key: cord-0797221-prqxu1dv authors: Dyson, L.; Hill, E. M.; Moore, S.; Curran-Sebastian, J.; Tildesley, M. J.; Lythgoe, K. A.; House, T.; Pellis, L.; Keeling, M. J. title: Possible future waves of SARS-CoV-2 infection generated by variants of concern with a range of characteristics date: 2021-06-10 journal: nan DOI: 10.1101/2021.06.07.21258476 sha: 076dbee5dbf15f7abc077d0f76f5086ebb5e9399 doc_id: 797221 cord_uid: prqxu1dv Ongoing infection with, and associated viral reproduction of, SARS-CoV-2 provides opportunities for the virus to acquire advantageous mutations, which may alter viral transmissibility and disease severity, and allow escape from natural or vaccine-derived immunity. The number of countries reporting Variants of Concern (VOCs) with such mutations continues to rise. Here, we investigate two scenarios for third waves of the COVID pandemic: one driven by increased transmissibility, and another driven by immune escape. We do this using three mathematical models: a parsimonious susceptible-latent-infectious-recovered (SEIR) deterministic model with homogeneous mixing, an age-structured SARS-CoV-2 transmission model and a stochastic importation model. We calibrated our models to the situation in England in May 2021, although the insights will generalise to other contexts. We therefore accurately captured infection dynamics and vaccination rates, and also used these to explore the potential impact of a putative new VOC-targeted vaccine. Epidemiological trajectories for putative VOCs are wide-ranging and heavily dependent on their transmissibility, immune escape capability, and the time at which a postulated VOC-targeted vaccine may be introduced. We demonstrate that a VOC with either a substantial transmission advantage over resident variants, or the ability to evade vaccine-derived and prior immunity, is expected to generate a wave of infections and hospitalisations comparable to those seen in the winter 2020-21 wave. Moreover, a variant that is less transmissible, but shows partial immune-escape could provoke a wave of infection that would not be revealed until control measures are further relaxed. Introduction 1 tory of the SARS-CoV-2 epidemic, there is burgeoning interest. One such paper used a deterministic 56 compartmental model to simulate the impact of the potential introduction of the more transmissible 57 variant, B.1.1.7, into a Colombian population in which previous strains were dominant [33] . The 58 authors considered the effect on prevalence hospitalisation and deaths, and concluded that the in- 59 troduction of such a variant would necessitate increased NPIs and an increased pace of vaccinations, 60 though the potential immune escape characteristics of a VOC were not explored. Another example 61 study devised a two-strain mathematical framework to model a resident-and a mutant-type viral 62 population to estimate the time at which a mutant variant is able to take over a resident-type strain 63 during an emerging infectious disease outbreak, with the spread of the B.1.1.7 variant in Ontario, 64 Canada used as a case study [34] . 65 In this study, we use three mathematical models of novel SARS-CoV-2 variant dynamics to evaluate 66 the driver, and the likely timescales, of SARS-CoV-2 VOC epidemics in England. We demonstrate 67 that a VOC can cause subsequent epidemic outbreaks comparable in magnitude to earlier waves in the 68 pandemic if it possesses either a large transmission advantage over the existing resident variants, or 69 the ability to evade immunity (either from infection-or vaccine-derived). Further, even when a novel 70 variant is less transmissible than the locally resident variants, immune escape can lead to a marked 71 wave of infection and consequential hospitalisations. In addition, the reduced transmissibility of such 72 a VOC can allow it to remain difficult to detect until NPIs are reduced. Finally, we explore the relative 73 timing of VOC-targeted vaccines versus the establishment of community transmission of an emergent 74 VOC, and show a multitude of projected possibilities, demonstrating the need to remain attentive to 75 all possible scenarios. 76 Modelling study outline 78 We investigate two ways in which variants may be concerning: either that they may be more trans-79 missible than the resident variants; or that they may evade immunity (infection-or vaccine-derived). 80 While there are indications of immune escape for some particular variants [22, 23] , the extent to which 81 these variants evade immunity in vivo is uncertain [26] , although vaccine breakthrough infections have 82 been reported. We therefore begin by exploring parameter space using a parsimonious deterministic 83 model with simple homogeneous mixing. While such a parsimonious model is useful for exploring 84 parameter space and understanding the essential dynamics, it is unsuited to understanding how infec-85 tion may be translated into disease burden. We therefore extend our analysis using a more complex 86 age-structured model: firstly to ensure that the simplifications made for the parsimonious model do 87 not have a large effect on the dynamics and secondly to investigate how the infections seen in the 88 parsimonious model may translate into hospitalisations. In particular, as the roll-out of vaccinations 89 progresses, we expect the proportion of infections that result in hospitalisations or death to decrease, 90 reducing the burden of large numbers of infections. Finally, we explore how the timing of the intro-91 duction of a putative VOC-targeted vaccine and the rate of VOC introductions into the population 92 (modelled using a Gillespie stochastic simulation) impact the trajectory of the epidemic. Supporting Information. While these scenarios focused on VOCs that had either an advantage in 102 terms of transmissibility or to escape previously acquired immunity (but not both), our sensitivity 103 analyses also considered VOCs possessing a combination of both advantages. 104 Table 1 : Transmissibility and infection immune escape properties for putative VOCs. In the main analysis we consider four VOCs (VOC MT, VOC E, VOC LT+E, VOC E+LH), with results for two additional VOCs (VOC Ev and VOC Ei) presented in the Supporting Information. Note that in the age-structured SARS-CoV-2 transmission model we also applied efficacy scalings upon both symptomatic disease and hospitalisations (severe disease). In the remainder of the Methods, we first overview the assumptions applied across all our models, 105 then present in turn each model and the analyses that was performed in each case, before closing by 106 summarising our vaccine efficacy assumptions. Model agnostic assumptions 108 Since we are primarily interested in the epidemiological impact of variants, in all models we assumed no 109 waning immunity (for immunity resulting from either natural infection or vaccination), no 'seasonality' 110 in the form of oscillatory rate constants, and no individual-level reinfection with the same variant. 111 This allows our results to capture the 'pure' signal from variant effects, although there is nothing in 112 our approach that precludes inclusion of additional phenomena if they are of scientific or practical 113 interest. Both transmission models introduced 2,000 VOC infected individuals (a prevalence of approximately 115 0.0035%) on 17th May 2021 unless stated otherwise, representing a comparable population to the new 116 non-B.1.1.7 VOCs reported in England in early to mid-May 2021 [35] . We consider the initial group 117 of VOC infected individuals to be large enough that the average dynamics are reasonably captured by 118 a deterministic system (see Section 4.4 of the Supporting Information). The number of initial VOC 119 infected individuals was taken from the portion of the population that were both unvaccinated and 120 not previously infected by any variant. To capture changes in contact/mobility in response to relaxations of NPIs at each Step of the roadmap 122 out of lockdown for England, we set estimates of R excluding immunity in each Step at central values 123 used by the University of Warwick SARS-CoV-2 transmission model for modelling assessing relaxation 124 of restrictions, in particular the Roadmap Step 3 modelling [36] . For the breakdown of R excluding 125 immunity values within each step, and the associated time intervals, see Table 2 . We developed a parsimonious deterministic ordinary differential equation (ODE) model consisting of 136 an SEIR disease state formulation for resident variants (including B.1.1.7) and a VOC (see Table 2 137 for parameterisation), with variant-specific transmissibility. Model equations can be found in Section 138 2 of the Supporting Information. 139 We initialised the proportion of the population vaccinated with the AZ vaccine and Pfizer/Moderna 140 vaccines using data reported from the National Immunisation Management Service (NIMS), the System 141 of Record for the NHS COVID-19 vaccination programme in England [37] (see Table 2 ). We used the 142 vaccine rollout speed to calculate the number of first doses administered per day. We assumed a 143 future mix of vaccinations in the ratio 60% (AZ), 30% (Pfizer) and 10% (Moderna) (as used in [38] ). 144 Where individuals were both recovered and vaccinated, we assumed they received the greater of the 145 two protections. 146 We used a population size of 56 million, comparable to the ONS mid-2019 estimate for the population 147 of England [39] . All simulations began from 10th May 2021 with a time horizon of 365 days. [39] ) and assumed final coverage (95%) AZ/non-AZ vaccine ratio 60%/40% Assumed mixture as in [38] 5 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 10, 2021. ; Investigating VOC outbreak potential and epidemic trajectories 149 We investigate the potential for illustrative VOCs to transmit widely amongst the community upon 150 its introduction by computing the value of 'R with immunity' over time. R with immunity includes 151 both the effects of immunity (due to vaccination or prior infection) and the level of NPIs in place at 152 the time. Thus, R with immunity represents the potential for a newly-introduced VOC to generate 153 a large epidemic at a particular time, assuming that there is no deviation from the roadmap prior to 154 that time. Exploration of parameter sensitivity 156 We next explored how varying the transmissibility and immune escape attributes affected the outbreak 157 size, peak in any resultant wave of infection and R with immunity (effective R, R VOC eff ). Our sensitivity 158 used a range of relative transmissibilities of the VOC versus the resident variants (from 0.5 to 1.5, 159 with an increment of 0.1), and a proportional efficacy against the VOC derived from vaccination or 160 prior natural-infection ranging from 0.5 to 1.0 (with an increment of 0.05). The age-structured SARS-CoV-2 transmission model 162 As part of the previously outlined parsimonious model, we did not include age-structure and only 164 considered SARS-CoV-2 infections. To assess the healthcare implications of a VOC that becomes 165 established amongst the community, we extended the University of Warwick SEIR-type compartmental 166 age-structured model, developed to simulate the spread of SARS-CoV-2 within regions of the UK [40] 167 to allow inclusion of a putative VOC. 168 The model has been fitted to UK outbreak data, giving a comparable match to deaths, hospital ad-169 missions, hospital occupancy and test positivity from community testing (Pillar 2 tests). The model 170 is formulated as a system of ordinary differential equations (Section 3 of the Supporting Informa-171 tion). The force of infection for this model was determined by the use of age-dependent (who acquires 173 infection from whom) social contact matrices for the UK [42, 43] . We assumed susceptibility and the 174 probabilities of becoming symptomatic, being hospitalised and mortality to be age-dependent. Our 175 model formulation accounted for the role of household isolation by allowing first infections within 176 a household to cause new secondary infections at an increased rate (more details may be found in 177 Keeling et al. [40] ). This allows secondary household contacts to be isolated and consequently play no 178 further role in the outbreak. Sensitivity of hospitalisations to VOC characteristics 180 Echoing the observed behaviour of COVID-19 infections, the model differentiates between individuals 181 who are symptomatic and those who are asymptomatic. Partitioning those infectious by symptom 182 status allows for the lower level of transmission believed to be associated with asymptomatic infection. 183 It also generates the possible progression of symptoms increasing in severity, leading to hospitalisation 184 and/or death. Utilising the case severity module of the model, we investigated daily hospital admis-185 sions, total hospital admissions and the impact on the infection age-distribution for our four main 186 VOC scenarios: VOC MT, VOC E, VOC E+LH and VOC LT+E (Table 1) . We simulated each VOC 187 alongside the existing resident variants by the duplication of the base model equations (Section 3 of 188 the Supporting Information). 189 6 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 10, 2021. All simulations began from January 2020 with a time horizon of 1095 days (through to December 190 2022), although results presented here are abridged due to uncertainties arising from a rapidly evolving 191 epidemic. The central estimates for R excluding immunity for Steps 3 and 4 matched those listed in 192 Table 2 . VOC outbreak potential and utility of VOC targeted vaccines 194 The previous analyses sought to evaluate the likely timescales, drivers and healthcare impact of CoV-2 VOC epidemics under a specific set of assumptions, along with their sensitivity to the variation 196 in epidemiological parameters that underpin the transmission dynamics. However, epidemics starting from a small number of seed introductions are inherently stochastic, and 198 deterministic models are unable to capture that stochasticity. To that end, we adopted a stochastic 199 modelling approach to explore the outbreak potential of a VOC post-emergence. Our VOC importation model was a Gillespie stochastic simulation [44, 45] with six types-at-birth and 201 12 disease states. The types-at-birth comprised combinatorial combinations of two infection history 202 states (either having had no prior-infection or to have been previously infected with resident variants) 203 and three vaccination states (unvaccinated, vaccinated with AZ, vaccinated with Pfizer/Moderna). 204 Infected individuals in these types could then be either latent infected or infectious, resulting in a 205 total of 12 disease states. Using the stochastic framework, we studied the dependence of the epidemic 206 probability (the probability of reaching a prevalence of 100 cases within 365 days) for a VOC E type 207 variant on its relative transmissibility compared to resident variants (from 0.5 to 1.5, with an increment 208 of 0.1) and on the amount of effective importations per day (from 0.02 to 0.40, with an increment of 209 0.02). We interpret importations as the second generation cases stemming from onward transmission 210 to contacts of a single index case. To cross-check the correctness of the simulation, we compared it 211 with analytical results for a continuous-time multi-type branching process model with immigration 212 (see Section 4 of the Supporting Information). Furthermore, another uncertain aspect of the system is the plethora of SARS-CoV-2 vaccines in devel-214 opment [46] and the prospect of previously approved vaccine formulations being updated to improve 215 protection against VOCs. For example, there has been in-vivo evidence regarding the efficacy of 216 the Novavax vaccine against the B.1.351 variant from phase 2 trials in South Africa, finding 51.0% 217 (95% CI: -0.6% to 76.2%) mild to moderate disease efficacy against B.1.351 in HIV negative individ-218 uals [47] . Using the parsimonious SARS-CoV-2 two-variant transmission model, we investigated the sensitivity 220 of a VOC with immune escape properties (VOC E) to the timing and properties of a VOC-targeted 221 vaccine. We sampled from the stochastic VOC importation model to initialise the introduction time 222 of 100 VOC infecteds and their distribution across the applicable infected compartmental states of 223 the parsimonious SARS-CoV-2 transmission model. We then appraised sensitivity to the date a 224 VOC targeted vaccine began to be administered (from 1st June 2021 to 1st November 2021, with an 225 increment of one month) versus the amount of effective VOC imports per day (from 0.12 to 0.40, with 226 an increment of 0.02). 227 We assumed individuals previously vaccinated were subsequently re-vaccinated, exploring prioritisation 228 being either initially given to previously vaccinated individuals or to unvaccinated individuals. In all 229 the above-described scenarios we fixed the R excluding immunity for resident variants in the stochastic 230 model at 3. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 10, 2021. For the parsimonious deterministic model, as part of the parsimonious approach, we assumed the total 240 vaccine infection efficacy effect was obtained after a single dose and that there was no delay in the onset 241 of protective effects post-vaccination. No efficacy estimates for symptomatic disease, hospitalisation 242 or death were used as the parsimonious model tracked infections only. In the age-structured SARS-CoV-2 transmission model, the effect of vaccination was realised at each 244 stage of case severity progression, including parameters, with increases for each between one and two 245 doses, for: (i) reduced infection, (ii) reduced symptoms, (iii) reduced hospitalisations (severe case 246 outcomes). As well as corresponding to protection of the individual, symptom efficacy also had an 247 impact on disease spread due to the assumption that a reduced viral load corresponds to a lower level of 248 infectiousness. We made an assumption that prevention of symptoms may be less affected by immune 249 escape than infection and fixed symptom efficacy at 90% of the estimated efficacy against resident 250 variants for VOC E (compared to 75% for infection efficacy). Symptom efficacy also provided a lower 251 bound for efficacy against hospitalisation, the latter taken between a 10% and 25% reduction for VOC 252 E. We present full details of all efficacies used in Table 3 , including the protection realised by previous 253 infection in each of the three actions considered by vaccination. Previously infected individuals were 254 assumed to have equal protection regardless of vaccination status. We carried out a sensitivity analysis 255 to explore a broader range of efficacy effects. 256 We also used the age-structured model to assess the impact on hospitalisations for a VOC with similar 257 characteristics to VOC E, except with proportional efficacy against severe disease (hospitalisations) 258 being unadjusted. We labelled this scenario as VOC E+LH (immune escape plus less hospitalisa-259 tions). Vaccine efficacy estimates against resident variants 261 Central vaccine efficacy estimates for both transmission models (Table 3 ) are based on the emerging 262 data in the UK population and elsewhere. Source studies for these estimates can be found in Table S1 263 in the Supporting Information. 264 Table 3 : Efficacy assumptions against the resident variants and for our illustrative VOCs with immune ecscape (VOC E and VOC LT+E, with efficacies for these VOCs stated in parentheses). We computed the efficacies against VOCs as the product of the proportional vaccine efficacy and the efficacy against the resident variants. For a summary CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 10, 2021. We summarise the transmissibility and infection immune escape properties for each of our putative 271 VOCs in Table 1 as proportions compared to the resident strains, with the efficacies for a subset of 272 our illustrative VOCs (VOC E and VOC LT+E) provided in Table 3 . Fig. 1(a) , black line). This is in 279 broad agreement with contemporaneous modelling of the roadmap relaxations [36] . On the other hand, VOCs can lead to waves of infection beyond what we would expect from the 281 resident variants. The introduction of a variant that was 1.5 times more transmissible than resident 282 variants (VOC MT) resulted in a surge of infection peaking in August 2021. Additionally, the peak 283 exceeded the estimated peak prevalence during the January 2021 wave in England as estimated from 284 the ONS infection survey [48] (Fig. 1(a) , blue line with square markers). Similarly VOC E, which, whilst no more transmissible than resident variants, had a degree of immune 286 escape from vaccination-derived immunity or prior infection (25% reduction compared to resident 287 variants), also provoked a considerable wave of VOC infections. Compared to the more transmissible 288 VOC MT, the epidemic wave was lagged by a month, with a peak in infectious prevalence in excess 289 of the estimated peak prevalence during the January 2021 wave ( Fig. 1(a) , orange line with plus sign 290 markers). VOCs that had only one component of immune escape, to either vaccination only or prior infection 292 only, displayed shallower and broader epidemic waves compared to VOC E. We found that VOC Ei 293 (immune escape to prior infection only ) peaked a month late with a higher magnitude and had a 294 longer epidemic tail than VOC Ev (immune escape to vaccination only, see Fig. S4 ). A variant that was less transmissible than the resident variants but had immune escape attributes, 296 VOC LT+E, could give rise to an elongated epidemic that was flatter, and more delayed, than VOC E 297 ( Fig. 1(a) ). These dynamics were a consequence of the relative growth of the two variants depending 298 on a combination of relative transmissibility and relative immunity. Relaxing measures at a pace that 299 kept resident variants under control naturally exposed other variants where the vaccines provide a 300 lower protective effect (Fig. 1(c) ). The trajectory of the initial resident variant was similar soon after the introduction of any of the VOCs. 302 Increases in VOC infections then translated into increased immunity against resident variant infections, 303 which resulted in trajectories diverging by late July 2021. As a consequence, the VOCS with large 304 resultant infection waves (VOC MT and VOC E) coincided with a shallower, earlier peak in resident 305 variant infectious prevalence and a shortened outbreak duration for resident variants (Fig. S5) . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 10, 2021. ; Both the outbreak size and peak in infectious prevalence for VOCs were sensitive to the transmissibility 307 and ability to evade existing immunity (Figs. 1(b) and 1(d) ). We found a highly transmissible VOC, 308 1.5 times more transmissible than resident variants, that also had a great ability to evade prior-309 infection and vaccine-derived immunity (proportional immune efficacy against the VOC of 0.5), could 310 cause outbreaks infecting the majority of the population and attain a peak infectious prevalence 311 approaching 10%. On the other hand, outbreaks were generally not sustained for VOCs that had a 312 combination of being less transmissible than resident variants with only minor evasion of infection-313 and vaccine-derived immunity. As time goes on, both the immunity of the population (via vaccinations and infections with resident 315 strains) and the level of NPIs change, leading to different dynamics depending on when a VOC is 316 introduced. Different types of VOCs have more advantage at different times, and this can be seen 317 in the value of the reproductive ratio, R, when population immunity and level of NPIs are included. 318 While more transmissible variants (such as VOC MT) have highest R with immunity early on, that 319 advantage is degraded over time as the population builds immunity (Fig. 1(c) ). Variants that have 320 a degree of immune escape then gain greater relative advantage in the long term (VOC E and VOC 321 LT+E). Notably, introducing either VOC MT or VOC LT+E from November 2021 or later resulted in 322 matched R with immunity values, plateauing at approximately 1.2. Conversely, before Step 4 of the 323 relaxation roadmap occurs, VOC LT+E may be quite indistinguishable from resident variants. These facets were borne out by comparing outbreak size and infectious case peak summary statistics; 325 an introduction of either VOC MT and VOC LT+E in late 2021 gave similar epidemic trajectories. 326 Further, VOC MT being introduced in late 2021, rather than 17th May 2021, resulted in a greater 327 than three-fold reduction in outbreak size and peak infectious prevalence. For VOC E, quantitatively 328 the impacts of a later introduction date were less marked. In particular, a later introduction date 329 led to only a small decrease in the outbreak size from approximately 60% (for an introduction date 330 of 17th May 2021) to 50% (for an introduction date in August 2021) of the population, respectively 331 (Fig. S6, top row) . Contrarily, there was less variability in the outbreak summary statistics for resident 332 variants, irrespective of the VOC that was introduced into the transmission dynamics (Fig. S6 , bottom 333 row). Furthermore, we sought to determine what characteristics a VOC needed to possess to both spread 335 through the population (i.e. R VOC eff ≥ 1) and outcompete resident variants (i.e R VOC eff > R res eff ). If the 336 VOC was introduced on 17th May 2021, immune escape was not necessarily required if the VOC was 337 more transmissible than resident variants (Fig. S7, left panel) . For VOCs that were less transmissible 338 than resident variants, a 10% decrement in relative transmissibility could be roughly offset by a 10% 339 decrement in the proportional efficacy of immunity against the VOC. For later VOC introduction 340 dates of 1st August 2021 (Fig. S7 , middle panel) and 1st November 2021 (Fig. S7 , right panel), higher 341 relative transmissibilities were required for VOCs that did not have much immune escape (proportional 342 efficacy against the VOC of 0.9 and above), but lower relative transmissibilities could be successful for 343 VOCs that had high immune escape (proportional efficacy against the VOC of 0.75 and below). Though individuals may develop immunity due to prior infection or vaccination, it can be imperfect 345 and breakthrough infections may occur. In these circumstances, the immune response could still cause 346 a reduction in the onward transmission of the virus. Including a degree of transmission blocking (by 347 either 25% or 50%) for those suffering breakthrough infection resulted in reduction in any resultant 348 wave of VOC infections and delayed the peak of the epidemic wave (Fig. S8) . For VOC E, in particular, 349 a 50% transmission blocking effect shifted the epidemic wave into late 2021 and early 2022, while 350 reducing the peak in infection to less than a third compared to no transmission blocking. Transmission 351 blocking from vaccinations also reduced the maximum attained effective R over the course of the 352 outbreak (Fig. S9) . For the less transmissible VOC LT+E, a 25% transmission blocking effect was 353 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 10, 2021. Step 3 R excl = 2.41 Step 4 R excl = 3.51 Fig. 1 : Infection burden for illustrative VOC scenarios, produced using the parsimonious SARS-CoV-2 transmission model. We considered three putative VOCs with differing transmissibility and immune escape characteristics: more transmissible (VOC MT, blue line with square markers), equal transmissibility with immune escape (VOC E, orange line with plus sign markers), less transmissible with immune escape (VOC LT+E, yellow line with circle markers), and resident variants alone in the absence of any VOC being introduced (black line with no markers). Additionally, in panels (a&c) we represent the vaccine uptake in the population through time via background shading, the transition time into Step 4 of the relaxation roadmap by the vertical solid line and we state the assumed R excluding immunity values for resident variants (R excl ) throughout Steps 3 and 4, respectively. (a) Infectious prevalence over time. In each scenario, alongside resident variants, we introduced one of the VOCs on 17th May 2021 with 2,000 initial infecteds. (c) R with immunity (y-axis) with respect to the date of a VOC being introduced (x-axis). For the 'Resident variants with no VOCs' scenario the displayed profile corresponds to the instantaneous R with immunity of resident variants. In panels (b&d) we explore the sensitivity of three epidemiological outcomes to the relative transmissibility of the VOC compared to resident variant and the proportional efficacy (vaccine and natural-immunity) against the VOC: (b) outbreak final size; (d) peak in VOC infection cases. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 10, 2021. Since the parsimonious model did not include age structure, it was unable to incorporate correlations 356 between individuals that are prioritised for vaccination, those that contribute most to transmission and 357 susceptibility to severe disease whose outcomes may require hospital treatment. In the UK older age 358 groups were prioritised for vaccination, representing a population that are most at risk of severe disease, 359 but contribute least to onward infection. To investigate the effect of this correlation, and include 360 reductions in the severity of cases due to vaccinations, we turned to a more complex age-structured 361 model. As before, we considered a range of potential effects on transmissibility and immunity, either 362 from prior infections or from vaccinations. In addition, we included the potential effect of a (partial) 363 immune-escape variant that assumed no reduction in vaccine-derived efficacy against hospitalisation 364 (VOC E+LH). Our results for the age-structured model broadly agreed with the parsimonious model in terms of 366 qualitative patterns between the illustrative VOC scenarios. When the relaxation roadmap in England 367 proceeded at the earliest stipulated dates, both a variant that was markedly more transmissible than 368 the resident variant with no immune escape attributes (VOC MT) or an equally transmissible VOC 369 with a reduction in efficacy from infection-and vaccine-derived immunity (VOC E) were sufficient to 370 see a substantial outbreak. Furthermore, these cases can result in appreciable hospital admissions, 371 which may exceed the daily peak attained during January 2021 of 3,700 admissions per day across 372 England ( Fig. 2(a) ). It is hoped that, even when the effect of current vaccines and natural immunity in preventing infec-374 tion are significantly compromised, they may still be effective in preventing severe symptom effects. 375 Nevertheless, when both vaccination and previous infection are equally effective at preventing hospi-376 talisations from both VOC and resident variants (VOC E+LH), we retain a large wave of resultant 377 hospitalisations generated by the variant, though the central trajectory is brought below the peak level 378 of daily hospital admissions during the January 2021 wave (Fig. 2(a) , purple line). The burden of cases with severe disease being admitted to hospital could be diminished with prolonged 380 use of NPIs. The stringency of these NPIs would depend on the characteristics of the variant, though 381 the non-COVID harms would also need consideration. Irrespective of the level of restrictions retained 382 in Step 4 of the roadmap, a high vaccine efficacy against severe disease reduces the estimated peak 383 in hospital occupancy (i.e. VOC E+LH lies below VOC E in Fig. 2(b) ). In particular, given the full 384 removal of NPIs from the outset of Step 4 (termed RM (roadmap) completion), our VOC E+LH 385 scenario gave a mean peak occupancy below the January 2021 peak of 34,336 COVID-19 patients, 386 whereas for VOC E the mean peak occupancy was approximately 60,000. In addition to these four illustrative VOC characteristics (VOC MT, VOC E, VOC LT+E and VOC 388 E+LH), additional sensitivity analyses of peak hospital occupancy to possible VOC efficacy and trans-389 mission are given in supplementary heat maps (Fig. S10) . We found that more severe immune escape 390 and/or a variant with both immune escape and increased transmissibility would likely result in sce-391 narios where reversion to more stringent NPI measures would be required to prevent hospitals being 392 quickly overwhelmed. The modelled outcomes involving large peaks in hospitalisations should be interpreted as being in-394 dicative of the relative extent of control measures required to keep the variant under control; we find 395 that the resistance of the variant to current vaccines was the most significant indicator of how much 396 measures may be safely relaxed. We stress that if there was a surge in hospital occupancy, shifts in 397 public behaviour and enaction of national legislation may limit the spread of infection [49] . Therefore, 398 our scenarios represent a pessimistic view of measures in response to a worsening outbreak. 399 We propose that the age-distribution of cases may give an early signal of whether a variant displays 400 12 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 10, 2021. ; immune escape or higher transmissibility (Fig. 2(c) ). Previous infections to date have been higher in 401 younger age groups who typically have higher rates of contact and are less likely to have been shielding 402 to the same degree as more vulnerable age groups. As a result, with the relaxation of NPIs we might 403 expect to see proportionally increased infection from resident variants in the older (60+ years) age 404 groups. On the other hand, as vaccinations were largely offered first to older age groups, we might 405 also expect to see a large proportional increase in infections amongst children (Fig. 2(c) , grey bars vs 406 black bars). Such effects were reduced for a VOC with increased transmission (e.g. VOC MT, blue 407 bars), as it is expected to cause an earlier surge in cases at a time when the vaccination program is less 408 advanced. VOCs with immune escape characteristics (VOC E, orange bars, and VOC LT+E, yellow 409 bars) were less affected by both previous infection and vaccination, resulting in an age-distribution 410 of infection that more closely matched the historical profile. Nonetheless, if the roadmap is run to 411 completion, the more relaxed levels of NPIs than have been previously seen is still expected to cause 412 significantly higher infections amongst the elderly than occurred to date. 413 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 10, 2021. ; Fig. 2 : Estimated COVID-19 hospitalisations, using the age-structured SARS-CoV-2 transmission model, across the illustrative VOC scenarios. We considered four putative VOCs with differing transmissibility, severity and immune escape characteristics: more transmissible (VOC MT, blue, square markers), equal transmissibility with immune escape (VOC E, orange, plus sign markers), less transmissible with vaccine immune escape (VOC LT+E, yellow, circle markers) and equal transmissibility with the same immune escape properties of VOC E with the exception of of a lesser reduction in vaccine-derived efficacy against hospitalisation (VOC E+LH, purple, inverted triangle markers). 14 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 10, 2021. ; https://doi.org/10.1101/2021.06.07.21258476 doi: medRxiv preprint Early phase VOC dynamics and the implications of VOC-targeted vaccines 414 Our final piece of analysis explored the outbreak potential of putative VOCs and evaluated the impact 415 on the infectious disease dynamics of the relative timing of a VOC-targeted vaccine, with improved 416 efficacy towards VOCs, becoming available. 417 For a given transmissibility and level of effective imports per day (the daily rate of second generation 418 cases that result from a single index case), we used the stochastic VOC importation model to calculate 419 the epidemic probability, which we subjectively defined as the probability of reaching a prevalence of 420 100 cases within 365 days (Fig. 3(a) ). We discerned two prominent features. A variant that was 421 less transmissible could be almost certain to become established if the effective importation rate was 422 high enough. Epidemic probabilities of 1 were attained for relative transmissibilities of 0.7 (when 423 effective imports per day were 0.22 or above), 0.8 (0.12 effective imports per day and above) and 424 0.9 (0.10 effective imports per day and above). This contrasts with a VOC that was substantially 425 more transmissible than resident variants, where even at low numbers of effective imports per day 426 (0.02 per day) it remained highly likely the VOC could become established; VOCs with a relative 427 transmissibility of 1.3 or above returned epidemic probabilities above 90%. Sampling from the stochastic VOC importation model to initialise the introduction time of 100 VOC 429 infected individuals and their distribution across the applicable infected compartmental states, we next 430 used the parsimonious SARS-CoV-2 transmission model to consider the sensitivity of the magnitude 431 and timing of a VOC caused resurgence of SARS-CoV-2 infection. We found that the introduction 432 date of a VOC targeted vaccine was much more important than the effective imports per day for the 433 final size (Fig. 3(b) ), peak (Fig. 3(c) ) and time of peak ( Fig. 3(d) ). Above all, if the VOC-targeted 434 vaccine was not introduced until August 2021 or later, the VOC attack rate was close to 50% of the 435 total population (Fig. 3(b) ), and the peak in infectious prevalence was in the region of 1-2% (Fig. 3(c) ) 436 and occurred during September/October 2021 (Fig. 3(d) ). Changing the prioritisation scheme for the VOC-targeted vaccine, to one in which unvaccinated in-438 dividuals were given precedence followed by those who had received one of the pre-existing vaccines, 439 resulted in qualitatively comparable findings (results not shown). 440 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted June 10, 2021. Through a set of mathematical modelling analyses, we have demonstrated the epidemiological trajec-442 tories for putative VOCs to be wide-ranging and heavily dependent on its transmissibility and immune 443 escape properties. Generally, any single cluster of infections with a VOC will be most easily controlled 444 whilst the case count is small. Early detection and efforts to extinguish infection clusters is therefore 445 paramount, as increased importation rates seed more clusters and will necessitate additional resources 446 to keep under control. Our findings are in concordance with illustrative modelling of novel variants conducted by three 448 academic groups in the UK contributing to SPI-M-O, which showed novel variants that either are 449 highly transmissible or substantially escape immunity have the potential to lead to resurgences (in 450 the absence of NPIs) that are larger than those seen in January 2021 in the UK [36] . Whilst the 451 assumptions that lead to a resurgence in hospitalisations to levels comparable to those witnessed in 452 the UK during January 2021 might seem extreme, SARS-CoV-2 has already demonstrated its adaptive 453 potential. At the time of writing in May 2021, there is no reason to believe that the SARS-CoV-2 virus 454 has yet settled at its fitness optimum in terms of replication and transmission capabilities. Given the 455 prospect of the virus undergoing a continued accumulation of adaptive mutations, we should remain 456 alert to all possible scenarios and continued evidence-based analysis of evolutionary change so that 457 public health measures can be adjusted in response to substantive changes in viral infectivity or severity 458 of COVID-19 (this has also been advocated by Day et al. [50] ). If a concerning novel variant is identified within a population, it is conceivable that the relationship 460 between the prevalence of the variant and any change in NPI policy could give a signal of its charac-461 teristics. We would expect that a variant with no immune escape properties, but that is even more 462 transmissible than resident variants, would display dynamics akin to the emergence and establishment 463 of B.1.1.7 in the UK. In particular, over a period of fairly static NPIs, it was observed that whilst growth 464 rates of resident variants were non-increasing, the B.1.1.7 variant had a positive growth rate [7, 8] . On 465 the other hand, a variant with no transmission advantage, but displaying immune escape, could be 466 identified through a shift in the distribution of cases between vaccinated and unvaccinated individuals. 467 In addition, the timing of a surge in a novel variant could also give a clue as to its characteristics. 468 As we continue with the vaccination rollout, reducing the level of NPIs could reveal less-transmissible 469 immune-escape variants, which were previously kept in check by control measures. Alongside the relative size of peaks in infection and hospitalisation, their timing may also be of great 471 importance. It is hoped that vaccines may by adapted to more effectively target emerging variants. 472 Within our model framework and utilised assumptions, our work suggests a critical interplay between 473 the timing of a VOC-targeted vaccine and the number of effective imports of a VOC. When the number 474 of effective imports per day is sufficiently low (less than 0.5 per day in our model), it was possible 475 for a new vaccine introduced early enough to have an appreciable effect on the VOC epidemic curve. 476 With reports that the mass production of AZ vaccine requires 60 days to grow the cells followed by 28 477 days of quality assurance [51] , one may reasonably expect an absolute minimum of three months from 478 identification of a novel SARS-CoV-2 variant to the possible initial administration of revised vaccines 479 that use the viral vector technology platform. Together with support of research to develop treatments 480 for mitigating disease impacts [52] , there is reason to believe that slowing importation of new variants 481 into the UK is an important priority to afford additional time to bolster vaccine-acquired immunity 482 throughout the population, heighten surveillance procedures and build capacity for locally targeted 483 interventions [53] . To that end, analysis of genomic and contact tracing data has demonstrated the 484 efficacy of travel restriction policy (travel corridors) enacted in England over the summer of 2020 in 485 reducing both the number of contacts reported by positive cases and the number of subsequent cases 486 due to onward transmission [54] . A concerted international COVID-19 pandemic response requires global situational awareness of how 488 the virus is mutating and identification of emergent variants that are of concern. Genomic sequencing 489 of SARS-CoV-2 viral samples is of paramount importance. The World Health Organization advocates 490 strengthening surveillance and sequencing capacity, and a systematic approach to provide a represen-491 tative indication of the extent of transmission of SARS-CoV-2 variants [1] . For example, extensive 492 surveillance of coronavirus has identified a number of cases of COVID-19 variants and mutations of 493 concern in England. In response, from 1st February 2021 the government began using 'surge testing' 494 (in combination with genomic sequencing) in specific locations to monitor and suppress the spread of 495 variants. At the time of writing in May 2021, surge testing involved increased testing, including of 496 those without symptoms of COVID-19 and door-to-door testing in some areas, and enhanced tracing 497 of close contacts of confirmed cases infected by the variant of concern [55] . 498 Our work demonstrates the use of parsimonious model structures to garner qualitative insights and 499 high-level quantification of the order of magnitudes of public health measurable quantities of inter-500 est (such as hospitalisations and deaths) that may be experienced. Operationally, there is a balance 501 between having a model of sufficient detail to provide robust insights on the objective and the time 502 required to obtain such insight. Models with additional complexities typically require longer devel-503 opment times and finer-resolution data to be reliably parameterised. In addition, higher dimensional 504 dynamical systems can result in parameter inference becoming more computationally intensive [56] . 505 In a global public health emergency such as a pandemic, policy processes tend to be very fast, requir-506 ing more limited methods to be used. Thus ensuring the timely delivery of findings before a policy 507 decision is taken can be worth more than using a more complex method and obtaining results after-508 wards, provided any methodological limitations are made clear [57] . Nevertheless, incorporating noted 509 heterogeneities in the infectious disease dynamics is a crucial consideration for interventions that are 510 targeted according to those heterogeneities (such as the prioritisation order of COVID-19 vaccination 511 in the UK being predominately determined by age). Where possible, we have taken a data-driven approach to parameterise the models. Nevertheless, 513 this work has made simplifying assumptions and our results therefore have limitations. We assumed 514 no waning of immunity to a specific variant induced via natural infection or vaccination, and note 515 that rapid waning of immunity would lead to more severe outcomes than presented here. Evidence 516 suggests previous infection with SARS-CoV-2 induces effective immunity to future infections in most 517 individuals, however natural protection for previously infected individuals can be temporary [58] [59] [60] [61] , 518 although the robust quantification of reinfection risk is also complicated by variants. We also did not 519 include any seasonal effects, that, if present, may impact the timing of future waves of infection [62] . 520 Our model parameterisation, vaccine rollout and NPI policy was tailored to England, and we would 521 not expect our findings to be directly applicable in other countries and regions, although the broad 522 messages may still be relevant. In the context of England, our analysis would also be affected by 523 deviations from the vaccination programme included here, such as the rollout speed and split between 524 the different vaccine types, or changes in NPI stringency (including the relaxation and/or strengthening 525 of measures). In summary, we have illustrated broad principles for the possible implications of the emergence of 527 SARS-CoV-2 variants that have particular transmissibility and immune escape attributes. More trans-528 missible or immune-escape variants may cause substantial waves of infection, even in the context of 529 considerable vaccine-derived immunity. Indeed, a less-transmissible variant with (partial) immune 530 escape could be revealed as NPIs are lifted, and cause an appreciable wave of infections, and even hos-531 pitalisations. The unpredictability in the epidemiological characteristics of novel pathogens mean our 532 ideas and understanding can change as new information on the outbreak is accrued. Close monitoring 533 of the evolution of SARS-CoV-2 across a range of geographical scales is needed to enhance local situ-534 ational awareness and quantify risk from variants that may be of concern, with reliable and accurate 535 18 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 10, 2021. ; https://doi.org/10.1101/2021.06.07.21258476 doi: medRxiv preprint data ensuring outputs from models of infectious disease dynamics are as informative as possible. 536 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 10, 2021. ; https://doi.org/10.1101/2021.06.07.21258476 doi: medRxiv preprint weekly epi update 42.pdf?sfvrsn=5b0bbc7c 5 SARS-CoV-2 incidence and vaccine escape A dynamic nomenclature proposal for SARS-CoV-2 lineages to assist genomic epidemiology World Health Organization. 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We thank the members of the JUNIPER consortium for helpful comments on the 540 manuscript.