key: cord-0699888-ly33oes7
authors: Hill, E. M.; Keeling, M. J.
title: Comparison between one and two dose SARS-CoV-2 vaccine prioritisation for a fixed number of vaccine doses
date: 2021-03-24
journal: nan
DOI: 10.1101/2021.03.15.21253542
sha: db66f21b0e75514076ae4670543f6cc5fc2d0e5c
doc_id: 699888
cord_uid: ly33oes7

Background: The swift development of vaccines targeting SARS-CoV-2, which have been shown to generate significant immune responses and offer considerable protection against disease, has been met with worldwide commendation. However, in the context of an ongoing pandemic there is an interplay between infection and vaccination. While infection can grow exponentially, potentially overwhelming healthcare resources, vaccination rates are generally limited by both supply and logistics. With the first SARS-CoV-2 vaccines receiving medical approval requiring two doses, there has been scrutiny on the spacing between doses; an elongated period between doses would allow more of the population to receive a first vaccine dose in the short-term generating wide-spread partial immunity. Methods: Focusing on data from England, we investigated prioritisation of a one dose or two dose vaccination schedule given a fixed number of vaccine doses and with respect to a measure of maximising averted deaths. We optimised outcomes for two different estimates of population size and relative risk of mortality for at-risk groups within the Phase 1 vaccine priority order in England, for different amounts of available vaccine and for different vaccine efficacies. Findings: We find that vaccines offering relatively high protection from the first dose (compared to the efficacy derived from two doses) favour strategies that prioritise giving more people one dose rather than a smaller number two. The optimal mix of one and two doses between the defined priority groups of Phase 1 shows a pattern of returning to give second doses to the highest risk groups as the number of available doses increases. Discussion: While this work highlights that an optimal timing of first and second doses between the Phase 1 priority groups can substantially reduce the overall mortality risk to the population, there also needs to be careful consideration of the precise timing between first and second doses as well as the logistics of vaccine delivery.

Vaccination has been seen as a key tool in the fight against SARS-CoV-2, although deployment provides 2 multiple unique challenges that are not encountered by other vaccination programmes. In short, there 3 is a race between infection and vaccination, with vaccination rates currently limited by supply and 4 logistics, whereas infection can grow exponentially. 5 The vaccines already developed represent a major technological achievement and have been shown to 6 generate significant immune responses, as well as offering considerable protection against disease [1] [2] [3] [4] [5] .

Field data from Israel and the UK suggests that protection against severe disease (hospitalisation or 8 death) may be even greater [6, 7] . 9 In the UK, the two vaccines currently being deployed as part of the vaccination programme (as of 10 March 2021) are the Pfizer/BioNTech and Oxford/AstraZeneca vaccines. The mRNA Pfizer/BioNTech 11 vaccine was approved by the Medicines and Healthcare products Regulatory Agency (MHRA) on 2nd 12 December 2020 [8] . The Oxford/AstraZeneca vaccine, a chimpanzee adenoviral vectored vaccine, has 13 been the main component of the UK vaccination program since it received approval for use by the 14 MHRA on 30th December 2020 [9] . Both require two doses to be administered to maximise efficacy 15 and longevity of immunity (with the duration of vaccine-derived immunity still uncertain). 16 A key question, given the urgency of achieving high levels of protection in the population, is the 17 appropriate interval between doses. A longer interval allows more people to be given partial protection 18 over relatively short-time scales, whereas a shorter interval will provide greater (although not complete) 19 protection to the most vulnerable. In deciding between these two options, a number of factors need to 20 be considered: the relatively high efficacy of the first dose from 3-12 weeks after vaccination [10] ; the 21 high levels of SARS-CoV-2 prevalence [11] , COVID-19 morbidity [12] and COVID-19 mortality [13] 22 since the start of the vaccine programme; the evidence that the Oxford/AstraZeneca vaccine provides 23 greater second dose efficacy with a spacing of 12 weeks or more [5] ; and the initial lack of Phase 3 trial 24 data on single dose vaccine performance beyond 3 weeks for the Pfizer/BioNTech vaccine [1] . 25 On short-term timescales, and in the absence of risk-structure or the potential for differential rates of 26 waning immunity, if the efficacy from one dose is more than half the efficacy from two doses, then it is 27 always preferable to prioritise vaccinating as many people as possible with one dose. Yet, given clear 28 variation in the burden of severe outcomes caused by COVID-19, the prioritisation of dosing schedules 29 merits quantitative evaluation; such analyses have been performed in a non-UK context [14] [15] [16] . 30 In this paper, we study prioritisation of a one dose or two dose vaccination schedule given a fixed 31 number of vaccine doses and with respect to a measure of maximising averted deaths. We performed 32 this analysis in the context of the English population and age-stratified risk mortality. We examined 33 two types of strategy for dose allocation: (i) giving as many people one dose or as many people two 34 doses as permitted by the number of doses available (homogeneous strategy); (ii) adding flexibility to 35 the allocation scheme by allowing for a given percentage of vaccine doses being used for first doses, 36 with the remainder used for second doses (heterogeneous strategy). Throughout, we explored the 37 sensitivity to the relative efficacy of the first vaccine dose (compared to the efficacy attained following 38 two vaccine doses). We acknowledge that this is a simplified representation of a complex dynamic 39 process, whereby new supplies of vaccine are being manufactured and distributed over time, where 40 second dose efficacy may change depending on the inter-dose separation and where there can be an 41 intrinsic feedback between vaccination and population-level incidence. In the discussion we expand on 42 how the findings from these theoretical results need to be interpreted to apply to the situation facing 43 England, the UK and other nations.

Data on age-dependent mortality risk 46 We base our analysis on the estimated age distribution of mortality due to COVID-19 in the UK, 47 with a particular focus on the Joint Committee on Vaccination and Immunisation (JCVI) Phase 1 48 priority groups for vaccination [17] . The nine target groups within the first phase of the vaccination 49 programme encompass care home residents and workers, health care workers, all those clinically ex-50 tremely vulnerable (CEV) and with underlying health conditions (UHC), and all those aged 50 years 51 and above.

Due to the absence of precise estimates for either the size of each priority group or the relative risk 53 of COVID-19 mortality for individuals in each group, we considered two different sets of assumptions 54 around these two statistics (labelled 'Age only' and 'Priority Group estimate'), with details of the two 55 estimates provided in Table 1 .

For the age-only model, estimation of risk was based solely on the age-distribution of mortality due to 57 COVID-19 in England (using deaths within 28 days of a confirmed COVID-19 positive test), during the 58 period 1st September 2020 until 1st February 2021, compared to the underlying population pyramid 59 for England using mid-2019 Office for National Statistics (ONS) population estimates (Fig. 1) [18] . It 60 is evident that older age groups suffered the greatest mortality, with 60% of deaths due to COVID-19 61 in those over 80 years of age even though they only comprise 5% of the population.

For the Priority Group estimate, we extended the formulation described for the age-only estimate 63 to include the priority groups, assuming that this did not change the relative mortality risk of the 64 age-groups (under 80 years old) previously calculated. The relative risk of care home residents and 65 staff is based upon approximately 14 thousand care home deaths in the period since 7th August 2020 66 to the beginning of February 2021 [19] , with the risk in the over-80s scaled to account for the greater 67 risk of death within care homes. We assumed risks for those clinically extremely vulnerable to be equal 68 to those aged 70-74, which also occupy priority group 4. We assumed risks for those with underlying 69 health conditions (group 6) to lie equidistant between groups 5 and 7. Population estimates for these 70 priority groups were provided by the Department of Health and Social Care (DHSC) [20] . Table 1 : Estimates of priority group population size and relative mortality risk. The age-only estimates were based on age-group data (mid-2019 estimates) for England [18] and the age distribution of mortality due to COVID-19 in the UK, during the period 1st September 2020 until 1st February 2021. We based the Priority Group estimate on age-structured mortality data in the second wave using priority group population estimates from DHSC [20] . All values are given to 1d.p. Using the population size data (P p ) for each priority group, the associated relative risk of COVID-19 73 mortality (RR p ) and estimates of vaccine efficacy following one or two doses (VE 1 and VE 2 ), we calcu-74 lated the deaths averted given an assumed distribution of vaccines between the priority groups:

where v 1 p and v 2 p are the proportions of each priority group p that receive just one dose or two doses 76 of the vaccine respectively. To further reduce the degrees of freedom of this calculation, it is sufficient 77 3 . CC-BY 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 March 24, 2021. ; Table 1 showing the estimated population size (red) and the relative risk of mortality from COVID-19 (blue) (a) The assumptions for the age-structured estimates. (b) The assumptions for the Priority Group estimates. Vertical spacing of the two graphs is such that the groups of similar ages match.

to know the ratio of the vaccine efficacy from the first dose compared to the second VE R = VE 1 /VE 2 , 78 which we term relative efficacy of the first dose.

Vaccine efficacy 80 Data on vaccine effectiveness in averting deaths due to SARS-CoV-2 infection following first and 81 second dose with the vaccine is extremely limited. We therefore use central estimates of vaccine 82 efficacy against disease to guide our range of relative efficacy: Pfizer/BioNTech (89% from first dose; 83 95% from two doses) [1] ; Oxford/AstraZeneca (76% from first dose; 81% from two doses) [5] . This 84 would imply that the relative efficacy of the first dose (VE R ) is in the region of 93% for the Pfizer 85 vaccine and the Oxford/AstraZeneca vaccine. More recent data from the UK on mortality in those 86 over 80 years old suggests that the first dose reduces deaths by around 80%, which acts as a lower 87 bound for the relative efficacy of the first dose against mortality [7] . 88 Strategies for vaccine dose allocation 89 We examined two types of strategy for dose allocation, which we describe as: (i) homogeneous strategy 90 and (ii) heterogeneous strategy.

Homogeneous strategy 92 For a given number of available doses (V ) and for a given relative efficacy from the first dose compared 93 to the second (VE R ), we first examined the question of whether to completely prioritise one dose or 94 two doses of the vaccine. This essentially is a question of whether there is a greater number of expected 95 deaths averted from giving as many people as possible one dose or two doses. 96 We compared the relative risks in the different age-groups (Table 1) 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 March 24, 2021. ; https://doi.org/10.1101/2021.03.15.21253542 doi: medRxiv preprint of deaths averted by the one dose and two dose strategies.

Deaths

where there is a strict limit on the number of available doses:

We 99 note that this is a relative measure as predicting the scale of the future cases, hospitalisation and 100 deaths is contingent on a number of policy decisions. In all scenarios we assumed 90% vaccine uptake 101 (v 1 p ≤ 0.9 or v 2 p ≤ 0.9), independent of age and priority group.

Given that the relative risk of COVID-19 mortality (RR p ) decreases monotonically between risk groups, 103 it is clear that the optimal deployment of either one of two doses must similarly decline monotonically 104

and similarly for the second dose 0.

). Moreover, it is always 105 better to maximally vaccinate the higher-risk groups before preceding to lower-risk ones; therefore, 106 solutions are generally of the form:

. . , 0.9, v 1 q , 0, . . . , 0) which 107 corresponds to completely vaccinating groups 1 to q − 1, partially vaccinating group q, and not yet 108 vaccinating the remaining lower-risk groups. This enables us to calculate the optimal deployment of 109 vaccine across all priority groups without having to perform an exhaustive combinatorial search.

Heterogeneous strategy 111 We extended our initial analysis to consider a heterogeneous strategy. For a given number of doses, 112 we sought the optimal deployment of a mixed scheme where some priority groups can be targeted for 113 two doses while others receive one.

As an example, based on English population data, supposing we had 6.6 million doses of vaccine, these could either give all those aged 80 and above two doses, or it could give everyone aged 75 and above, and some of those in the 70-74 years age group, one dose. Again, our aim is to maximise the number of deaths averted, subject to the constraint on the total amount of vaccine available (V ):

Again, due to the monotonicity on the relative risk of mortality, we can insist on a simple ordering of 115 vaccination (0.

; and again, we expect to maximally 116 vaccinate higher risk groups before moving to lower ones. This essentially means we search over the 117 number of vaccines allocated to second rather than first doses. 118 We studied the optimal allocation of vaccine for the two estimates of priority group size and relative 119 risk (either based on age-structure only or using priority groups estimates), and for a range of relative 120 efficacy of one dose compared to two doses (75% ≤ VE R ≤ 90%). We assumed vaccine uptake of 90% 121 (to set the scale of vaccination in each priority group) and ignored the impact of transmission blocking 122 (which is difficult to incorporate in this static model and is still not well quantified). is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint For a given number of vaccine doses (V ) and considering vaccine targeting towards age-group based 127 priority groups, we considered when it is optimal to focus all vaccine resources on maximising the 128 number of people receiving one dose or concentrate on ensuring that the most vulnerable groups get 129 two doses.

When the number of vaccines available is insufficient to cover a specified age range or priority group, 131 there is a choice between giving one dose to some proportion of the over 80's or two doses to only half 132 that number. In this situation, and ignoring the implications of generating long-term immunity, a one 133 dose strategy would be favoured if 2VE 1 > VE 2 (VE R > 0.5). For a larger available number of vaccine 134 doses, we are faced with the dilemma between giving one dose to ages that are at slightly less risk or 135 giving two doses to those that are most vulnerable. Using England once more as an example, supposing 136 we had 5.5 million doses of vaccine, these could either be used to give all those aged 80 and above 137 two doses, or could give everyone aged 75 and above, and some of those in the 70-74 years age group, 138 one dose. To qualitatively assess this situation, we examined optimisation outcomes based on the two 139 estimates for vaccination priority group population size and relative risk of mortality (Table 1) .

For the age-only estimate of relative risk, the separation between prioritising first dose or second doses 141 ( Fig. 2(a) ) was relatively smooth. For low numbers of available doses (< 2 million) and greater than 142 50% relative efficacy, the optimal policy is to prioritise one dose. For larger stockpiles of vaccine, the 143 relative efficacy needs to be higher to prioritise giving one dose to as many people as possible. Within 144 the plausible range of relative efficacy values (75% -90%), we found a steady switch to prioritising 145 the second dose as the amount of available vaccine increases from 4 million to 18 million doses.

For the Priority Group estimate (Fig. 2(b) ), we observed a broadly similar pattern; however, the very 147 high relative risk associated with care home residents and workers (priority group 1) means that, for 148 a low number of doses and a low relative efficacy, it can be optimal to prioritise giving two doses to 149 the care home group. With this estimated set of relative risks, there was also an even stronger effect 150 (compared to the age-only estimate) of high relative first dose efficacy, leading to a wider parameter 151 space where the first dose was prioritised.

Heterogeneous strategy 153 We next considered strategies where a given proportion of the available vaccine are used for first doses 154 and the remainder for second doses. We performed this assessment under an assumption of maximising 155 the number of deaths averted and a vaccine uptake of 90%.

Given a relative efficacy for the first dose of below 50%, the optimal strategy is to use half of the 157 available vaccine for second doses, such that everyone prioritised for vaccination receives two doses 158 (Fig. 3) . Above this threshold of 50% relative efficacy from the first dose, the pattern of doses reserved 159 for second doses approximately follows the same pattern as the homogeneous strategy (cyan and pink 160 lines in Fig. 3 are the same as in Fig. 2 ). We found a smaller region of parameter space where the 161 optimal strategy is to only give one dose (dark blue, and only for a low number of doses or very high 162 levels of relative efficacy of the first dose). The distinct banding observed is due to the switch between 163 different priority groups as the amount of available vaccine increases. For the Priority Group estimate, 164 as with the homogeneous strategy, a distinct structure was visible in the results: a two dose strategy 165 (focused on care homes) was optimal at around 2 million doses and for a relative first-dose efficacy of 166 up to 70% (Fig. 3(b) ).

For a given ratio of first and second doses, the associated distribution of vaccine between the priority 168 6 . CC-BY 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted March 24, 2021. ;

(a) (b) Fig. 2 : Optimisation of dosing strategy with respect to the number of vaccine doses and the relative efficacy of the first dose compared to the second dose. Panels correspond to outputs for two different estimates of vaccination priority group population size and relative risk of mortality (see Table 1 for further details): (a) Age groups only. (b) Priority Group estimate, which included specific groups for care homes and those with underlying health conditions. In all panels, and given a metric of maximising deaths averted, dark shaded regions correspond to parameter sets where it was determined optimal to prioritise first doses, with light shaded regions corresponding to parameter sets where two dose vaccination was optimal. The maximal number of doses considered corresponds to being able to give all individuals in the priority groups one dose, assuming 90% uptake. 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 March 24, 2021. ; groups can again be calculated due to the monotonicity of the relative risk. We show the optimal 169 distribution for a distinct set of relative efficacies from the first dose (VE R = 70%, 80%, 90%) and 170 for a specified number of doses (4, 8, 12, 16, 20 and 24 million) (Fig. 4) . We show as stacked bars 171 the number of first (left) and second (right) doses given to each priority group for both the simple 172 age-structured estimates of risk and for the full Priority Group estimates.

At 70% relative efficacy, there was a strong tendency to offer second doses shortly after the first. Thus 174 at 4 million doses, the optimal strategy was to begin offering second doses to either the oldest age-175 group or priority group 1. For higher levels of vaccine availability (e.g. 24 million doses), although the 176 distribution of second doses lags behind the first, we consistently predict at least 50% of the groups 177 receiving two doses of vaccine is optimal.

178 When relative efficacy is higher (80% or 90%) there is more of a delay before it becomes optimal 179 to begin second vaccinations. At 4 million doses, the optimal strategy became focused on delivering 180 single doses only; with second doses being introduced more gradually. At the most extreme parameters 181 investigated (90% relative vaccine efficacy and full priority group estimates), even at 20 million doses, 182 the only group to have received their second dose was priority group 1 (care home residents and 183 staff).

Although we generated these figures by simply considering the optimal use of a fixed pool of available 185 vaccine -with no reference to how lower amounts of vaccine have been used -it is still possible to 186 read the graphs as a chronological sequence, due to the monotonicity of the relative risk. As such, 187 for any given relative efficacy, the first V doses of vaccine are always distributed in the same manner 188 (Fig. 5 ). An alternative way to view the same information is to consider at what point in the delivery 189 programme it becomes optimal to give first and second doses to each of the priority groups. For the 190 relative risk of mortality estimated for the full priority groups, this visualisation clarifies that at high 191 relative efficacy from the first dose of vaccine (90%) the optimal distribution of vaccine is substantially 192 weighted towards early prioritisation of first doses with a substantial delay until the second dose is 193 offered. For completion of the first four priority groups (everyone over 70, health care workers, care 194 home staff and residents and those that are clinically extremely vulnerable) we estimate that the 195 optimal delay between finishing the first doses and finishing the second doses is: 12.83 million doses 196 (for a relative efficacy of 70%); 19.58 million doses (for a relative efficacy of 80%) and 24.01 million 197 doses (for a relative efficacy of 90%) -which is between 6 and 12 weeks if delivery is maintained at 2 198 million doses a week. 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 March 24, 2021. ; is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint shows the optimal groups that should be prioritised for vaccination. We show a smaller range of total doses for (a) compared to (b), as the total number of individuals over 50 years old is smaller than the number in priority groups 1-9.

. CC-BY 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 Here we have developed a simple algorithmic method that can optimise the distribution of a fixed 201 number of vaccine doses, allowing us to maximise averted deaths. The JCVI Phase 1 priority groups 202 have been defined such that early groups have a higher risk of mortality than lower ones. There is 203 hence a natural ordering in which, theoretically, we would wish to vaccine priority group 1 before 204 moving to priority group 2. The more challenging question that we address here is whether it is better 205 to give high-risk groups their second dose of vaccine before giving lower-risk groups (in the priority 206 order) their first dose. In the context of UK vaccination policy, the key question was around the delay 207 between the first and second dose, with a longer delay allowing more individuals to be given some level 208 of protection in the short-term. For the Oxford/AstraZeneca vaccine there is also compelling evidence 209 that a delay of 12 weeks or more provides greater second dose vaccine efficacy [5] , strengthening the 210 case for an early prioritisation of first doses.

In countries where the total supply of vaccine is more limited, similar calculations could inform whether 212 a strategy that attempted to maximise coverage by only giving a single dose would be of benefit -213 although, in this scenario, far more information would be required on the long-term protection offered 214 by a single dose.

The key parameter in our model is the relative efficacy provided by the first dose of vaccine compared 216 to the level of protection offered by two doses. Here, we have focused on COVID-19 mortality using 217 the relative risk of infection and death for each of the nine JCVI priority groups, and hence we are 218 most interested in efficacy against death. Unfortunately, efficacy against death is extremely difficult 219 to measure from Phase 3 trials (no-one taking part in the Pfizer/BioNTech trials, in either the control 220 or vaccine arm, died with COVID-19 [1] , with one COVID-19-related death in one participant in the 221 control group of Oxford/AstraZeneca trials [5] ), and so we need to rely on data from the large-scale 222 national programmes. Early data from the UK on those over 80 years of age (and therefore amongst 223 the first to receive the vaccine) suggests that a first dose of the Pfizer/BioNTech vaccine generates 224 a vaccine efficacy against symptomatic infection of 70% (95% CI 59-78%) after four weeks and an 225 additional 51% (95% CI 37-62%) lower risk of death if infected, giving a combined efficacy against 226 death of 85% [7] . This is therefore a lower-bound on our required relative efficacy. 227 We predict that, for relatively high protection from the first dose (compared to the efficacy derived 228 from two doses), a substantial number of first doses should be administered before attention switches 229 to giving second doses (Fig. 5) . We expect these simple trade-offs to occur either if there is a lim-230 ited supply of vaccine, or until that point is reached in an on-going campaign. As such, under these 231 circumstances, early vaccine roll-out ought to be targeted towards giving as many people one dose 232 as possible, until the switch-point is reached. Our results agree with findings from earlier modelling 233 work (applied in a non-UK context) that found, when a single dose retains the majority of the ef-234 fectiveness against disease of two doses, immunising as many persons as possible with a single-dose 235 regimen may achieve a greater reduction in disease from COVID-19 than a 2-dose regimen in a smaller 236 population [14] [15] [16] .

While this modelling provides important generic insights into the benefits of first and second doses, 238 there are a number of elements that are absent from this simple analysis. Most notably, the vaccination 239 programme is a dynamic process in which different amounts of vaccine are available at different points 240 in time; therefore, while it is possible to read Fig. 5 as a chronology, it does not take into account the 241 necessary restrictions on the separation between doses. Our model computes the protection derived 242 from a specified amount of vaccine doses being instantaneously administered amongst the population. 243 This lack of a dynamic perspective means that we cannot address questions that relate to the precise 244 timing of vaccination. In particular, very long delays between doses may have implications for both 245 short-and long-term immunity; similarly the model cannot directly capture the delay between vacci-246 nation and the development of immunity. In addition, our model also assumes that priority groups 247 are completed in order of greatest risk -whereas in practice, and for a number of practical reasons, 248 the delivery schedule is blurred, often vaccinating groups that are most easy to reach.

Our determination of dose allocation was based on averting deaths, with no regard for hospital admis-250 sions (and therefore pressure on the health services), the implications of long-COVID nor any form 251 of life-years lost or quality adjusted life year assessment. The prioritisation of first doses compared 252 to second doses, for a given relative efficacy, may differ under an alternative metric or collection of 253 measures (as found in the study by Matrajt et al. [16] , who determined that the optimal allocation 254 strategy with one and two doses of vaccine was different when minimising one of five distinct metrics of 255 disease and healthcare burden under various degrees of viral transmission). Furthermore, in terms of 256 the demography and empirical data on mortality risk due to COVID-19, our analysis has been carried 257 out using data corresponding to the population of England. Thus, these findings will not necessarily 258 directly translate to other settings, in particular where the population structure and mortality are 259 vastly different. Finally, our static modelling framework does not account for the transmission dy-260 namics of infection; the fact that individuals have been immunised does not change the risk to the 261 remaining population and hence we do not capture the structured reduction in risk that can occur. 262 General declines (or increases) in risk that apply equally to the entire population do not affect our 263 results.

In summary, given the strong evidence that a single dose is highly effective, our model results would 265 indicate that early prioritisation of one dose (compared to re-vaccinating with a second doses) averts 266 the greater number of deaths. The precise timing of first and second doses is contingent on the speed 267 of the delivery programme, with more rapid delivery favouring early deployment of second doses. The 268 policy adopted in the UK was dependent upon a number of practical considerations -not least the 269 greater second dose efficacy of the Oxford/AstraZeneca vaccine after a 12-week delay [5] , and the 270 need for a simple, consistent message across all priority groups and vaccines. However, this work 271 clearly shows that, given particular combinations of demographic and vaccine attributes, a strategy of 272 prioritising first doses can have substantial public health benefits. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The data used to conduct this study are provided in the main manuscript. Code is available at 292 https://github.com/EdMHill/fixed num vaccine doses one vs two dose prioritisation.

Competing interests 294 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

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