanding pandemics and how to control them.

New disease challenges, societal demands and better or novel types of data, drive innovations in the structure, formulation and analysis of epidemic models. Innovations in modelling can lead to new insights into epidemic processes and better use of available data, yielding improved disease control and stimulating collection of better data and new data types. Here we identify key challenges for the structure, formulation, analysis and use of mathematical models of pathogen transmission relevant to current and future pandemics.

Challenges in estimation, uncertainty quantification and elicitation for pandemic modelling.

The estimation of parameters and model structure for informing infectious disease response has become a focal point of the recent pandemic. However, it has also highlighted a plethora of challenges remaining in the fast and robust extraction of information using data and models to help inform policy. In this paper, we identify and discuss four broad challenges in the estimation paradigm relating to infectious disease modelling, namely the Uncertainty Quantification framework, data challenges in estimation, model-based inference and prediction, and expert judgement. We also postulate priorities in estimation methodology to facilitate preparation for future pandemics.

Challenges for modelling interventions for future pandemics.

Mathematical modelling and statistical inference provide a framework to evaluate different non-pharmaceutical and pharmaceutical interventions for the control of epidemics that has been widely used during the COVID-19 pandemic. In this paper, lessons learned from this and previous epidemics are used to highlight the challenges for future pandemic control. We consider the availability and use of data, as well as the need for correct parameterisation and calibration for different model frameworks. We discuss challenges that arise in describing and distinguishing between different interventions, within different modelling structures, and allowing both within and between host dynamics. We also highlight challenges in modelling the health economic and political aspects of interventions. Given the diversity of these challenges, a broad variety of interdisciplinary expertise is needed to address them, combining mathematical knowledge with biological and social insights, and including health economics and communication skills. Addressing these challenges for the future requires strong cross-disciplinary collaboration together with close communication between scientists and policy makers.

Growth, reproduction numbers and factors affecting the spread of SARS-CoV-2 novel variants of concern in the UK from October 2020 to July 2021: a modelling analysis.

OBJECTIVES: Importations of novel variants of concern (VOC), particularly B.1.617.2, have become the impetus behind recent outbreaks of SARS-CoV-2. Concerns around the impact on vaccine effectiveness, transmissibility and severity are now driving the public health response to these variants. This paper analyses the patterns of growth in hospitalisations and confirmed cases for novel VOCs by age groups, geography and ethnicity in the context of changing behaviour, non-pharmaceutical interventions (NPIs) and the UK vaccination programme. We seek to highlight where strategies have been effective and periods that have facilitated the establishment of new variants. DESIGN: We have algorithmically linked the most complete testing and hospitalisation data in England to create a data set of confirmed infections and hospitalisations by SARS-CoV-2 genomic variant. We have used these linked data sets to analyse temporal, geographic and demographic distinctions. SETTING AND PARTICIPANTS: The setting is England from October 2020 to July 2021. Participants included all COVID-19 tests that included RT-PCR CT gene target data or underwent sequencing and hospitalisations that could be linked to these tests. METHODS: To calculate the instantaneous growth rate for VOCs we have developed a generalised additive model fit to multiple splines and varying day of the week effects. We have further modelled the instantaneous reproduction number Rt for the B.1.1.7 and B.1.617.2 variants and included a doubly interval censored model to temporally adjust the confirmed variant cases. RESULTS: We observed a clear replacement of the predominant B.1.1.7 by the B.1.617.2 variant without observing sustained exponential growth in other novel variants. Modelled exponential growth of RT PCR gene target triple-positive cases was initially detected in the youngest age groups, although we now observe across all ages a very small doubling time of 10.7 (95% CI 9.1 to 13.2) days and 8 (95% CI 6.9 to 9.1) days for cases and hospitalisations, respectively. We observe that growth in RT PCR gene target triple-positive cases was first detected in the Indian ethnicity group in late February, with a peak of 0.06 (95% CI 0.07 to 0.05) in the instantaneous growth rate, but is now maintained by the white ethnicity groups, observing a doubling time of 6.8 (95% CI 4.9 to 11) days. Rt analysis indicates a reproduction number advantage of 0.45 for B.1.617.2 relative to B.1.1.7, with the Rt value peaking at 1.85 for B.1.617.2. CONCLUSIONS: Our results illustrate a clear transmission advantage for the B.1.617.2 variant and the growth in hospitalisations illustrates that this variant is able to maintain exponential growth within age groups that are largely doubly vaccinated. There are concerning signs of intermittent growth in the B.1.351 variant, reaching a 28-day doubling time peak in March 2021, although this variant is presently not showing any evidence of a transmission advantage over B.1.617.2. Step 1b of the UK national lockdown easing was sufficient to precipitate exponential growth in B.1.617.2 cases for most regions and younger adult age groups. The final stages of NPI easing appeared to have a negligible impact on the growth of B.1.617.2 with every region experiencing sustained exponential growth from step 2. Nonetheless, early targeted local NPIs appeared to markedly reduced growth of B.1.617.2. Later localised interventions, at a time of higher prevalence and greater geographic dispersion of this variant, appeared to have a negligible impact on growth.

Insights gained from early modelling of COVID-19 to inform the management of outbreaks in UK prisons.

PURPOSE: In this work, the authors present some of the key results found during early efforts to model the COVID-19 outbreak inside a UK prison. In particular, this study describes outputs from an idealised disease model that simulates the dynamics of a COVID-19 outbreak in a prison setting when varying levels of social interventions are in place, and a Monte Carlo-based model that assesses the reduction in risk of case importation, resulting from a process that requires incoming prisoners to undergo a period of self-isolation prior to admission into the general prison population. DESIGN/METHODOLOGY/APPROACH: Prisons, typically containing large populations confined in a small space with high degrees of mixing, have long been known to be especially susceptible to disease outbreaks. In an attempt to meet rising pressures from the emerging COVID-19 situation in early 2020, modellers for Public Health England's Joint Modelling Cell were asked to produce some rapid response work that sought to inform the approaches that Her Majesty's Prison and Probation Service (HMPPS) might take to reduce the risk of case importation and sustained transmission in prison environments. FINDINGS: Key results show that deploying social interventions has the potential to considerably reduce the total number of infections, while such actions could also reduce the probability that an initial infection will propagate into a prison-wide outbreak. For example, modelling showed that a 50% reduction in the risk of transmission (compared to an unmitigated outbreak) could deliver a 98% decrease in total number of cases, while this reduction could also result in 86.8% of outbreaks subsiding before more than five persons have become infected. Furthermore, this study also found that requiring new arrivals to self-isolate for 10 and 14 days prior to admission could detect up to 98% and 99% of incoming infections, respectively. RESEARCH LIMITATIONS/IMPLICATIONS: In this paper we have presented models which allow for the studying of COVID-19 in a prison scenario, while also allowing for the assessment of proposed social interventions. By publishing these works, the authors hope these methods might aid in the management of prisoners across additional scenarios and even during subsequent disease outbreaks. Such methods as described may also be readily applied use in other closed community settings. ORIGINALITY/VALUE: These works went towards informing HMPPS on the impacts that the described strategies might have during COVID-19 outbreaks inside UK prisons. The works described herein are readily amendable to the study of a range of addition outbreak scenarios. There is also room for these methods to be further developed and built upon which the timeliness of the original project did not permit.

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

Viral reproduction of SARS-CoV-2 provides opportunities for the acquisition of advantageous mutations, altering viral transmissibility, disease severity, and/or allowing escape from natural or vaccine-derived immunity. We use three mathematical models: a parsimonious deterministic model with homogeneous mixing; an age-structured model; and a stochastic importation model to investigate the effect of potential variants of concern (VOCs). Calibrating to the situation in England in May 2021, we find epidemiological trajectories for putative VOCs are wide-ranging and dependent on their transmissibility, immune escape capability, and the introduction timing of a postulated VOC-targeted vaccine. We demonstrate that a VOC with a substantial transmission advantage over resident variants, or with immune escape properties, can generate a wave of infections and hospitalisations comparable to the winter 2020-2021 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.

Hospital length of stay for COVID-19 patients: Data-driven methods for forward planning.

BACKGROUND: Predicting hospital length of stay (LoS) for patients with COVID-19 infection is essential to ensure that adequate bed capacity can be provided without unnecessarily restricting care for patients with other conditions. Here, we demonstrate the utility of three complementary methods for predicting LoS using UK national- and hospital-level data. METHOD: On a national scale, relevant patients were identified from the COVID-19 Hospitalisation in England Surveillance System (CHESS) reports. An Accelerated Failure Time (AFT) survival model and a truncation corrected method (TC), both with underlying Weibull distributions, were fitted to the data to estimate LoS from hospital admission date to an outcome (death or discharge) and from hospital admission date to Intensive Care Unit (ICU) admission date. In a second approach we fit a multi-state (MS) survival model to data directly from the Manchester University NHS Foundation Trust (MFT). We develop a planning tool that uses LoS estimates from these models to predict bed occupancy. RESULTS: All methods produced similar overall estimates of LoS for overall hospital stay, given a patient is not admitted to ICU (8.4, 9.1 and 8.0 days for AFT, TC and MS, respectively). Estimates differ more significantly between the local and national level when considering ICU. National estimates for ICU LoS from AFT and TC were 12.4 and 13.4 days, whereas in local data the MS method produced estimates of 18.9 days. CONCLUSIONS: Given the complexity and partiality of different data sources and the rapidly evolving nature of the COVID-19 pandemic, it is most appropriate to use multiple analysis methods on multiple datasets. The AFT method accounts for censored cases, but does not allow for simultaneous consideration of different outcomes. The TC method does not include censored cases, instead correcting for truncation in the data, but does consider these different outcomes. The MS method can model complex pathways to different outcomes whilst accounting for censoring, but cannot handle non-random case missingness. Overall, we conclude that data-driven modelling approaches of LoS using these methods is useful in epidemic planning and management, and should be considered for widespread adoption throughout healthcare systems internationally where similar data resources exist.