key: cord-0699775-tgjlkngz authors: Viana, J.; van Dorp, C. H.; Nunes, A.; Gomes, M. C.; van Boven, M.; Kretzschmar, M. E.; Veldhoen, M.; Rozhnova, G. title: Controlling the pandemic during the SARS-CoV-2 vaccination rollout: a modeling study date: 2021-04-04 journal: nan DOI: 10.1101/2021.03.24.21254188 sha: 4b2f678e85b8b6e2abb07285341f3d382345f50c doc_id: 699775 cord_uid: tgjlkngz There is a consensus that mass vaccination against SARS-CoV-2 will ultimately end the COVID-19 pandemic. However, it is not clear when and which control measures can be relaxed during the rollout of vaccination programmes. We investigate relaxation scenarios using an age-structured transmission model that has been fitted to age-specific seroprevalence data, hospital admissions, and projected vaccination coverage for Portugal. Our analyses suggest that the pressing need to restart socioeconomic activities could lead to new pandemic waves, and that substantial control efforts prove necessary throughout 2021. Using knowledge on control measures introduced in 2020, we anticipate that relaxing measures completely or to the extent as in autumn 2020 could launch a wave starting in April 2021. Additional waves could be prevented altogether if measures are relaxed as in summer 2020 or in a step-wise manner throughout 2021. We discuss at which point control of COVID-19 would be achieved for each scenario. SARS-CoV-2. [40,50) [50,60) [60,70) (95%CrI 3.47-5.91%) for 20 to 40 years old adults (Figure 2 a) . The total seroprevalence steadily increased with The data (dots and error bars) are based on the cross-sectional seroepidemiological survey (First National Serological Survey) conducted after the first pandemic wave [54] . a The violin shapes represent the marginal posterior distribution of the age-specific seroprevalence in the model. b The black line and the gray shaded region show the median total seroprevalence and 95% credible intervals. The uncertainty in the model is based on 2,000 parameter samples from the posterior distribution. The total seroprevalence refers to population older than 1 year [54] . Time-varying contact patterns and effective reproduction number 85 We estimated how age-specific contact rates in the population changed due to control measures as the pandemic 86 developed. These contact rates denote the average number of transmission-relevant contacts per day a person in 87 a given age category has with persons in other age categories. We further calculated the time-dependent effective 88 reproduction number, R e (t), defined as the average number of secondary infections caused by one infectious indi-89 vidual in the population with age-specific contact patterns and age-specific seroprevalence at time t. R e (t) < 1 90 signifies the control of the pandemic with possibly some of control measures in place. The full control of COVID-19 91 is achieved when R e (t) < 1 and the contact rates in the population are restored to the pre-pandemic level. Our findings are summarized in Figure 3 , where we show the total daily hospitalizations (Figure 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. (which was not certified by peer review) The copyright holder for this preprint this version posted April 4, 2021. ; https://doi.org/10.1101/2021.03.24.21254188 doi: medRxiv preprint lifted, the number of contacts increased to 5.9 (95%CrI 5.1-6.6) and R e increased to almost 1 and stayed nearly 100 constant throughout summer 2020. At the start of the second wave in autumn 2020 that followed the opening of 101 schools and the associated changes in the contact patterns of the rest of the population, the average number of 102 contacts further increased to about 7.6 (95%CrI 6.7-8.3) and R e to 1. 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 April 4, 2021. ; 10,800,000 * The Portuguese vaccination plan assumes that all persons in the population will be vaccinated with a two-dose vaccine schedule. In the model, the maximum vaccination coverage in any age group is 90%. * * According to the current guidelines, persons under 18 years old are not eligible for vaccination. In the model, we assumed that the age group of 0 to 20 years old is not vaccinated. We implemented the rollout of vaccination against SARS-CoV-2 as set out by the Directorate-General of Health -108 a division of Portuguese Ministry of Health concerned with public health ( Table 1 ). The mass vaccination started 109 on 27 December 2020, is planned to proceed in three phases that will cover the whole population of Portugal More details of the vaccination model are given in Methods. 121 We used the rollout schedule (Table 1 ) and data (Figure 4 a) on the age distribution of morbidities among the 122 Portuguese residents and age distribution of prioritized vaccination categories (e.g., healthcare workers, long-term 123 7 . 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 April 4, 2021. Table 1 ). The age-specific vaccination rates are given in Figure S3 . Vaccination coverage by age Figure S4 for the absolute numbers of vaccinated persons). The coverage for ages [0,20) is zero. The ECDC vaccination rollout data in b are shown as red (1 dose) and blue (2 doses) dots. 8 . 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 April 4, 2021. ; https://doi.org/10.1101/2021.03.24.21254188 doi: medRxiv preprint Hospitalizations 200 300 400 500 600 700 Scenario 2 Step 2 (1 June) and Step 3 (1 October) increase R e above 1 (Figure 7 c) leading to waves of infections ( Figure S5 ) 165 10 . 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 April 4, 2021. ; https://doi.org/10.1101/2021.03.24.21254188 doi: medRxiv preprint immediately upon getting vaccinated (see Figure S7 ). . 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 April 4, 2021. ; https://doi.org/10.1101/2021.03.24.21254188 doi: medRxiv preprint In this study, we used an age-structured model for SARS-CoV-2 transmission to generate several scenarios for A strength of our analyses is that we calculate the effective reproduction number using the estimated current levels 205 of age-specific seroprevalence and vaccination coverage in the population instead of reducing the value of R e at 206 the beginning of the pandemic homogeneously across age groups as it is done in e.g. the study for China [28] . 207 Another strength is that, unlike this study [28] and the studies for the UK [26, 27], the parameters of our model 208 are statistically evaluated to match the course of the Portuguese pandemic as reflected by age-specific hospital 209 admissions and age-specific seroprevalence [54] . In addition, our fitting procedure allows for estimation of temporal 210 changes in age-dependent contact patterns as a response to prior control measures during this pandemic. Therefore, 211 instead of modeling specific relaxation policies, that are notoriously hard to implement in mechanistic transmission 212 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 April 4, 2021. ; https://doi.org/10.1101/2021.03.24.21254188 doi: medRxiv preprint models, we model several scenarios using the estimated contact structure after relaxation of measures in summer 213 and autumn 2020. In light of these past measures, our findings are easy to interpret and contain an important message for local 215 policymakers. School opening is thought to be the main driver of the changes observed in autumn 2020, although 216 an increase in socializing indoors in general caused by weather alone must also have played a role. If the relaxation 217 planned for April 2021 includes school reopening in full after Easter and resuming indoor service in restaurants and 218 bars, then it is very likely that the average contact rate in the population will reach levels very similar to those 219 in autumn 2020. As a consequence, this might lead to a new wave of hospitalizations as illustrated in Scenario 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 April 4, 2021. ; https://doi.org/10.1101/2021.03.24.21254188 doi: medRxiv preprint n = 2, 301 Portuguese residents, aged 1 year or older, after the first wave. The survey sample was selected using a 279 two-stage stratified non-probability sampling design (quota sampling) [54] . SARS-CoV-2 IgM and IgG antibodies 280 were measured in serum samples by enzyme-linked immunosorbent assay. Further details of the study are given 281 in [54] . For the model fitting, we used the sample size, the number of positive samples and 95% confidence intervals 282 stratified by age group reported in [54] . (Table S1 ). The vaccination rollout data for Portugal was 289 taken from the ECDC website. 15 . 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 April 4, 2021. ; https://doi.org/10.1101/2021.03.24.21254188 doi: medRxiv preprint We extended an age-stratified SARS-CoV-2 transmission model from [43] to include vaccination (Figure 8 ). The 296 model has susceptible-exposed-infectious-recovered structure, whereby susceptible persons (S) may become latently 297 infected (E) before progressing to become infectious (I). Infectious persons either get hospitalized (H) or recover 298 without hospitalization (R). Disease-related mortality and discharge from the hospital are not explicitly modeled. Therefore, the H-compartment contains the cumulative number of persons who experience severe symptoms and 300 recover (or die) after admission to the hospital. Similarly, the R-compartment contains the cumulative number 301 of persons who recover after having mild or no symptoms. The force of infection is given by a weighted sum of 302 the fraction of the infectious population in different age groups (red dashed boxes in Figure 8 ). We consider a 303 stable population and thus do not include natural birth and death processes. The contact rates, forces of infection, 304 susceptibilities and hospitalization rates are age-specific. In line with the current guidelines, we assume that vaccine can be delivered to all people independently from their 306 disease history with the exception of those who might be currently infectious (I-compartment). Not vaccinating in-307 fectious compartment implies that vaccine is not given to asymptomatic persons but these represent a small fraction 308 of the population at any given time. We also vaccinate the H-compartment as this compartment comprises everyone 309 who has ever been admitted to hospital. Whilst this assumption means that the currently hospitalized persons are The equations for the numbers of unvaccinated persons in age group k, k = 1, . . . , n, who are susceptible (S k ), 325 16 . 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 April 4, 2021. ; https://doi.org/10.1101/2021.03.24.21254188 doi: medRxiv preprint . The equations for the numbers of vaccinated persons in age group k who are vaccinated susceptible (S V k ), exposed 332 (E V k ), infectious (I V k ), recovered (R V k ) and hospitalized (H V k ) are given by . Persons get vaccinated in S, E, R and H states. The vaccination rates r k are age-specific. We denote the contact 339 rate of an unvaccinated person in age group k with persons in age group l, c kl (t), and the contact rate of a vaccinated where N k is the number of individuals in age group k, 17 . 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 April 4, 2021. ; https://doi.org/10.1101/2021.03.24.21254188 doi: medRxiv preprint The initial condition for the model was E k (t = 0) = I k (t = 0) = 1 2 θN k and S k (t = 0) = (1 − θ)N k , where t = 0 is 351 26 February 2020. The parameter θ denotes the initial fraction of the population that was infected (split equally 352 between infectious and exposed). This parameter accounts for importation of new cases at the start of the pandemic 353 and was estimated jointly with other parameters. Importation of cases was not implemented at later stages of the 354 pandemic due to a large pool of infectious individuals within the country. The rapid spread of B.1.1.7 variant, that is estimated to be about 50% more transmissible based on the data from The seroprevalence data were stratified into the five age groups [1, 10) , [10, 20) , [20, 40), [40, 60) and 60+ [54] . Hence, 371 for the hospitalization data and the transmission model, a finer age stratification is used than for the seroprevalence 372 data. We assume that individuals in seroprevalence age group G s i were sampled from hospitalization age class G h k 373 with probability p ik proportional to the relative population size of G h k compared to G s i , i.e. As before [43], we assume that the seroprevalence data represents a random sample from each age group. Hence, 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. The copyright holder for this preprint this version posted April 4, 2021. ; https://doi.org/10.1101/2021.03.24.21254188 doi: medRxiv preprint the population size N 1 with the size of the age group [0, 1) (86, 579 persons) in Eq. (6) and Eq. (5). The prior distribution of the model is specified in Table S3 . The model was fitted with Stan [70] in R 3.6.0 and R 383 Studio 1.3.1056. We used 4 parallel chains, each of length 1,000, with a warm-up period of 500, resulting in 2,000 384 samples from the posterior distribution. Convergence was assessed with the Gelman-RubinR-statistic, which was 385 close to 1 for all parameters. The estimated model parameters are shown in Figures S1 and S2 . We denote c kl (t) the contact rate for a person in age group k (k = 1, . . . , n) with persons in age group l (l = 1, . . . , n) for example, due to mask-wearing or physical distancing when a contact took place. Therefore, the baseline (pre-405 pandemic) contact rates are described by the matrix b kl , and the contact rates after the first lockdown are described 406 by the matrix ζa kl . The pre-pandemic matrix b kl for Portugal was taken from [67] (Figure 9 a) . The matrix after the first lockdown 408 a kl was inferred using the contact matrix for the Netherlands based on a cross-sectional survey carried out in April 409 2020 (PIENTER Corona study) [68] . Since measures enforced during the first lockdown in the two countries were 410 similar (e.g., all schools were closed, all non-essential work was done from home etc.) we reduced the age-specific 411 . 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. 20 . 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 April 4, 2021. ; https://doi.org/10.1101/2021.03.24.21254188 doi: medRxiv preprint contact rates for Portugal after the lockdown by the same percentage as it was observed in the Netherlands ( Figure 412 9 b). The resulting number of daily contacts for a person in given age group at baseline and after the lockdown 413 in April 2020 is shown in Figure 9 c. Like for the Netherlands [68], we observe larger reductions in contacts for 414 children (due to school closure) and smaller reductions for elderly because most of their contacts were essential 415 (e.g., with healthcare personnel or caretakers) and thus were not affected by the lockdown. The parameter ζ that 416 multiplies the inferred matrix a kl can account for discrepancies between the real and inferred matrix. To describe the contact rates after transitions 1)-4) have taken place, we assume that these can be written as a This contact structure can, therefore, interpolate between the first (most strict) lockdown and no measures in place 421 at all. Since the third lockdown was similar to the first lockdown, the transition 5) was modelled as a return to 422 the lockdown contact matrix ζb kl . As before, the transitions between the contact rates during periods 1)-5) are (8) 428 All the parameters that describe c kl (t), except for the last transition 5) for which hospitalization data are not 429 available, are estimated (Table S4 ). The estimates for these 15 parameters ζ, u i (i = 1, . . . , 4), t i (i = 0, . . . , 4) and K i (i = 0, . . . , 4) are shown in Figure S2 . The estimated logistic functions are plotted in Figure 9 d. In the main analyses (Figures 6 and 7) , the contact rates for vaccinated persons were equal to those unvaccinated, 432 c V kl (t) = c kl (t). In the sensitivity analyses ( Figure S7 ), they were set to pre-pandemic contacts as follows, c V kl (t) = b kl . The contact rate presented in Figures 3, 6 and 7 was the average contact rate in the population calculated as The relaxation scenarios during the vaccination rollout are modelled as a transition from the contact rate described Table S4 . . 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 April 4, 2021. ; https://doi.org/10.1101/2021.03.24.21254188 doi: medRxiv preprint The basic reproduction number, R 0 , is the average number of secondary infections caused by a single infectious 442 individual at the beginning of the epidemic in a disease-free, totally susceptible population. If R 0 > 1 the disease 443 will spread exponentially. If R 0 < 1 the number of infectious persons declines exponentially and the disease is not 444 able to spread. In general, R 0 depends on the type of virus but also on the contact patterns in the population. When the disease has already spread and we have no longer a fully susceptible population but some part of the 446 population is immune due to natural infection or vaccination, the generalization of R 0 is given by the effective 447 reproduction number, R e (t). R e (t) depends on the type of virus, the level of population immunity and the contact 448 patterns in the population. The full control of the disease is achieved when R e (t) < 1 and the contact rates in 449 the population are at their pre-pandemic levels, i.e., not anymore affected by control measures. A partial control 450 is achieved when R e (t) < 1 but the contact rates have not been restored to their pre-pandemic levels yet as is 451 currently the case for SARS-CoV-2 in Portugal. In a deterministic compartmental model such as the one employed here, the calculation of R 0 and R e (t) can be For R 0 calculation, the disease-free equilibrium is For R e (t) calculation with or without vaccination, the disease-free equilibrium is where the time-dependent variables S k (t) and S V k (t) are obtained from the solutions of the full model given by Eqs. (1) and (2). Following [71], the Jacobian J may be recast as follows [ . 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. 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 April 4, 2021. 28 . 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 April 4, 2021. . 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 April 4, 2021. . 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. Figure S1 . Estimated hospitalization rates. The histograms of age-specific hospitalization rates estimated by the model. The solid and the dashed lines are, respectively, the medians and the 95% credible intervals based on 2,000 parameter samples from the posterior distribution. . 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. Figure S3 . Age-specific vaccination rates. Vaccination rate (number of persons vaccinated per day) per age group calculated using the national vaccination plan ( Table 1 ) and age distribution of various vaccination categories (Figure 4 a) . The vertical lines indicate the starting dates of different phases of vaccination (Table 1) . According to the current guidelines persons under 18 years old are not eligible for vaccination. In the model, we assumed that the age group of 0 to 20 years old is not vaccinated. Vaccinated persons (x 100,000) Figure S4 . Number of vaccinated persons per age group during the vaccination rollout. These numbers were calculated using the national vaccination plan ( Table 1 ) and age distribution of various vaccination categories (Figure 4 a) . The vertical lines indicate the starting dates for vaccination of different phases of vaccination (Table 1) . According to the current guidelines persons under 18 years old are not eligible for vaccination. In the model, we assumed that the age group of 0 to 20 years old is not vaccinated. . 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. (Table 1) . 35 . 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 April 4, 2021. Pessimistic vaccine efficacies and pre-pandemic contacts rates for vaccinated population Figure S7 . Impact of vaccine efficacies and contact rates of vaccinated individuals. Scenario 4 ( Figure 7 in the main text) but with a pessimistic set of vaccine efficacies (Table S2 ). In addition to using a pessimistic set of vaccine efficacies, we allow for behavior compensation post-vaccination modelled as a return to pre-pandemic contact rates among vaccinated persons as compared to unvaccinated persons who may continue to have reduced contact rates due to control measures. The hospitalization data are shown as red dots. The solid lines are the median trajectories estimated from the model. The gray shaded regions correspond to 95% credible intervals. The blue vertical lines indicate the mid-points of relaxation steps (1 April, 1 June, 1 October 2021). The gray vertical lines indicate the starting dates for different vaccination phases (Table 1) . . 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 April 4, 2021. ; https://doi.org/10.1101/2021.03.24.21254188 doi: medRxiv preprint -2: a systematic review and meta-analysis. The Lancet Global Health. XXXX CoV-2 seroprevalence worldwide: a systematic review and meta-analysis Imperial College London: Unlocking roadmap scenarios for 588 Vaccination and non-pharmaceutical interventions 591 for COVID-19: a mathematical modelling study. The Lancet Infectious Diseases. XXXX Can a COVID-19 vaccination program guarantee the return to a pre-pandemic lifestyle? 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The black line is the median trajectory estimated from the model. The gray shaded region corresponds to 95% credible intervals. The blue vertical lines indicate the mid-points of relaxation steps The gray vertical lines indicate the starting dates for different vaccination phases Table S3 . Prior distribution of the statistical model. Prior Description Uniform(0, 1) Flat prior θ Uniform(10 −7 , 5 · 10 −4 ) Vague prior allowing for 1 to 5000 infected individuals on day t = 0 φ Lognormal(5, 2) Vague prior a α InvGamma(32. 25, 9 .75) 99% of the prior density of α −1 is between 2 and 5 days γ InvGamma(80, 20) 95% of the prior density of γ −1 is between 5.3 and 8.