key: cord-0990929-1u2trfor authors: Moore, S.; Hill, E. M.; Tildesley, M.; Dyson, L. M.; Keeling, M. J. title: Vaccination and Non-Pharmaceutical Interventions: when can the UK relax about COVID-19? date: 2021-01-02 journal: nan DOI: 10.1101/2020.12.27.20248896 sha: e4ba95fcf78899fbf3411582d5f508aa245fe1df doc_id: 990929 cord_uid: 1u2trfor The announcement of efficacious vaccine candidates against SARS-CoV-2 has been met with worldwide acclaim and relief. Many countries already have detailed plans for vaccine targeting based on minimising severe illness, death and healthcare burdens. Normally, relatively simple relationships between epidemiological parameters, vaccine efficacy and vaccine uptake predict the success of any immunisation programme. However, the dynamics of vaccination against SARS-CoV-2 is made more complex by age-dependent factors, changing levels of infection and the potential relaxation of non-pharmaceutical interventions (NPIs) as the perceived risk declines. In this study we use an age-structured mathematical model, matched to a range of epidemiological data, to consider the interaction between the UK vaccination programme and future relaxation (or removal) of NPIs. Our predictions highlight the population-level risks of early relaxation leading to a pronounced wave of infections, and the individual-level risk relative to vaccine status. While the novel vaccines against SARS-CoV-2 offer a potential exit strategy for this outbreak, this is highly contingent on the transmission blocking action of the vaccine and the population uptake, both of which need to be carefully monitored as vaccine programmes are rolled out in the UK and other countries. The outbreak of SARS-CoV-2 that began in Wuhan, China, in late 2019 has dramatically shaped life in 2 2020 as a world-wide pandemic emerged [1] . In the UK, the first cases were identified on 31st January 3 2020 [2] , with February and March witnessing an exponential rise in cases [3] . The first lockdown began 4 on 23rd March and reversed the growth in infection, although important health metrics such as hospital 5 occupancy and deaths continued to increase for several days [4] . The steady, but spatially heterogeneous, 6 decline continued until August 2020 when a relaxation of controls and increased mixing as a result of this 7 precipitated a second wave and, subsequently, a second lock-down in November 2020. By early December 8 2020, the UK had suffered over 60,000 deaths and 225,000 hospital admissions due to ; and yet it 9 is estimated that less than 20% of the population have been exposed to the virus [5] suggesting the outbreak 10 is far from complete. Mass vaccination, and hence protection, of the population offers a potentially rapid 11 exit strategy. between infection and vaccination -vaccination rates are limited by supply and logistics, whereas infection 31 can grow exponentially. However, the infection rate can be reduced by a range of non-pharmaceutical 32 interventions whilst a vaccine can be targeted to where it will have the most impact [11] . The future of 33 COVID-19 control is therefore dependent, in a complex non-linear way, on the initial prevalence of infection, 34 the level of non-pharmaceutical interventions (NPIs) and therefore the rate of growth or decay, the speed with 35 which the vaccine can be rolled out, the targeting and uptake of the vaccine and the vaccine characteristics. 36 The uncertainties and interactions between these components necessitates the use of mathematical models 37 to explore scenarios. 38 Here, we present an age-structured mathematical model, matched to a range of epidemiological data, to 39 forecast the dynamics of COVID-19 into 2021 and beyond based on multiple combinations of scenarios. 40 These model results provide likely bounds on the expected number of deaths and hospitalisations and hence 41 provide important policy insights into the interaction between continued non-pharmaceutical interventions 42 and the forthcoming vaccination programme. We focus on the risk-structured delivery programme for the 43 UK and the potential risks of relaxing NPIs; we also consider the individual risks and how these are mitigated 44 by vaccination. 45 2 The mathematical model and vaccination assumptions 46 We adapt an existing age and regionally structured model of SARS-COV-2 dynamics that has been matched 47 to UK data [12, 13] to include the consequences of vaccination [11] . The model captures the historic trends of 48 infection, hospitalisation and deaths in the UK, including the scale of the first and second waves. Including 49 vaccination into this model shows how prioritising the oldest age-groups leads to the greatest reduction in 50 deaths [11] . Here we increase the realism of the vaccination dynamics, including the timing of vaccine roll 51 out across the population and the need to administer two doses. One key issue that the model cannot 52 address is the level of non-pharmaceutical interventions (NPIs) that will be imposed in the future and the 53 level of support (and therefore adherence to NPIs) from the general population. We have optimistically 54 assumed that controls in the short-term are sufficient to keep the reproductive number (R) just below one; 55 we then relax controls at various times throughout 2021 to investigate the level of protection generated by 56 vaccination. All results represent the mean of multiple simulations which explore the inferred epidemiological 57 parameter space determined by matching to a range of epidemiological time series; credible intervals for the 58 predictions are shown in the Supporting Information (Section S2). 59 Vaccination schedules for the UK are still not determined over long time scales, although the immediate 60 priority order has been defined [11, 14] . We implement a three phase programme that approximates a plau-61 sible (but optimistic) roll-out of SARS-CoV-2 vaccination in the UK (Figure 1a ), following in each stage 62 the identified priority ordering: 63 Phase 1a Pfizer/BioNTech vaccine alone for the first 4M doses (= 2M persons) with roll-out from 8th 64 December and lasting approximately one month. We assumed vaccine efficacy to be 90%. Phase 1b A mixture of vaccines are deployed until everyone aged over 50 and those with comorbidities 66 classifying them as high risk have been targeted. This takes approximately 3 more months starting from 67 1st January, and we assumed the mean vaccine efficacy to be 80%. Phase 2 Vaccines are offered to remaining adults below the age of 50 and above the age of 18, taking 69 approximately three and a half more months with completion occurring by late July. For this phase we 70 again assumed the mean vaccine efficacy to be 80%. Throughout we assume 95% uptake in care homes and 75% elsewhere, with vaccination randomly distributed 73 across the population. These may be optimistic assumptions; uptake could be lower in younger age-groups 74 due to a belief that COVID-19 infection is likely to have mild symptoms and therefore vaccination does 75 not have a major individual health benefit. In practice, vaccination is also likely to be highly correlated 76 within households and socio-demographic groups [15] , which will weaken the population-scale impact of any 77 transmission blocking by the vaccine. 78 We use a 2-dose model to simulate the impact of vaccination in both reducing disease and in reducing onward 79 transmission. We assume that delivery of the second dose is prioritised over new first doses (Figure 1a ). In 80 the absence of detailed vaccine specific information, we also assume a stepped efficacy over time following 81 the first dose, which scales with the assumed final vaccine efficacy (VE): from the first dose to day 7, zero 82 efficacy; from day 7 to second dose on day 28, 50% VE; from day 28 to day 35, 50% VE; from day 35 83 onwards, 100% VE (Supplementary Material). Vaccine efficacy against disease is assumed to be high (in 84 keeping with preliminary reports): 90% during the earliest phase, dropping to 80% when multiple vaccines 85 2 . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted January 2, 2021. are in use. The role of vaccines in blocking transmission is less clear so we consider a range of transmission 86 efficacy from 0% to 75%, which we assume operates by preventing primary infection. We note that the 87 disease efficacy takes into account both infection blocking and the reduction of severe symptoms if infection 88 does occur (Supporting Information, Section S1.1). While efficacy against disease is of major early benefit in protecting individuals against severe disease, it is 90 the transmission blocking potential of the vaccine that leads to a reduction in the intrinsic growth rate and 91 the reproduction number, R. Figure 1b shows the reproduction number R, on release of non-pharmaceutical 92 interventions, as the vaccine programme progresses for four different assumptions of transmission efficacy. 93 For zero transmission efficacy (orange line), R ≈ 2.2 a reduction from the observed growth in the first wave 94 due to the slight depletion in susceptibles from natural infection; whereas when transmission efficacy is 95 high (75% transmission blocking, green line), vaccination can generate a substantial decline in the repro-96 ductive number, although still insufficient to drive R below 1 for our default assumptions about vaccine 97 uptake. 99 We simulate the infection dynamics from February 2020, matching to the observed pattern of cases, hos-100 pitalisations and deaths, and then predict the impact of vaccination on daily deaths until the end of 2021 101 ( Figure 2 ). Unsurprisingly, in the absence of vaccination (blue line) we observe the largest waves of infection 102 with the most deaths, which are reduced by increasing levels of transmission efficacy. Early, modest relax-103 ation of NPIs (Figure 2a) , matched to the levels observed in early September when R was between 1.2 and 104 1.4 across different English regions and devolved nations, leads to subsequent waves of infection even under 105 the most efficacious assumptions (green line shows a vaccine that blocks 75% of infection). Later relaxation 106 of NPIs (April 2021 in Figure 2b ) provides a greater opportunity for some level of herd-immunity to have 107 accrued if the vaccine is moderately effective at blocking infection. 108 We consider the total number of deaths predicted by the model (Figure 2c ), which equates to the areas 109 under the curve in the preceding graphs. This provides an opportunity to consider sensitivity to vaccine 110 uptake. The central bar represents 75% uptake in the general population (as shown in Figure 1 and the 111 rest of Figure 2 ), whereas the lower limits of each box correspond to more optimistic up-take, corresponding 112 to an increased 85% uptake in those above 50 years old, and the upper limits represent a more pessimistic 113 scenario with 65% uptake in this older age-group and 45% uptake in the remaining population. The main 114 panel shows the predicted mortality from the start of 2021 for different dates at which NPI are partially 115 relaxed (to the level observed in early September 2020). Even maintaining these levels of NPI control and 116 having a highly efficacious vaccine (green bars), we estimate over ten thousand deaths are likely to occur 117 due to the slow decline in cases from its current high level; early relaxation of control measures or low 118 transmission efficacy can lead to a pronounced subsequent wave of infection. If we wish to completely lift all restrictions once both phases of the vaccination campaign is complete, then 120 3 . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted January 2, 2021. ; https://doi.org/10.1101/2020.12.27.20248896 doi: medRxiv preprint (c) Figure 2 : Predicted daily deaths in the UK following the start of an immunisation program and relaxation or removal of NPIs. Panels (a) and (b) show the effect of relaxing current NPI measures down to those seen in early September 2020 (R ∼ 1.2 − 1.4) from January or April 2021 respectively. Panel (c) displays the aggregate effects of partial release of NPI measures at different dates during the vaccination programme (left) compared with complete release from July 2021 (right); the upper limit, central bar and lower limit of each box corresponds to pessimistic, default and optimistic assumptions about vaccine uptake. The lower panels (d) and (e) correspond to a gradual reduction in NPIs until all controls are removed, as illustrated by the grey area. The default scenario (a,b, d & e) assumes 75% uptake in the general population; the optimistic scenario has an increased uptake at 85% in those above 50; while the pessimistic scenario has a decreased 65% uptake in the over 50's and 45% uptake in the remaining population. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted January 2, 2021. ; we predict a substantial outbreak with a large number of associated deaths (Figure 2c right-hand panel). 121 When the vaccine is not transmission blocking removing NPIs trigger an uncontrolled wave of infection in 122 which only those successfully immunised (approximately 80% of 75%) will escape. Optimistic assumptions 123 for both vaccine and uptake can still lead can still lead to 49 thousand deaths; with 13 thousand from 124 January to July, and 36 thousand from July onwards when NPIs are released. The step-wise release of all NPIs (Figure 2c right-hand panel, Supporting Information) modelled so far 126 generates an over-shooting wave of infection; a more gradual release of restrictions mitigates against these 127 effects (Figure 2d & e) . A slow release of NPIs (as illustrated in Figure 2e ) generates the fewest deaths, which 128 under the most optimistic assumptions we predict around 39 thousand deaths (from January 2021). The precise dynamics and outcomes are contingent on the assumed intrinsic growth rate before the relaxation 130 of NPIs, which here is approximately R = 0.95 -other values for this quantity will change the precise curves 131 but do not change the qualitative conclusions. We see similar behaviour if we examine the number of 132 daily hospitalisations (Supporting Information, Section S2), with a notable third wave predicted if NPIs are 133 relaxed too early or if the vaccine has a limited impact on transmission. While we have predominantly focused on the population-level consequences of the vaccination programme, 136 one key question is the likely vaccination status of individuals that are severely ill. We characterise this 137 relationship as a function of the number of doses delivered so far (as part of the mass vaccination programme) 138 and for a consistent 75% vaccine uptake across all age-groups ( Figure 3 ). We display findings assuming 50% 139 transmission efficacy, with similar results obtained for all levels of transmission efficacy. We consider four 140 categories of individual: those who have not yet been offered the vaccine (grey); those who are in an eligible 141 age-group but due to health reasons or personal beliefs remain unvaccinated (yellow); those who had received 142 one dose so far (light blue); and those that have received both doses dark blue). Those individuals that have 143 not been offered the vaccine declines linearly, while those unvaccinated but in eligible age groups and those 144 that have received two doses grow linearly ( Figure 3a ). The unfolding epidemic (matched to Figure 2a ) is 145 then distributed across these four status groups (Figure 3b ). For low numbers of doses, deaths are dominated 146 by those who have yet to be offered the vaccine and those that have only received one dose; for moderate 147 numbers of doses (15-40M) deaths are dominated by those that have not been vaccinated but are in the 148 eligible age groups. By plotting the proportion of all deaths associated with each status we observe that around 40% of deaths 150 can be expected in those that have been vaccinated (Figure 3c ). We stress that while at the individual-151 level two doses of vaccine reduces the risk of mortality by 80%, because vulnerable vaccinated people 152 rapidly outnumber vulnerable unvaccinated people we should expect to see a high proportion of vaccinated 153 individuals suffering severe disease and mortality. The final shape of these distributions is a function of vaccine uptake in the most at-risk; increasing vaccine 155 uptake reduces the number of deaths but paradoxically increases the contribution of vaccinated individuals 156 to the proportion of deaths. There is also a strong influence of how well the vaccine protects against severe 157 disease -greater efficacy against the most severe disease will again reduce the number of deaths and will also 158 decrease the proportions associated with vaccinated individuals. However, if the vaccine is less efficacious 159 in the elderly this trend would be reversed. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted January 2, 2021. ; The proportion of deaths. We display simulations assuming a consistent 75% vaccine uptake across all age-groups, assuming 50% transmission efficacy, and with a moderate reduction in NPIs at the start of 2021 (corresponding to the yellow curve in Figure 2a ). Here we have shown that high efficacy vaccines which provide a substantial level of transmission blocking 162 offer a means of eventually relaxing controls without suffering a large subsequent wave of hospitalisations 163 and deaths. Our conclusions rely on not only the vaccine characteristics but also upon the uptake in the pop-164 ulation; in particular the most vulnerable groups, but also in the general population if transmission blocking 165 is to be successful. We examined this in Figure 2e considering three different assumptions about vaccine 166 uptake, but in practice vaccine uptake is likely to be regionally and socio-demographically correlated [16, 17] . 167 Such correlations may potentially lead to pockets of high susceptibility in the population which can act as 168 locations of small-scale outbreaks and reduce herd immunity [18] . It is also likely that vaccine uptake will 169 vary in time as the population's perceived risk varies [19, 20] , with high levels of hospitalisations and deaths 170 leading to a greater demand for the vaccine. We expect there to be a complex four-way interaction between 171 levels of infection, NPI policy, NPI adherence and vaccine uptake. From a public health perspective, it is 172 therefore key to understand the drivers of vaccine uptake and vaccine hesitancy, identify groups that may 173 have lower than average uptake and plan accordingly.. Early relaxation of non-pharmaceutical interventions (NPIs), before sufficient immunity is established, has 175 been shown to precipitate a large wave of infection with resultant hospitalisations and deaths; a similar 176 impact is predicted from any final release of NPIs if herd immunity has not been achieved ( Figure 2 ). Even 177 with high levels of vaccine uptake, a substantial fraction of the population needs to be immunised to prevent 178 subsequent waves of infection (Figures 1 and 2) , and strong NPIs will still be required even when Phase 1 179 of the vaccination programme is complete. We have focused on scenarios where NPIs are switched off in a 180 step-wise manner, but even a more measured approach in which NPIs are gradually released over a period 181 of many months does not prevent the worse effects (Supporting Information, Section S2). We stress that 182 as hospitalisations and deaths increased we would expect both national legislation and emergent behaviour 183 to limit the spread [21] . Therefore, our scenarios represent a pessimistic view of measures in response to a 184 worsening outbreak. At the time of writing only two vaccine manufacturers have peer-reviewed publications presenting the 186 findings of their phase 3 trials [6, 7] . These have been used to provide approximate parameters for this 187 modelling work, but many questions have not been quantitatively addressed. However, a number of key 188 vaccine parameters within the model are based on parsimonious assumptions. We identify the following three 189 6 . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted January 2, 2021. ; issues that require additional experimental data to refine model assumptions: as elucidated throughout this 190 paper determining whether the vaccine blocks transmission is key for the development of herd immunity and 191 hence the role of vaccination in the long-term control of COVID-19; we have assumed that efficacy against 192 disease applies equally across the entire spectrum of disease, however if the vaccine has differential protection 193 against the most severe disease this will impact our predictions for hospital admissions and deaths. Finally, 194 we expect efficacy to vary with age and between risk groups; incorporating such heterogeneity into models 195 is key for more robust predictions. 196 Over longer time scales the possibilities of waning immunity and mutation may upset these predictions. 197 Waning immunity, either naturally derived or from vaccination, may necessitate seasonal vaccination pro-198 grammes against SARS-CoV-2 protecting the most vulnerable in a similar manner to seasonal influenza 199 vaccines [22] . Again we are lacking in our fundamental understanding of SARS-CoV-2 epidemiology, in par-200 ticular whether subsequent infections have the same severity as primary infections, as well as the duration 201 of protection. Both of these elements can be factored into the prediction mechanisms, but without detailed 202 evidence such long-term forecasts are speculation. Effective vaccines with high uptake are likely to be an essential element in the long-term control and 204 potential elimination of COVID-19. However, experience with other diseases has illustrated that elimination 205 is difficult and generally requires a targeted multi-strategy approach [23] , the same is likely to be true for 206 SARS-CoV-2. While mass vaccination will inevitably reduce the reproductive number R and reduce disease 207 prevalence, other measures, such as intensive test-trace-and-isolate, will be needed to target pockets of 208 infection. Ultimately whether we achieve eradication of SARS-CoV-2 is likely to depend on the long-term 209 natural history of infection and the public health importance attached to this goal. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted January 2, 2021. The data were supplied from the CHESS database after anonymisation under strict data protection protocols 232 agreed between the University of Warwick and Public Health England. The ethics of the use of these 233 data for these purposes was agreed by Public Health England with the Government's SPI-M(O) / SAGE 234 committees. Competing interests 236 All authors declare that they have no competing interests. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted January 2, 2021. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted January 2, 2021. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted January 2, 2021. ; https://doi.org/10.1101/2020.12.27.20248896 doi: medRxiv preprint The model involves an extended SEIR-type framework: susceptibles (S) may become infected and move into a latent exposed (E) state before progressing to become infectious. Echoing the observed behaviour of COVID-19 infections, the model differentiates between individuals who are symptomatic (D, and hence likely to be detected) and those who are asymptomatic (U , likely to remain undetected). Partitioning those who are infectious by symptom status allows for a lower level of transmission believed to be associated with asymptomatic infection. It also generates the possible progression of symptoms increasing in severity, leading to hospitalisation and/or death. Here we present the basic model formulation that underpins the age-structured predictions of COVID-19 dynamics in the UK, and how the parameters of this model have been inferred from the available data. We used a compartmental age-structured model, developed to simulate the spread of SARS-CoV-2 within ten regions of the UK (seven regions in England: East of England, London, Midlands, North East & Yorkshire, North West, South East and South West; and the devolved nations: Northern Ireland, Scotland and Wales) [12] , with parameters inferred to generate a good match to deaths, hospitalisations, hospital occupancy and serological testing [24] . The model population is stratified by age, with force of infection determined by the use of an age-dependent (who acquires infection from whom) social contact matrix for the UK [25, 26] . Additionally, we allow susceptibility and the probabilities of becoming symptomatic, being hospitalised and the risk of dying to be age dependent; these are matched to UK outbreak data. Finally, we account for the role of household isolation, by separating primary and secondary infections within a household (more details may be found in [12] ). This allows us to capture household isolation by preventing secondary infections from playing a further role in onward transmission. Model parameters were inferred on a regional basis using regional time series of recorded daily hospitalisation numbers, hospital bed occupancy, ICU occupancy and daily deaths [24] . We first show the underlying system of equations that account for the transmission dynamics, including symptomatic and asymptomatic transmission, household saturation of transmission and household quarantining. The population is stratified into multiple compartments: individuals may be susceptible (S), exposed (E), infectious with symptoms (I), or infectious and either asymptomatic or with very mild symptoms (A). Asymptomatic infections are assumed to transmit infection at a reduced rate given by τ . To some extent, the separation into symptomatic (I) and asymptomatic (A) within the model is somewhat artificial as there are a wide spectrum of symptom severities that can be experienced. We let superscripts denote the first infection in a household (F ), a subsequent infection from a symptomatic household member (SI) and a subsequent infection from an asymptomatic household member (SA). A fraction (H) of the first detected cases (necessarily symptomatic) in a household are quarantined (QF ), as are all their subsequent household infections (QS) -we ignore the impact of household quarantining on the susceptible population as the number in quarantine is assumed small compared with the rest of the population. The recovered class is not explicitly modelled, although it may become important once we have a better understanding of the duration of immunity. We omitted natural demography and disease-induced mortality in the formulation of the epidemiological dynamics. We extended the model formulation to capture a range of vaccination scenarios. We modelled two vaccination classes for individuals where it has been 7 days since they received their first and second dose of the vaccine, where the 7-day delay allows partial immunity to develop ( Figure S2 ). We included these within the S and E class by adding an additional vaccination subscript for the number of doses received; hence S a,0 corresponds to susceptible unvaccinated individuals while S a,2 corresponds to those that received their second dose of vaccine at least 7 days ago. . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted January 2, 2021. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted January 2, 2021. ; https://doi.org/10.1101/2020. 12.27.20248896 doi: medRxiv preprint The full equations are given by Here we have included m latent classes, giving rise to an Erlang distribution for the latent period, while the infectious period was exponentially distributed. Throughout we have taken M = 3. The forces of infection which govern the non-linear transmission of infection obey: where β H represents household transmission and β N = β S + β W + β O represents all other transmission locations, comprising school-based transmission (β S ), work-place transmission (β W ) and transmission in all other locations (β O ). These matrices are taken from Prem et al. [26] to allow easily translation to other geographic settings, although other sources such as POLYMOD [25] could be used. Two key parameters, together with the transmission matrix, govern the age-structured dynamics: σ a corresponds to the age-dependent susceptibility of individuals to infection; d a the age-dependent probability 13 . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted January 2, 2021. ; https://doi.org/10.1101/2020.12.27.20248896 doi: medRxiv preprint of displaying symptoms (and hence potentially progressing to more severe disease). Both of these are also modified by the vaccine status, such that those that have received one or two doses of vaccine have a lower risk of infection and a lower risk of developing symptoms. The action of vaccine on the parameter σ captures the transmission blocking aspect of the vaccine, while the action on d captures the efficacy against disease ( Figure S2 ). We also define τ as the reduced transmission from asymptomatic infections compared to symptomatic infections; given the probability of displaying symptoms is less in the younger age groups, this parameter shapes the role of younger ages in onward transmission. We require our model to capture both individual level quarantining of infected individuals and isolation of households containing identified cases. In a standard ODE framework this level of household structure is only achievable at large computational expense [27, 28] . Thus, we instead made a relatively parsimonious approximation to achieve a comparable effect. We assume that all within household transmission originates from the first infected individual within the household (denoted with a superscript F , or QF if they become quarantined). This allows us to assume that secondary infections within a household in isolation (denoted with a superscript QS or Q) play no further role in any of the transmission dynamics. As a consequence, high levels of household isolation can drive the epidemic extinct, even if within household transmission is high -an effect not achievable with the standard SEIR-type modelling approach. This improved methodology also helps to capture to some degree household depletion of susceptibles (or saturation of infection), as secondary infections in the household are incapable of generating additional household infections. We obtained age-structured contact matrices for the United Kingdom from Prem et al. [26] . We used these contact matrices to provide information on normal levels household transmission (β H ab , with the subscript ab corresponding to transmission from age group a against age group b), school-based transmission (β S ab ), work-place transmission (β W ab ) and transmission in all other locations (β O ab ). We assume that any instigated non-pharmaceutical interventions (patterns of social-distancing or lockdown measures) leads to a reduction in the work, school and other matrices while increasing the strength of household contacts. Any given level of non-pharmaceutical interventions (NPIs), captured by the parameter φ between zero and one, therefore scales the four transmission matrices between their normal values (when φ = 0) and their value under the most severe lockdown (φ = 1). We infer the level of NPIs as a slowly varying parameter in the MCMC processes on a weekly basis. In turn, the weekly value of φ allows us to calculate the growth rate r (and hence the reproductive number R) by an eigenvalue approach. As with any model of this complexity, there are multiple parameters that determine the dynamics. Some of these are global parameters and apply for all geographical regions, with others used to capture the regional dynamics. Some of these parameters are matched to the early outbreak data (including the resultant agedistribution of infection), however the majority are inferred by an MCMC process (Table 1) . We would highlight that the parameters of α and τ are key in determining age-structured behaviour and are therefore essential in quantifying the role of school children in transmission [29] . We argue that a low τ and a low α are the only combination that are consistent with the growing body of data suggesting that levels of seroprevalence show only moderate variation across age-ranges [30] , yet children are unlikely to display major symptoms, suggesting their role in transmission may be lower than for other respiratory infections [31, 32] . Throughout the current epidemic, there has been noticeable heterogeneity between the different regions of England and between the devolved nations. In particular, London is observed to have a large proportion of early cases and a relatively steeper decline in the subsequent lock-down than the other regions and the devolved nations. In our model this heterogeneity is captured through three regional parameters (D R S , H R S and I R S ) which act on the heterogeneous population pyramid of each region to generate key observables. 14 . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted January 2, 2021. ; https://doi.org/10.1101/2020.12.27.20248896 doi: medRxiv preprint The main model equations focus on the epidemiological dynamics, allowing us to compute the number of symptomatic and asymptomatic infectious individuals over time. However, these quantities are not directly measured -and even the number of confirmed cases (the closest measure to symptomatic infections) is highly biased by the testing protocols at any given point in time. It is therefore necessary to convert infection estimates into quantities of interest that can be compared to data. We considered six such quantities which we calculated from the number of new symptomatic infections on a given day I d a . 1. Hospital Admissions: An age-dependent fraction of symptomatic individuals are assumed to need hospital treatment, with a distributed lag between infection and hospitalisation. Similarly, an age-dependent fraction of symptomatic individuals are assumed to need treatment in an Intensive Care Unit. This is not a quantity that is generally reported, and therefore we cannot match our model predictions to this data source. 3. Hospital Beds Occupied: By convolving hospital admissions with the distributions of lengths of stay, we can estimate the number of hospital beds occupied. A similar process generates the number of occupied ICU beds. Mortality is assumed to occur to a fraction of hospitalised individuals, with the probability of mortality dependent upon age, and occuring after a distributed lag. 6. Proportion of Pillar 2 positives: Given that the raw number of detected cases in any region is substantially influenced by the number of tests conducted, we consider the proportion of pillar 2 tests that are positive as a less biased figure. We assume that those symptomatically infected with COVID- . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted January 2, 2021. ; 19 compete with individuals suffering symptoms for other infections for the available testing capacity. This leads to proportion of pillar 2 tests that are positive being a saturating function of the number of symptomatic infections, with a single scaling parameter. We compared these model predictions to the data by assuming that the true numbers are drawn from a negative binomial distribution with the model value as the mean, while the true proportions (Pillar 2 positives) are from a beta-binomial. In the main text we focused on a few chosen scenarios that illustrate the range of plausible behaviours, and only considered COVID-19 related deaths. Here, we show some other representative scenarios and the impact on the number of hospitalisations under all of these cases. We also display the 95% credible intervals, as defined by the variability in inferred parameters; these shaded regions contain 95% of all simulations at every point in time. ( We note that any one prediction will not necessarily follow the upper or lower bound, these are envelopes that contain predictions that may wander both above and below the mean.) is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted January 2, 2021. ; https://doi.org/10.1101/2020.12.27.20248896 doi: medRxiv preprint Figure S4 : Effect of gradual relaxation of NPI measures on deaths across the UK following the start of vaccination. In panels (a)-(d) different relaxation scenarios are shown with NPIs reduced linearly from December levels down to complete release over different time periods represented by the height of the grey shading. Panel (e) compares the total predicted deaths from Jan-21 onwards between the scenarios for each vaccine efficacy. . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted January 2, 2021. ; https://doi.org/10.1101/2020.12.27.20248896 doi: medRxiv preprint is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted January 2, 2021. ; https://doi.org/10.1101/2020.12.27.20248896 doi: medRxiv preprint Figure S6 : Effect of gradual relaxation of NPI measures on hospital admissions across the UK following the start of vaccination. In panels (a)-(d) different relaxation scenarios are shown with NPIs reduced linearly from December levels down to complete release over different time periods represented by the height of the grey shading. Panel (e) compares the total predicted hospital admissions from Jan-21 onwards between the scenarios for each vaccine efficacy. . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted January 2, 2021. ; https://doi.org/10.1101/2020.12.27.20248896 doi: medRxiv preprint Covid-19 infection: Origin, transmission, and characteristics of human coronaviruses Novel coronavirus disease (Covid-19): The first two patients in the UK with person to person transmission UK government The impact of government measures and human mobility trend on covid-19 related deaths in the UK Office for National Statistics. 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