Statistical and agent-based modelling of the transmissibility of different SARS-CoV-2 variants in England and impact of different interventions (preprint)

The English SARS-CoV-2 epidemic has been affected by the emergence of new viral variants such as B.1.177, Alpha and Delta, and changing restrictions. We used statistical models and calibration of an stochastic agent-based model Covasim to estimate B.1.177 to be 20% more transmissible than the wild type, Alpha to be 50-80% more transmissible than B.1.177 and Delta to be 65-90% more transmissible than Alpha. We used these estimates in Covasim (calibrated between September 01, 2020 and June 20, 2021), in June 2021, to explore whether planned relaxation of restrictions should proceed or be delayed. We found that due to the high transmissibility of Delta, resurgence in infections driven by the Delta variant would not be prevented, but would be strongly reduced by delaying the relaxation of restrictions by one month and with continued vaccination.

Compositional modelling of immune response and virus transmission dynamics (preprint)

Transmission models for infectious diseases are typically formulated in terms of dynamics between individuals or groups with processes such as disease progression or recovery for each individual captured phenomenologically, without reference to underlying biological processes. Furthermore, the construction of these models is often monolithic: they don't allow one to readily modify the processes involved or include the new ones, or to combine models at different scales. We show how to construct a simple model of immune response to a respiratory virus and a model of transmission using an easily modifiable set of rules allowing further refining and merging the two models together. The immune response model reproduces the expected response curve of PCR testing for COVID-19 and implies a long-tailed distribution of infectiousness reflective of individual heterogeneity. This immune response model, when combined with a transmission model, reproduces the previously reported shift in the population distribution of viral loads along an epidemic trajectory.

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.

Modelling the impact of reopening schools in early 2021 in the presence of the new SARS-CoV-2 variant and with roll-out of vaccination against COVID-19 (preprint)

Background Following the resurgence of the COVID-19 epidemic in the UK in late 2020 and the emergence of the new variant of the SARS-CoV-2 virus, B.1.1.7, a third national lockdown was imposed from January 5, 2021. Following the decline of COVID-19 cases over the remainder of January 2021, it is important to assess the conditions under which reopening schools from early March is likely to lead to resurgence of the epidemic. This study models the impact of a partial national lockdown with social distancing measures enacted in communities and workplaces under different strategies of reopening schools from March 8, 2021 and compares it to the impact of continual full national lockdown remaining until April 19, 2021. Methods We used our previously published model, Covasim, to model the emergence of B.1.1.7 over September 1, 2020 to January 31, 2021. We extended the model to incorporate the impacts of the roll-out of a two-dose vaccine against COVID-19, assuming 200,000 daily doses of the vaccine in people 75 years or older with vaccination that offers 95% reduction in disease acquisition and 10% reduction of transmission blocking. We used the model, calibrated until January 25, 2021, to simulate the impact of a full national lockdown (FNL) with schools closed until April 19, 2021 versus four different partial national lockdown (PNL) scenarios with different elements of schooling open: 1) staggered PNL with primary schools and exam-entry years (years 11 and 13) returning on March 8, 2021 and the rest of the schools years on March 15, 2020; 2) full-return PNL with both primary and secondary schools returning on March 8, 2021; 3) primary-only PNL with primary schools and exam critical years (Y11 and Y13) going back only on March 8, 2021 with the rest of the secondary schools back on April 19, 2021 and 4) part-Rota PNL with both primary and secondary schools returning on March 8, 2021 with primary schools remaining open continuously but secondary schools on a two-weekly rota-system with years alternating between a fortnight of face-to-face and remote learning until April 19, 2021. Across all scenarios, we projected the number of new daily cases, cumulative deaths and effective reproduction number R until April 30, 2020. Results Our calibration across different scenarios is consistent with the new variant B.1.1.7 being around 60% more transmissible. Strict social distancing measures, i.e. national lockdowns, are required to contain the spread of the virus and control the hospitalisations and deaths during January and February 2021. The national lockdown will reduce the number of cases by early March levels similar to those seen in October with R also falling and remaining below 1 during the lockdown. Infections start to increase when schools open but if other parts of society remain closed this resurgence is not sufficient to bring R above 1. Reopening primary schools and exam critical years only or having primary schools open continuously with secondary schools on rotas will lead to lower increases in cases and R than if all schools open. Under the current vaccination assumptions and across the set of scenarios considered, R would increase above 1 if society reopens simultaneously, simulated here from April 19, 2021.Findings Our findings suggest that stringent measures are necessary to mitigate the increase in cases and bring R below 1 over January and February 2021. It is plausible that a PNL with schools partially open from March 8, 2021 and the rest of the society remaining closed until April 19, 2021 may keep R below 1, with some increase evident in infections compared to continual FNL until April 19, 2021. Reopening society in mid-April, with the vaccination strategy we model, could push R above 1 and induce a surge in infections, but the effect of vaccination may be able to control this in future depending on the transmission blocking properties of the vaccines.

Modelling the impact of reopening schools in early 2021 in the presence of the new SARS-CoV-2 variant and with roll-out of vaccination against COVID-19 (preprint)

Background Following the resurgence of the COVID-19 epidemic in the UK in late 2020 and the emergence of the new variant of the SARS-CoV-2 virus, B.1.1.7, a third national lockdown was imposed from January 5, 2021. Following the decline of COVID-19 cases over the remainder of January 2021, it is important to assess the conditions under which reopening schools from early March is likely to lead to resurgence of the epidemic. This study models the impact of a partial national lockdown with social distancing measures enacted in communities and workplaces under different strategies of reopening schools from March 8, 2021 and compares it to the impact of continual full national lockdown remaining until April 19, 2021. Methods We used our previously published model, Covasim, to model the emergence of B.1.1.7 over September 1, 2020 to January 31, 2021. We extended the model to incorporate the impacts of the roll-out of a two-dose vaccine against COVID-19, assuming 200,000 daily doses of the vaccine in people 75 years or older with vaccination that offers 95% reduction in disease acquisition and 10% reduction of transmission blocking. We used the model, calibrated until January 25, 2021, to simulate the impact of a full national lockdown (FNL) with schools closed until April 19, 2021 versus four different partial national lockdown (PNL) scenarios with different elements of schooling open: 1) staggered PNL with primary schools and exam-entry years (years 11 and 13) returning on March 8, 2021 and the rest of the schools years on March 15, 2020; 2) full-return PNL with both primary and secondary schools returning on March 8, 2021; 3) primary-only PNL with primary schools and exam critical years (Y11 and Y13) going back only on March 8, 2021 with the rest of the secondary schools back on April 19, 2021 and 4) part-Rota PNL with both primary and secondary schools returning on March 8, 2021 with primary schools remaining open continuously but secondary schools on a two-weekly rota-system with years alternating between a fortnight of face-to-face and remote learning until April 19, 2021. Across all scenarios, we projected the number of new daily cases, cumulative deaths and effective reproduction number R until April 30, 2020. Results Our calibration across different scenarios is consistent with the new variant B.1.1.7 being around 60% more transmissible. Strict social distancing measures, i.e. national lockdowns, are required to contain the spread of the virus and control the hospitalisations and deaths during January and February 2021. The national lockdown will reduce the number of cases by early March levels similar to those seen in October with R also falling and remaining below 1 during the lockdown. Infections start to increase when schools open but if other parts of society remain closed this resurgence is not sufficient to bring R above 1. Reopening primary schools and exam critical years only or having primary schools open continuously with secondary schools on rotas will lead to lower increases in cases and R than if all schools open. Under the current vaccination assumptions and across the set of scenarios considered, R would increase above 1 if society reopens simultaneously, simulated here from April 19, 2021. Findings Our findings suggest that stringent measures are necessary to mitigate the increase in cases and bring R below 1 over January and February 2021. It is plausible that a PNL with schools partially open from March 8, 2021 and the rest of the society remaining closed until April 19, 2021 may keep R below 1, with some increase evident in infections compared to continual FNL until April 19, 2021. Reopening society in mid-April, with the vaccination strategy we model, could push R above 1 and induce a surge in infections, but the effect of vaccination may be able to control this in future depending on the transmission blocking properties of the vaccines.

Extremely high SARS-CoV-2 seroprevalence in a strictly-Orthodox Jewish community in the UK (preprint)

Abstract Background Ethnic and religious minorities have been disproportionately affected by SARS-CoV-2 worldwide. The UK strictly-Orthodox Jewish community has been severely affected by the pandemic. This group shares characteristics with other ethnic minorities including larger family sizes, higher rates of household crowding and relative socioeconomic deprivation. We studied a UK strictly-Orthodox Jewish population to understand how COVID-19 had spread within this community. Methods We performed a household-focused cross-sectional SARS-CoV-2 serosurvey specific to three antigen targets. Randomly-selected households completed a standardised questionnaire and underwent serological testing with a multiplex assay for SARS-CoV-2 IgG antibodies. We report clinical illness and testing before the serosurvey, seroprevalence stratified by age and gender. We used random-effects models to identify factors associated with infection and antibody titres. Findings A total of 343 households, consisting of 1,759 individuals, were recruited. Serum was available for 1,242 participants. The overall seroprevalence for SARS-CoV-2 was 64.3% (95% CI 61.6-67.0%). The lowest seroprevalence was 27.6% in children under 5 years and rose to 73.8% in secondary school children and 74% in adults. Antibody titres were higher in symptomatic individuals and declined over time since reported COVID-19 symptoms, with the decline more marked for nucleocapsid titres. Interpretation In this tight-knit religious minority population in the UK, we report one of the highest SARS-CoV-2 seroprevalence levels in the world to date. In the context of this high force of infection, all age groups experienced a high burden of infection. Actions to reduce the burden of disease in this and other minority populations are urgently required.

Estimated transmissibility and severity of novel SARS-CoV-2 Variant of Concern 202012/01 in England (preprint)

A novel SARS-CoV-2 variant, VOC 202012/01 (lineage B.1.1.7), emerged in southeast England in November 2020 and is rapidly spreading towards fixation. Using a variety of statistical and dynamic modelling approaches, we estimate that this variant has a 43-90% (range of 95% credible intervals 38-130%) higher reproduction number than preexisting variants. A fitted two-strain dynamic transmission model shows that VOC 202012/01 will lead to large resurgences of COVID-19 cases. Without stringent control measures, including limited closure of educational institutions and a greatly accelerated vaccine roll-out, COVID-19 hospitalisations and deaths across England in 2021 will exceed those in 2020. Concerningly, VOC 202012/01 has spread globally and exhibits a similar transmission increase (59-74%) in Denmark, Switzerland, and the United States.

The potential contribution of face coverings to the control of SARS-CoV-2 transmission in schools and broader society in the UK: a modelling study (preprint)

Recent findings suggest that an adequate test-trace-isolate (TTI) strategy is needed to prevent a secondary COVID-19 wave with the reopening of society in the UK. Here we assess the potential importance of mandatory masks in the parts of community and in secondary schools. We show that, assuming current TTI levels, adoption of masks in secondary schools in addition to community settings can reduce the size of a second wave, but will not prevent it; more testing of symptomatic people, tracing and isolating of their contacts is also needed. To avoid a second wave, with masks mandatory in secondary schools and in certain community settings, under current tracing levels, 68% or 46% of those with symptomatic infection would need to be tested if masks' effective coverage were 15% or 30% respectively, compared to 76% and 57% if masks are mandated in community settings but not secondary schools.

Determining the level of social distancing necessary to avoid a second COVID-19 epidemic wave: a modelling study for North East London (preprint)

Background: As England is starting to ease lockdown restrictions in a phased manner, it is important to determine the level of social distancing compliance, quantified here as the daily number of social contacts per person, i.e. the daily contact rate, needed to maintain control of the COVID-19 epidemic and not exceed acute bed capacity in case of a secondary wave later this year. This work uses mathematical modelling to simulate the levels of COVID-19 in North East London (NEL) and inform the level of social distancing necessary to protect the public and the healthcare demand from a secondary COVID-19 wave during 2020. Methods: We used a Susceptible-Exposed-Infected-Removed (SEIR) model describing the transmission of SARS-CoV-2 in North East London (NEL), calibrated to data on confirmed COVID-19 associated hospitalisations, hospital discharges and in-hospital deaths in NEL. To account for the uncertainty in both the infectiousness period and the proportion of symptomatic infection, we simulated nine scenarios for different combinations of infectiousness period (1, 3 and 5 days) and proportion of symptomatic infection (70%, 50% and 25% of all infections). Across all scenarios, the calibrated model was used to assess the risk of occurrence and forecast the strength and timing of a second COVID-19 wave under varying levels of daily contact rate from July 04, 2020. Specifically, the daily contact rate required to suppress the epidemic and prevent resurgence of COVID-19 cases, and the daily contact rate required to stay within the acute bed capacity of the NEL system without any additional intervention measures after July 2020, were determined across the nine different scenarios. Results: Our results caution against a full relaxing of the lockdown, predicting that a return to pre-COVID-19 levels of social contact from July 04, 2020 may induce a second wave up to eight times the original wave. With different levels of social distancing continuing into next year, the second wave can be avoided or the strength of the second wave can be mitigated. Keeping the daily contact rate lower than 5 or 6, depending on scenarios, for the rest of this year, can prevent increase in the number of COVID-19 cases, could keep the effective reproduction number R below 1 and a second COVID-19 wave may be avoided in NEL. A daily contact rate between 6 and 7, across scenarios, is likely to increase R above 1 and result in a secondary COVID-19 wave with significantly increased COVID-19 cases and associated deaths, but with demand for hospital based care remaining within the bed capacity of the NEL health and care system. In contrast, an increase in daily contact rate above 8 to 9, depending on scenarios, will likely exceed the acute bed capacity in NEL and may potentially require additional lockdowns. This scenario is associated with significantly increased COVID-19 cases and deaths, and acute COVID-19 care demand is likely to require significant scaling down of the usual operation of the health and care system, and should be avoided.Conclusions: Our findings suggest that to avoid a second COVID-19 wave and to stay within the acute bed capacity of the NEL health and care system, phased relaxing of the social distancing in NEL is advised with a view to limiting the average number of social interactions in the population. Increasing the social interaction rapidly could result in a second COVID-19 wave that will likely exceed the acute bed capacity in the system, and depending on the strength of the resurgence may require additional lockdown measures. 

Modelling the Health and Economic Impacts of Population-Wide Testing, Contact Tracing and Isolation (PTTI) Strategies for COVID-19 in the UK (preprint)

Background: The COVID-19 epidemic in the UK has resulted in over 280,000 reported cases and over 40,000 deaths as of 5th June 2020. In the context of a slower increase in reported cases and deaths associated with COVID-19 over the last few weeks compared to earlier in the epidemic, the UK is starting to relax the physical restrictions (‘lockdown’) that have been imposed since 23 March 2020. This has been accompanied by the announcement of a strategy to test people for infection, trace contacts of those tested positive, and isolate positive diagnoses. While such policies are expected to be impactful, there is no conclusive evidence of which approach to this is likely to achieve the most appropriate balance between benefits and costs. This study combines mathematical and economic modelling to estimate the impact, costs, feasibility, and health and economic effects of different strategies. Methods: We provide detailed description, impact, costing, and feasibility assessment of population-scale testing, tracing, and isolation strategies (PTTI). We estimate the impact of different PTTI strategies with a deterministic mathematical model for SARS-CoV-2 transmission that accurately captures tracing and isolation of contacts of individuals exposed, infectious, and diagnosed with the virus. We combine this with an economic model to project the mortality, intensive care, hospital, and non-hospital case outcomes, costs to the UK National Health Service, reduction in GDP, and intervention costs of each strategy. Model parameters are derived from publicly available data, and the model is calibrated to reported deaths associated with COVID-19. We modelled 31 scenarios in total (Panel 2). The first 18 comprised nine with ‘triggers’ (labelled with the -Trig suffix) for subsequent lockdown periods (>40,000 new infections per day) and lockdown releases (<10,000 new infections per day), and nine corresponding scenarios without triggers, namely: no large-scale PTTI (scenario 1); scale-up of PTTI to testing the whole population every week, with May–July 2020 lockdown release (scenario 2b), or delayed lockdown release until scale-up complete on 31 August 2020 (scenario 2a); these two scenarios with mandatory use of face coverings (scenarios 3a and 3b); and scenarios 2a, 2b, 3a, 3b replacing untargeted PTTI with testing of symptomatic people only (scenarios 4a, 4b, 4c, 4d). The final 13 scenarios looked at: whole population weekly testing to suppress the epidemic with lower tracing success (scenarios 3b-Trig00, 3b-Trig10, 3b-Trig20, 3b-Trig30) and switched to targeted testing after two months when it may suppress the epidemic (scenarios 3b-Trig00-2mo and 3b-Trig30-2mo), and targeted testing with lower tracing success (scenarios 4d-Trig10, 4dTrig20, 4d-Trig30, 4d-Trig40, 4d-Trig50, 4d-Trig60, 4d-Trig70). Findings: Given that physical distancing measures have already been relaxed in the UK, scenario 4d-Trig (targeted testing of symptomatic people only, with a mandatory face coverings policy and subsequent lockdown triggered to enable PTTI to suppress the epidemic), is a strategy that will result in the fewest deaths (~52,000) and has the lowest intervention costs (~£8bn). The additional lockdown results in total reduction in GDP of ~£503bn, less than half the cost to the economy of subsequent lockdowns triggered in a scenario without PTTI (scenario 1-Trig, ~£1180bn reduction in GDP, ~105,000 deaths). In summer months, with lower cold and flu prevalence, approximately 75,000 symptomatic people per day need to be tested for this strategy to work, assuming 64% of their contacts are effectively traced (~80% traced with 80% success) within the infectious period (most within the first two days and nearly all by seven days) and all are isolated – including those without any symptoms – for 14 days. Untargeted testing of everyone every week, if it were feasible, may work without tracing, but at a higher cost (scenario 3b-Trig00). This cost could be reduced by switching to targeted testing after the epidemic is suppressed (scenario 3b-Trig30-2mo), though we note the epidemic could be suppressed with targeted testing itself providing tracing and isolation has at least a 32% success rate (scenario 4dTrig40). Interpretation: PTTI strategies to suppress the COVID-19 epidemic within the context of a relaxation of lockdown will necessitate subsequent lockdowns to keep the epidemic suppressed during PTTI scale-up. Targeted testing of symptomatic people only can suppress the epidemic if accompanied by mandated use of face coverings. The feasibility of PTTI depends on sufficient capacity, capabilities, infrastructure and integrated systems to deliver it. The political and public acceptability of alternative scenarios for subsequent lockdowns needs to take account of crucial implications for employment, personal and national debt, education, population mental health and non-COVID-19 disease. Our model is able to incorporate additional scenarios as the situation evolves. Funding: No specific funding was received in support of this study. Grant support for specific authors is as follows: WW acknowledges support from the Chief Scientist Office (COV/EDI/20/12) RR, JPG and EP are supported by the National Institute for Health Research ARC North Thames. NMcG is a recipient of an NIHR Global Health Research Professorship award (Ref: RP-2017-08-ST2-008). The views expressed in this independent research are those of the authors and not necessarily those of the National Institute for Health Research or the Department of Health and Social Care. KMG is supported by the UK Medical Research Council (MC_UU_12011/4), the National Institute for Health Research (NIHR Senior Investigator (NF-SI-0515-10042) and NIHR Southampton Biomedical Research Centre (IS-BRC-1215-20004)), British Heart Foundation (RG/15/17/3174) and the US National Institute On Aging of the National Institutes of Health (Award No. U24AG047867). GY acknowledges her research partially supported from the Newton Fund through a UK-China ARM Partnership Hub award (No:MR/S013717/1).Declaration of Interests: All authors declare no competing interests.

Testing, tracing and isolation in compartmental models (preprint)

Existing compartmental mathematical modelling methods for epidemics, such as SEIR models, cannot accurately represent effects of contact tracing. This makes them inappropriate for evaluating testing and contact tracing strategies to contain an outbreak. An alternative used in practice is the application of agent- or individual-based models (ABM). However ABMs are complex, less well-understood and much more computationally expensive. This paper presents a new method for accurately including the effects of Testing, contact-Tracing and Isolation (TTI) strategies in standard compartmental models. We derive our method using a careful probabilistic argument to show how contact tracing at the individual level is reflected in aggregate on the population level. We show that the resultant SEIR-TTI model accurately approximates the behaviour of a mechanistic agent-based model at far less computational cost. The computationally efficiency is such that it be easily and cheaply used for exploratory modelling to quantify the required levels of testing and tracing, alone and with other interventions, to assist adaptive planning for managing disease outbreaks.