key: cord-0985977-r0r65f9t authors: Moore, S.; Hill, E. M.; Dyson, L.; Tildesley, M.; Keeling, M. J. title: Modelling optimal vaccination strategy for SARS-CoV-2. date: 2020-09-24 journal: nan DOI: 10.1101/2020.09.22.20194183 sha: f66ac369dffa3c4f2856266af3691147684d8c5d doc_id: 985977 cord_uid: r0r65f9t The COVID-19 outbreak has highlighted our vulnerability to novel infections. Faced with this threat and no effective treatment, most countries adopted some form of enforced social distancing (lockdown) to reduce transmission - in most cases successfully reducing the reproductive number,R, below one. However, given the large pool of susceptible individuals that remain, complete relaxation of controls is likely to generate a substantial second wave. Vaccination remains the only foreseeable means of both containing the infection and returning to normal interactions and behaviour. Here, we consider the optimal targeting of vaccination with the aim of minimising future deaths or quality adjusted life year (QALY) losses. We show that, for a range of assumptions on the action and efficacy of the vaccine, targeting older age groups first is optimal and can avoid a second wave if the vaccine prevents transmission as well as disease. After its initial detection in late 2019, the SARS-CoV-2 virus has spread across the globe with more [8] , which uses an inactive version of the virus; a vaccine created by Novavax (NVX-CoV2373) [9] 24 and one under development by GlaxoSmithKline/Sanofi Pasteur [10] , both using protein adjuvants to 25 stimulate an immune response. 26 With an array of possibilities, differing in mechanism and still in varying stages of development, 27 estimating response characteristics is infeasible. While the ideal vaccine would work to decrease 28 susceptibility [11] , thus limiting viral spread, the first successful candidate may just limit the occurrence 29 or severity of symptoms. Moreover, it is still unclear when any vaccine will reach the final stage of 30 being ready for mass deployment. Finally, while some promise has been shown in small human and 31 animal studies -the success of the Oxford vaccine in a trial involving Rhesus Macaques [7] generated 32 considerable excitement for instance -robust evidence as to how any vaccine candidate will perform 33 in the wider human population is currently lacking [12] . 34 Due to this uncertainty, we utilise a previously developed SARS-CoV-2 transmission model [13, 13] to 35 understand the likely dynamics following the deployment of a vaccine. Rather than testing a single 36 specific vaccine product, we assess three types of vaccines throughout our analysis to produce an 37 evaluation that is as informative as possible for any likely set of vaccine characteristics. Explicitly, these 38 comprise of: a vaccine that reduces susceptibility, thus being effective in inhibiting viral transmission 39 as well as protecting the individual; one that reduces the probability of becoming symptomatic, which 40 still has some benefit in reducing transmission as the model implicitly assumes that transmission 41 from asymptomatic infections is less than from symptomatic ones; and one that protects against 42 symptoms becoming severe, providing the direct protection against disease to the vaccinated individual 43 only. 44 For each vaccine type we predict the impact of a range of possible scenarios by analysing sensitivity 45 to vaccine efficacy, which may be uniform or age dependent, as well as the scale and targeting of 46 deployment. Further, by considering different orders of prioritisation in terms of age group and 47 health conditions, we arrive at an optimal targeting strategy for vaccination that achieves the greatest 48 reduction in disease impact for the number of doses administered. 49 For a variety of other diseases, there is a precedent for combining modelling approaches with health 50 economic evaluations to inform vaccine policy decisions based on a willingness to pay for each Quality 51 Adjusted Life Year (QALY) saved [14] [15] [16] [17] . Utilising this framework, we also consider how vaccination 52 may be optimised to minimise the loss in QALYs, rather than simply the number of deaths. This 53 methodology could allow a monetary value to be assigned to each dose of vaccine; while some cost 54 benefit analysis has been pursued in relation to SARS-CoV-2 [18, 19] , the unprecedented scale of 55 the pandemic invalidates the usual metrics in this approach. We therefore do not utilise this health-56 economic approach as the main focus of our paper. 57 Despite the obvious need for both country-specific and more generic forecasts of the effects of vacci-58 nation on the COVID-19 outbreak, it has received relatively limited attention. As far as we are aware 59 only two studies exist, both based on US data [20, 21] . Our study adds a UK perspective to these 60 studies and generates a wider perspective on how the type of protection offered by the vaccine as well 61 as the underlying efficacy interact with targeting risk-groups to generate maximal benefit. Model Formulation 63 We used a compartmental age-structured model, developed to simulate the spread of SARS-CoV-2 64 within regions of the UK [22] , with parameters inferred to generate a good match to deaths, hospitali-65 sations, hospital occupancy and serological testing [13] . It involves an extended SEIR-type framework: 66 susceptibles (S) may become infected and move into a latent exposed (E) state before progressing to 67 become infectious. Echoing the observed behaviour of COVID-19 infections, the model differentiates 68 -Age, comorbidity and possible vaccination stratification σ -Susceptibility λ -Force of infection (as a function of U, D ) ε -Rate from exposure to infection d -Probability of becoming symptomatic γ -Rate to recovery/death s -Probability of symptoms becoming severe 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 September 24, 2020. . https://doi.org/10.1101/2020.09. 22.20194183 doi: medRxiv preprint between individuals who are symptomatic (D, likely to be detected) and those who are asymptomatic 69 (U, likely to remain undetected). Partitioning those infectious by symptom status allows for the lower 70 level of transmission believed to be associated with asymptomatic infection. It also generates the 71 possible progression of symptoms increasing in severity, leading to hospitalisation and/or death (Fig 72 1 ). The model is stratified by age structure, with force of infection determined by the use of age-dependent 74 (who acquires infection from whom) social contact matrices for the UK [23, 24] . Additionally, we 75 assumed susceptibility and the probabilities of becoming symptomatic, being hospitalised and dying 76 to be age dependent, and are matched to UK outbreak data. Finally, our model formulation accounted 77 for the role of household isolation by allowing first infections within a household to cause new secondary 78 infections at an increased rate (more details may be found in [22] ). This allows secondary household 79 contacts to be isolated and consequently play no further role in the outbreak. Model parameters were 80 inferred on a regional basis using local time series of recorded daily hospitalisation numbers, hospital 81 bed occupancy, ICU occupancy and daily deaths [13] . This model formulation is then extended to capture a range of vaccination scenarios. Below we detail 83 how vaccination of different forms is introduced into the model; the degree to which non-pharmaceutical 84 interventions are reduced; and how the population is partitioned according to high-risk comorbidities 85 -to assess if these are a priority group for immunisation. Alongside age, it is well understood that underlying health conditions are critically important in deter-88 mining the likelihood of individuals to experience severe symptoms; in younger, healthier populations 89 a relatively low symptomatic rate has been observed [25] [26] [27] [28] and there are few severe cases. To ac-90 count for heterogeneity of risk that is not attributable to age, we therefore allowed the probability of 91 experiencing severe health outcomes (as a result of COVID-19 disease) to be dependent on underlying 92 health conditions. 93 We calculated the additional risk by comparing the prevalence of conditions amongst COVID-19 94 mortalities within the general population. For the purpose of simplification, we used a binary system 95 to divide the population into those with significant health conditions and those without, rather than 96 considering individual conditions separately [29] . 97 We estimated the proportion of the population at heightened risk, due to the presence of a cormobidity, 98 using the twelve health conditions with the highest associated risk factors as identified in a recent study 99 by Williamson et al. [30] . We summarise these conditions, alongside their prevalence and individual 100 risk, in table 1. For the 18.42% of the population with one or more of the comorbidity conditions listed in Table 1 , 102 we calculated that the average increase in the risk of morbidity is 2.43 (mean value) -suggesting 103 that individuals with these risk factors are more than twice as likely to die from COVID-19 infection 104 compared to others of the same age. The distribution of these combined symptoms by age group 105 was calculated using data from the Royal College of General Practitioners Research and Surveillance 106 Centre [31] combined with statistics on cancer and diabetes prevalence found in [32, 33] . The comorbidities associated with increased risk from COVID-19 infection are found to occur pre-108 dominantly in elder age groups (Fig 2a) , with individuals above 75 years of age more likely than not 109 to have underlying health problems. When these factors are incorporated into the predictive model, 110 we see that deaths are dominated by older age groups and individuals with underlying comorbidities 111 (Fig 2b) . 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 September 24, 2020. [30] . For each condition we give the estimated prevalence in the population as well as the increased risk of death found as a hazard ratio calculation adjusted for demographics and coexisting conditions. 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 September 24, 2020. The use of non-pharmaceutical social-distancing (or lockdown) measures has already proven to have 114 substantially reduced the scale of the pandemic [34] . We include such measures into our model through 115 a reduction in the relevant contact matrices (i.e. scaling down matrices associated with schools, work 116 places and other settings) whilst increasing the level of contact within household environments [13, 13] . 117 Additionally, we incorporate household quarantining by transferring a proportion of the symptomatic 118 individuals to a quarantined state with a still greater reduction in external contact. Test and trace is 119 not yet included in the model, due to lack of data on its current scale or effectiveness. It is expected that a sustained level of social-distancing measures will continue to be used to mitigate 121 the disease until pharmaceutical approaches are available. As such, in all simulations, we initially 122 simulate the first wave of the UK epidemic to date, followed by a continuation of current lock-down 123 measures (generating R ≈ 1.0) until vaccination is completed. As exemplified by simple models [35, 36] , the impact of any vaccination campaign is highly dependent 125 upon both the proportion of the population successfully immunised and the reproductive ratio. As 126 such, we expect the success of any COVID-19 vaccine programme to depend on the reproductive ratio 127 R when the programme begins, which in turn is dependent upon the level of non-pharmaceutical in-128 terventions (NPIs) and the proportion of the population already infected. and concern in the population, we take R ≈ 1.8 as our base-case during the majority of our simu-132 lations, but do assess a return to pre-COVID behaviour (R ≈ 2.3) on completion of the vaccination 133 campaign. The novelty of the virus, combined with the urgency in finding a response, has resulted in a plethora 136 of possible vaccine candidates in various stages of development across the globe [37, 38] . To account 137 for uncertainty in both the type and the degree of protection a vaccine may provide, we test the effects 138 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 September 24, 2020. . of three different vaccination mechanisms within our model, each over a range of efficacy: 139 1. Reduction in susceptibility (type 1): We reduce the rate at which the vaccinated susceptibles 140 may become infected. This is the most effective form of vaccine as it may significantly reduce R 141 as well as protecting the individual. 142 2. Reduction in becoming symptomatic (type 2): The age and health dependent probabilities of 143 becoming symptomatic are adjusted according to vaccine efficacy. This type of vaccine therefore 144 has a substantial impact on disease, but also has some impact on infection spread (and hence 145 R) due to asymptomatic individuals being less infectious. The action of these three vaccination types are shown in Fig 1. It should be noted that, whilst instan-151 taneous vaccination may not be a literal possibility, due to the uncertainty on time scales combined 152 with the potential for a second infection wave to be delayed by social-distancing measures during 153 vaccine deployment, it is a reasonable modelling assumption for our exploratory purposes. Simulation specifics 155 In all simulations, we ran the model for an initial period (until the end of 2020) without any form 156 of vaccination, to create a base-line population of susceptible, infectious and recovered (immune) 157 individuals that approximates the state of population when vaccination begins. Given that during 158 this period R is close to, but below one, the precise timing of the start of the vaccination programme 159 has little effect. Similarly, if NPIs are maintained until vaccination is complete, the speed of vaccination 160 is unlikely to play a major role. At the start of 2021, to simulate rapid immunisation, we transfer a specified proportion of the remaining 162 susceptible individuals into a vaccinated state; the action of infection on individuals in the vaccinated 163 class is dependent on vaccine type. 164 We now outline the four/five different approaches we use to quantify the optimal targeting of vaccine 165 and the sensitivity to key uncertainties. Priority order of vaccination 167 To determine a vaccination priority order for who should receive the vaccine first, we ranked each 168 group by the ratio of the number of doses administered to the reduction in the outcome measure of 169 interest. Our two selected outcome measures were: (i) deaths post-2020; (ii) quality adjusted life 170 years (QALYs) lost post-2020. We divided the population into 20 year age bands (0-19,20-39,40-59,60-171 79,80+), together with an additional group of people with comorbidities independent of age. For 172 each vaccination scenario considered, we exhaustively tested the order of deployment amongst these 173 groups. Prioritisation of healthcare workers 175 Due to their significantly heightened exposure, another group that may benefit from early targeted 176 vaccination is healthcare workers (HCWs). Proportionally, 11.6 times more cases have been observed 177 in UK HCWs than the general populous -this can partially be explained by the increased testing 178 in hospital environments. Yet, even accounting for this increased testing, HCWs are estimated to 179 experience a 3.40 (3.37-3.43) fold increase in infection risk [39] . 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 September 24, 2020. . We included this increased risk to HCWs in our model by adjustment of the susceptibility parame-181 ters, using a similar methodology that was applied to underlying health conditions. This increased 182 susceptibility was applied to all of the 1,134,824 full time NHS employees [40] , which we assumed to 183 be evenly distributed (age and region proportional) amongst the working age group . Sensitivity to vaccine characteristics 185 Using the identified optimal prioritisation order for the given vaccine type, with a maximum vac-186 cine uptake of 70% across each sub-group in the population, we analyse the sensitivity of number 187 of deaths and QALYs lost to vaccine efficacy, considering vaccines with 50%, 70% and 90% efficacy. 188 Here we define an efficacy of n% to give an n% reduction in susceptibility/chance of becoming symp-189 tomatic/chance of developing severe symptoms for a type 1/2/3 vaccine respectively. Sensitivity to speed of vaccine deployment 191 In the majority of the modelling we assume that the time needed to vaccinate the population and for 192 the vaccine to confer immunity is short. This assumption has little impact if the reproduction number 193 R is below one while the vaccine program is being undertaken. To explore the impact of slow vaccine deployment in the face of increasing infection we utilise sim-195 ulations in which NPIs are relaxed, to bring R up to 1.8, two months before a type 1 vaccine with 196 70% efficacy begins deployment, thus delivery occurs alongside an already widespread and increasing 197 epidemic. We simulate gradual delivery dynamics by running our model over daily time steps with 198 fixed number of susceptible or asymptomatic individuals being successfully immunised at each inter-199 val. More realistic delivery scenarios may be simulated as vaccination deployment plans are better 200 understood. Sensitivity to age-dependent efficacy 202 Many existing vaccines are not uniformly effective and response may vary significantly due to factors 203 including age [41] . In the case of a virus where severity of symptoms are age-dependent, like SARS-204 CoV-2, age-dependent vaccine efficacy may have a significant impact. Of particular concern is whether 205 an age-dependent decline in efficacy could alter the group priority order for receiving a vaccine, and 206 the potential scale of the subsequent outbreak. We test the likely implications of reduced vaccine 207 effectiveness in the elderly by considering an array of different efficacy profiles consisting of a base 208 efficacy uniform amongst those below the age of 45 with linearly declining efficacy to a minimal value 209 shared by those above the age of 85. For each of the scenarios described above and for each combination of considered vaccine type, efficacy 211 and priority order, we performed 100 separate simulations. Each simulation used a distinct parameter 212 set drawn from posterior parameter distributions, which were obtained from the inference procedure 213 that tuned the model to the available COVID-19 health outcome data streams for the UK [13] . We now consider the ordering of vaccination and its impact in terms of the number of deaths and as-216 sociated QALYs lost. For the majority of the situations we consider, we plot the number of individuals 217 vaccinated on the x-axis (assuming a maximum of 70% of susceptible or asymptomatically infected 218 individuals are vaccinated in any group) and the resultant number of deaths or QALY losses on the 219 y-axis. The priority ordering is determined by which groups generate the greatest reduction for the 220 number of doses administered (steepest decline on the graphs). 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 September 24, 2020. In every case, optimising for either a reduction in death or a reduction in QALYs was found to give 223 consistent ordering, due to the substantive contribution of mortality events to the overall QALY loss 224 (Fig 4) . When structuring by age alone, the most efficacious reduction was found through an oldest 225 first approach -despite not being the most crucial group in terms of transmission, the considerably 226 heightened vulnerability amongst the elderly means that priority should be given to protecting them 227 directly. We also highlight the substantial advantages of a strategically targeted vaccine over an 228 unbiased (random) approach in every scenario (blue line, Fig 4) . In contrast, there was less consistency in the optimal position of vaccinating comorbidities in the 230 priority order, which varied between just before and just after the 60-80 age group. One such instance 231 in which the discrepancy may be seen is when contrasting the type 1 and type 3 vaccine with a low 232 level of NPIs (R ≈ 1.8, Fig 4 a and b) . While the cost-benefit implications of this variation are often 233 found to be small, due to the large overlap between the group of people with comorbidities and the 234 9 . 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 September 24, 2020. elderly, it is substantial enough that it may be worth critical consideration in a scenario where vaccine 235 quantity and/or deployment rate are limited. Healthcare workers 237 We now consider the addition of healthcare workers (HCW) as an additional risk group, and assess 238 their optimal position in the order of vaccination priority. For a type 1 vaccine (for which there is 239 benefit in targeting infection spreaders as well as the vulnerable) we associate high important to the 240 vaccination of HCW, second only to the most elderly age group of those aged 80 and above (Fig 5) . It is 241 important to note that our treatment of HCWs only accounts for increased personal risk. We have not 242 taken into account the increased contact between HCWs and the vulnerable which may significantly 243 amplify their risk as spreaders of infection, increasing their priority for vaccination. Given also the 244 relatively small number of HCWs (less than 2% of the population), we conclude that this group should 245 be included as a high priority group for vaccination. However, for vaccines of type 2 or 3 that do not 246 significantly reduce infection spread, the HCW group may be considerably less important and their 247 priority should be judged accordingly. 249 For the three types of vaccine action, and for three different levels of efficacy we consider the impact 250 of a vaccine program targeted by age and comorbidity under weak non-pharmaceutical interventions 251 (R ≈ 1.8). For Type 1 vaccines, which have the greatest impact, we also consider complete lifting of 252 all non-pharmaceutical interventions (R ≈ 2.3). Due to the ability of a type 1 vaccine in preventing the spread of infection as well as protecting specific 255 individuals, we find that such a vaccine, even with relatively low efficacy, could be highly effective in 256 preventing further COVID-19 mortality when combined with limited social-distancing measures (i.e 257 when R ≈ 1.8). The best performing prioritisation order begins with those aged 80 and above, followed by those with 259 health conditions, before the rest of the population in age order. Under such an ordering, we estimate 260 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 September 24, 2020. . 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 September 24, 2020. . https://doi.org/10.1101/2020.09.22.20194183 doi: medRxiv preprint a vaccine with 50% efficacy delivered to 70% of the population above the age of 20 to be sufficient 261 to prevent a SARS-CoV-2 resurgence in our considered scenario (Fig 6 top row) , although a more 262 efficacious vaccine could achieve the same results with only vaccinating those above 40. When combined with limited social-distancing measures (such that R = 1.8), a type 2 vaccine (that 265 reduces the chance of becoming symptomatic) with reasonable efficacy may still be sufficient to prevent 266 a significant mortality in a second wave (Fig 6 second row) . However, due to only providing a limited 267 reduction in transmission little additional benefit is to be found in vaccinating those in low risk 268 (younger age) categories. Again we identify that it is best to prioritise those above the age of 80, 269 followed by those with health conditions, before the rest of the population in age order. For type 270 2 vaccines that generate an efficacy of 50% or below we would predict a large-scale second wave of 271 infection when control measures are relaxed with a comparable number of deaths to experienced in 272 the first wave. Contrary to the other three vaccination types, here we find it best to prioritise 60-80 year olds above 281 all those with health conditions. We postulate this is due to the lack of reduction in transmission, such 282 that the higher degree of social contact amongst the younger people within the comorbidity group is 283 not an influencing factor. The most desirable vaccine would be one that is sufficient to entirely contain the pandemic without 286 the need for any other intervention (when we estimate R ≈ 2.3). Amongst our set of vaccine scenarios, 287 we find the only plausible candidate for preventing a SARS-CoV-2 resurgence (in the absence of any 288 other intervention) would be a type 1 vaccine with an efficacy above 80% and with 70% of the entire 289 population vaccinated (Fig 6 bottom row) . Other levels of vaccine efficacy would naturally trade-off 290 with a different proportions of the population needing to be vaccinated; similarly a higher uptake 291 in the older at-risk populations would also mean that fewer younger individuals would need to be 292 immunised. For a type 1 vaccine in a scenario without additional measures (R ≈ 2.3), we find scant difference 294 between taking a fully age ordered strategy, and one including comorbidity, leaving no clear point at 295 which those we categorise as having health conditions should be prioritised (Fig 4d) . The results presented so far are based on a model with instantaneous vaccination delivery. This is 298 deemed sufficient for a generic understanding of the impacts of vaccination, varying uptake levels and 299 targeting. Additionally, if NPI remain in place (such that R < 1) until vaccination is completed, the 300 time taken to implement a slower vaccination campaign will lead to there being fewer cases when NPIs 301 are finally relaxed. It is also the case that, since temporal factors such as deployment speed and a 302 12 . 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 September 24, 2020. . start date for delivery are largely unknown, there is limited value in incorporating complex dynamics 303 at this time. More realistic delivery scenarios may be simulated as vaccination deployment plans are 304 better understood. In a scenario where R is greater than one during the vaccine program, such that there is a race between 306 vaccination to reach herd-immunity and the rise of the epidemic, the speed of vaccine deployment is 307 key (Fig 7) ; a rapidly deployed untargeted campaign is far more successful than a slow but optimally 308 targeted one. Importantly, we find that the optimal vaccination strategy (in terms of the ordering of age 309 and risk groups) is independent of delivery speed. However, for very rapid vaccine deployment (when all 310 groups can be vaccinated before there are many more infections) or for very slow deployment (when the 311 epidemic is complete before many individuals are immunised) the ordering is far less important. The total number of (left) deaths and (right) QALYs lost resulting from a second epidemic wave vs speed of deployment for a type 1 vaccination with 70% uptake and 70% efficacy. Vaccine deployment is started 2 months after stricter NPIs are relaxed to leave low level measures sufficient to keep R ≈ 1.8. The purple line (and shaded prediction region) represents projected outcomes under the identified optimal ordering with age and comorbidity groups, the orange line outcomes using the identified optimal ordering accounting for age groups only (without comorbidity), and the blue line outcomes with an unbiased population wide delivery. To simulate reduced efficacy of the vaccine in older age groups, we allow efficacy to be age-dependent 314 -attaining a high maximum value for individuals below age 45, then dropping linearly to age 85 when 315 the efficacy reaches a minimum value (Fig 8a inset) . There is again a surprising robustness in ordering (Fig 8a) with the elderly (over 80 years old) remaining 317 the key group to initially target, even when the efficacy in this age group drops to just 20%. Even 318 lower efficacies necessitate a switch with individuals with underlying comorbidities or aged 40-60 being 319 prioritised. Lower efficacy vaccines are, unsurprisingly, associated with larger subsequent epidemics 320 and therefore more deaths; much of this increase is concentrated, however, in low efficacy regions 321 of parameter-space, with the estimated number of deaths being relatively constant across a range of 322 efficacy values for both older and younger age-groups. While here we focus on a type 1 vaccine; the results for vaccine types 2 and 3 are found to be more 324 extreme, as the drop in efficacy aligns with the age-groups most in need of protection. For a type 3 325 vaccine the elderly are found to remain the initial targeting priority up to a reduction in efficacy down 326 to just 10%. 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 September 24, 2020. A maximum efficacy value is applied to all individuals below the age of 45 and a minimum level to individuals above the age of 85. Efficacy is assumed to decay linearly between these two levels to give the efficacy for intermediary age groups. This distribution is represented by the inset in panel (a). Panel (a) shows when, dependent on minimum and maximum efficacy, the two groups deemed most significant for vaccination impact vary. In the purple region it is optimal to vaccinate those above the age of 80 followed by comorbidities, in the red comorbidities followed by 80+ and in the yellow those in the 40-60 age group followed by comorbidities. Panel (b) shows the expected further mortality resulting from a second infection wave with 70% of the whole population vaccinated for different minimum/maximum type 1 vaccine efficacies. The large dark blue region corresponds to less than 10,000 deaths in any second wave following vaccination. 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 September 24, 2020. It has often been stated that the only way for population behaviour to return to normal is through 329 achieving herd-immunity. Allowing this to occur through natural infection is far too dangerous, even 330 if the most at-risk groups are shielded, making vaccination the only viable alternative. While there are 331 huge efforts being undertaken to develop a vaccine, less attention has been paid to how such a vaccine 332 would be deployed. For SARS-CoV-2, the infection is relatively homogeneous across age-groups with 333 a slight bias towards younger adults [42] , but disease -especially severe disease -is associated with 334 old age and a range of comorbidities. As with many vaccines, there is tension between vaccination 335 of those most responsible for driving transmission (vaccination to reduce R) and vaccination of those 336 most likely to suffer severe health outcomes (vaccination to limit disease) [43] . Here, using detailed 337 mathematical models that have been matched to UK COVID-19 outbreak data, we find that vaccine 338 strategies targeting the elderly are optimal in terms of reducing future mortality (Fig 4) , even if 339 vaccinating younger group-ages would have a greater impact on the reproductive number, R. 340 We have found that five main factors influence the success of any vaccination programme (Fig 6) . 4. The proportion of the population vaccinated: throughout we have assumed that at most 70% 352 of any age or risk group would be vaccinated, however there is a natural relationship between 353 vaccine efficacy and proportion vaccinated that generates the same level of overall protection; 354 5. Who is vaccinated: we have consistently shown that prioritising the vaccination of the elderly 355 is by far the most effective strategy for reducing the number of deaths in any second wave. It 356 is only for vaccines that have a vastly reduced efficacy in the elderly (below 20%) that other 357 prioritisation orderings become more effective. In the majority of this work, we have focused on the resultant outbreak after protection by vaccination 360 is complete. It is likely that any future vaccine will require (at least) two doses, and there will be 361 a delay between vaccination and protection. If the reproductive ratio remains below one while these 362 events take place, then in general the delays are irrelevant. However, in the scenario where NPIs are 363 relaxed before immunisation of the population is complete, rapid deployment of the vaccine is critical 364 to success (Fig 7) . Our analysis has also focused throughout on two differing outcome measures, both the number of 367 deaths and the expected QALY loss. Given that QALYs give greater weight to preventing illness or 368 death in younger age-groups, it is somewhat surprising that the optimal order of vaccination remains 369 unchanged. This can only be attributed to the far greater severity of disease experienced by the elderly. 370 We have purposefully not performed a full cost-benefit analysis on the vaccine, as in many ways the 371 outcome of this pandemic is difficult to capture in monetary terms. However, under the assumption 372 . 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 September 24, 2020. . that R ≈ 1.8, an unvaccinated population would experience a loss of 1.58 (1.29-1.78) million QALYs 373 during a second wave, which could be prevented by vaccination of 20.6 (18.9-22.3) million targeted 374 individuals or 41.2 (37.8-44.6) million doses of a vaccine with 90% efficacy (assuming the need for 375 a primary and booster dose). This simple calculation, together with a standard cost-effectiveness 376 threshold of £20,000 per QALY, would suggest that the UK should be willing to pay around £767 377 (£578-£942) per dose of vaccine -highlighting its huge public health benefit. Our mathematical model has been carefully matched to the observed dynamics in the UK [13] , captur-380 ing the fundamental age-structured epidemiology. In contrast, little is known about the characteristics 381 of any new vaccine and the associated model parameters. Many more details could therefore be in-382 corporated within the model structure when these become known for any emerging vaccine candidate. 383 We have, for simplicity, assumed 70% vaccine uptake across all age-groups based on what has been 384 obtainable for other vaccines, such as within elder age groups and healthcare workers for the UK sea-385 sonal influenza vaccination programme [44] . It is likely that the public's response to a SARS-CoV-2 386 vaccine may be different, depending on perceived risk which is likely to be age dependent. Similarly, 387 the assumed efficacy has either been taken as constant across all age-groups or obeying a simple de-388 clining function with age; incorporating more realistic estimates about the action of any vaccine is 389 a vital first step in assessing the benefits. To a large extent, we have also ignored the time delays 390 between the start of any vaccine program and the protection of the vaccinated individuals; the full 391 implications of any delays can only be calculated once more is known about the mechanisms and limits 392 on delivery, as well as a better understanding of the reproductive number (R) during and after the 393 campaign. Including these elements within the model is feasible, but is presently hampered by a lack 394 of data for parameter inference. This work has focused on the dynamics within the UK, but the robustness of our conclusions, that 396 the vaccine should be optimally targeted at the elderly, suggests that this finding should hold for 397 many countries with similar age-profiles and age-structured mixing patterns. Ultimately, vaccination 398 remains our only way out of this pandemic, and it is therefore important that the vaccine is deployed 399 as efficiently as possible such that early limited supplies are used to greatest effect. 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 September 24, 2020. The data were supplied from the CHESS database after anonymisation under strict data protection 423 protocols agreed between the University of Warwick and Public Health England. The ethics of the 424 use of these data for these purposes was agreed by Public Health England with the Government's 425 SPI-M(O) / SAGE committees. Competing interests 427 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 September 24, 2020. . https://doi.org/10.1101/2020.09.22.20194183 doi: medRxiv preprint Covid-19 situation update worldwide, as of 16 Check if you or your child has coronavirus symptoms Coronavirus vaccine: Uk government signs deals for 90 million doses Evaluation of the immunogenicity of prime-boost vaccination with the replication-deficient viral vectored covid-19 vaccine candidate chadox1 ncov-19 Safety and immunogenicity of the chadox1 ncov-19 vaccine against sars-cov-2: a preliminary report of a phase 1/2, single-blind, randomised controlled trial Ad26-vector based covid-19 vaccine encoding a prefusion stabilized sars-cov-2 spike immunogen induces potent humoral and cellular immune responses Phase 1/2 study to describe the safety and immunogenicity of a covid-19 rna vaccine candidate (bnt162b1) in adults 18 to 55 years of age: interim report Sars-cov-2 spike glycoprotein vaccine candidate nvx-cov2373 elicits immunogenicity in baboons and protection in mice Gsk vaccine press release A snapshot of the global race for vaccines targeting sars-cov-2 and the covid-19 pandemic Coronavirus vaccine trials have delivered their first results-but their promise is still unclear Fitting to the uk covid-19 outbreak, short-term forecasts and estimating the reproductive number Cost-effectiveness of childhood influenza vaccination in england and wales: results from a dynamic transmission model Extending the elderly-and risk-group programme of vaccination against seasonal influenza in england and wales: a cost-effectiveness study Assessing the cost-effectiveness of hpv vaccination strategies for adolescent girls and boys in the uk Seasonal influenza: Modelling approaches to capture immunity propagation Providing care for the 99.9% during the covid-19 pandemic: How ethics, equity, epidemiology, and cost per qaly inform healthcare policy Evidence-based, cost-effective interventions to suppress the covid-19 pandemic: a rapid systematic review Vaccine optimization for covid-19, who to vaccinate first? medRxiv Vaccine efficacy needed for a covid-19 coronavirus vaccine to prevent or stop an epidemic as the sole intervention Predictions of covid-19 dynamics in the uk: short-term forecasting and analysis of potential exit strategies Social contacts and mixing patterns relevant to the spread of infectious diseases Projecting social contact matrices in 152 countries using contact surveys and demographic data Forecasting the scale of the covid-19 epidemic in kenya COVID-19 Infection in Children: Estimating Pediatric Morbidity and Mortality. medRxiv preprint pages Epidemiology of COVID-19 Among Children in China Susceptibility to and transmission of COVID-19 amongst children and adolescents compared with adults: a systematic review and meta-analysis Assessment of workers personal vulnerability to covid-19 using covid-age. medRxiv Opensafely: factors associated with covid-19-related hospital death in the linked electronic health records of 17 million adult nhs patients Royal college of general practitioners (rcgp) research and surveillance centre National diabetes audit mortality analysis Cancer incidence by age The effect of nonpharmaceutical interventions on COVID-19 cases, deaths and demand for hospital services in the UK: a modelling study Infectious diseases of humans: dynamics and control Modeling infectious diseases in humans and animals The early landscape of covid-19 vaccine development in the uk and rest of the world Developing covid-19 vaccines at pandemic speed Risk of covid-19 among front-line health-care workers and the general community: a prospective cohort study Nhs workforce statistics Antibody response to influenza vaccination in the elderly: a quantitative review Community prevalence of sars-cov-2 virus in england during may 2020: React study. medRxiv Targeting vaccination against novel infections: risk, age and spatial structure for pandemic influenza in great britain