We used Covasim, a stochastic individual-based model of SARS-CoV-2 transmission across a population. We have previously applied Covasim to explore the impact of different test-trace-isolate strategies when schools reopened in the UK during autumn 2020 in the absence  and presence  of requirements to wear masks. Development and implementation details can be found at http://docs.covasim.org with the methodology outlined in a previous report . The code used to run the simulations reported in this paper is available from https://github.com/Jasminapg/Covid-19-Analysis.
For this study, as in our previous work [7-8], we used Covasim’s default parameters, pre-populated demographic data on population age structures and household sizes and contact patterns in school, community and household setting for the UK, and the population stratified across four population contact network layers: schools, workplaces, households and community settings. The per-contact transmission probability (the risk of transmission during a contact between an infectious individual and a susceptible individual) was assumed to depend on the contact network.
Test, trace and isolation strategies
Covasim accounts for testing strategies via parameters that determine the probabilities with which people with different symptoms receive a test each day, both for symptomatic and asymptomatic people. Tracing is quantified by parameters controlling the probability of reaching the contacts of those testing positive, as well as the time taken to reach them. Within Covasim we can also quantify the level of adherence to isolation as model parameters describing the level of isolation across different layers of the population.
For this study we model a vaccine reducing disease acquisition and transmission with a two-dose regime given 10 weeks apart, to reflect our understanding of vaccination guidelines in place in January 2021 . We model that the full two-dose course reduces the probability of developing symptoms by 95% and per-exposure transmission probability by 10%. Single dose efficacy is assumed to be 70% of the full two-dose course. Second dose is administered after a delay of 10 weeks after the first dose and with immunity from the vaccination assumed to increase from around 14 days after immunisation with full effect after 21 days after vaccination. Doses are allocated to 200,000 people per day on average, with people 75 or older targeted first.
Data sources and calibration
Using Covasim’s default contact network generation algorithm, we generated a population of 100,000 agents who interact over the four contact networks layers (households, workplaces, schools, and communities), which we then rescaled to the UK population size using the dynamic rescaling algorithm described in .
Unlike our previous work [19-20] where we modelled one strain of the SARS-CoV-2, here we have modelled the implications of two strains of the virus by simulating a single strain with time-varying infectiousness. Specifically, we assume that the new variant is more transmissible, and that the relative proportion of the new strain increased from September 1, 2020 to January 31, 2021 following a logistic growth function, such that 30% of infections in December and 90% of infections by the end of January 2021 were caused by the new variant. This allowed us to model different levels of infectiousness of B.1.1.7 compared to the previous strain, in an approach similar to recent work .
We calibrated the model to the UK epidemic by adjusting (a) the number of infected people on January 21, 2020 (b) the per-contact transmission probability for SARS-CoV-2 (c) the parameters associates with the time-varying infectiousness of the virus (d) the testing, tracing and isolation parameters for November-January and (e) the levels of transmission across different society levels between November 2020-January 2021. Calibration minimised the differences between the model’s estimates of COVID-19 cases, deaths and severe infections and empirical data on cumulative infections, cumulative deaths and admissions to hospital by reported date between January 21, 2020 and January 25, 2021 collated from the UK government’s COVID-19 dashboard (https://coronavirus.data.gov.uk).
Within the model we also simulated the effect of the two previous national lockdowns. For the first national lockdown, when schools closed and as in [19,20], we modelled a 98% reduction in the per-contact transmission probabilities from March 23, 2020 within schools and an 80% reduction in transmission within workplace and community settings, and increased these in a phased way since the phased relaxing of the lockdown measures from June 1, 2020. For the second lockdown, between November 5, 2020 and December 3, 2020 during which schools remained open, we assumed a reduction in the per-contact transmission probabilities by 37% in schools i.e. simulated 63% of transmission within schools remaining from September. This was modelled as aggregated reduction in transmission due to hygiene, mask usage and other social distancing measures in place within schools to reduce transmission, and as described in details in .
The level of reduction in transmission in households, workplaces and community that we modelled was a combination of using Google mobility data  within households, workplaces and community but also fitting to data during the calibration process. Specifically, for the household transmission we modelled increased transmission since November 2020 of 25% and in line with the average monthly level of increased household mobility in the Google data . For the workplaces and community, during the November lockdown, we also used Google mobility data to obtain a broad range of the change, but we also needed to adjust these during the calibration process. Specifically, we simulated workplace and community transmission to be reduced by 80% and 80% of their pre-COVID-19 levels during the first lockdowns, and 70% and 60% during the second lockdown.
We also used publicly available weekly data from NHS Test and Trace to estimate the rate of tracing of contacts of those testing positive since the start of the programme on May 28, 2020 . For each weekly period, we collated the percentage of people testing positive who were interviewed, the percentage of those reporting contacts and the percentage of contacts traced. We used these percentages to produce an overall estimate of the percentage of contacts of those tested positive who were traced. We then computed the monthly average effective contact tracing level and in our previous work, we used this data to produce a monthly effective contact tracing level. As an extension, here we additionally assumed that tracing levels differ depending on the type of contact, and assumed that 100% of household contacts can be traced within the same day, 50% of school and workplaces can be traced within one day and 10% of community contacts can successfully be traced within 2 days; giving an average of 53% of contacts traced across different layers and comparable with reported monthly values from . We also assumed that asymptomatic testing is available across all society layers and modelled this in line with reported numbers in the UK (0.076% May-August 2020, 0.28% August-October 2020 and 0.63% since November 2020 from https://ourworldindata.org/coronavirus-testing).
We modelled five different scenarios as postulated reductions in transmission within schools, community and workplaces, which are shown in Table 1 and briefly summarised below. For each scenario we predicted the number of new daily cases, cumulative deaths and R until April 30, 2021.
Scenario 1: FNL between January 5 and April 19, 2021, with all schools and reduction in transmission within workplaces, homes and community modelled as in the November 2020 lockdown until April 19.
Scenario 2: Staggered PNL: FNL between January 5 and March 8, 2021 with PNL after March 8, 2021 with all schools opening in a staggered way: primary schools and years 11 and 13 of secondary schools from March 8 and the rest of secondary school years from March 15. A reduction in transmission within workplaces, homes and community is modelled as in the November 2020 lockdown until April 19.
Scenario 3: Full-return PNL: FNL between January 5 and March 8, 2021 with PNL after March 8, 2021 with all schools opening from March 8. A reduction in transmission within workplaces, homes and community is modelled as in the November 2020 lockdown until April 19.
Scenario 4: Primary-only PNL: FNL between January 5 and March 8, 2021 with PNL after March 8, with only primary schools and exam critical years (years 11 and 13) opening on March 8 and the rest of the secondary schools opening on April 19 when society also reopens. A reduction in transmission within workplaces, homes and community is modelled as in the November 2020 lockdown until April 19.
Scenario 5: Part-Rota PNL: FNL between January 5 and March 8, 2021 with PNL after March 8 with all schools opening from March 8 with primary schools remaining continuously open but secondary schools open on a two-weeks rota system until April 19 when schools and society reopen. A reduction in transmission within workplaces, homes and community is modelled as in the November 2020 lockdown until April 19.
There is still some uncertainty about the relative susceptibility to the virus for children compared to adults. To account for this, in the main analysis we assume that primary school children (0-10 years old) are 50% less susceptible than secondary school children (11-18 years old) or adults (>18 years old), with these two latter groups having the same susceptibility . The sensitivity analysis then explored whether the results changed if all age groups have the same susceptibility as adults.
There is also some contention  regarding the degree to which transmission in society increases as a result of schools reopening. Our main scenarios assume that it would not, but we also conduct additional sensitivity analyses to explore how the results would change if community transmission increased as a result of reopening of schools.