key: cord-0262443-iudh7fzb
authors: Teslya, A.; Rozhnova, G.; Pham, T. M.; van Wees, D. A.; Nunner, H.; Godijk, N. G.; Bootsma, M. C.; Kretzschmar, M. E.
title: The importance of sustained compliance with physical distancing during COVID-19 vaccination rollout
date: 2021-09-26
journal: nan
DOI: 10.1101/2021.09.22.21263944
sha: c53c28882567002adbe7b9c5ec5cdc83af557184
doc_id: 262443
cord_uid: iudh7fzb

Mass vaccination campaigns against SARS-CoV-2 are ongoing in many countries with increasing vaccination coverage enabling relaxation of lockdowns. Vaccination rollout is frequently supplemented with advisory from public health authorities for continuation of physical distancing measures. Compliance with these measures is waning while more transmissible virus variants such as Alpha (B.1.1.7) and Delta (B.1.617.2) have emerged. In this work, we considered a population where the waning of compliance depends on vaccine coverage. We used a SARS-CoV-2 transmission model which captures the feedback between compliance, infection incidence, and vaccination coverage to investigate factors that contribute to the increase of the prevalence of infection during the initial stages of the vaccination rollout as compared to no vaccination scenario. We analysed how the vaccine uptake rate affects cumulative numbers of new infections three and six months after the start of vaccination. Our results suggest that the combination of fast waning compliance in non-vaccinated population, low compliance in vaccinated population and more transmissible virus variants may result in a higher cumulative number of new infections than in a situation without vaccination. These adverse effects can be alleviated if vaccinated individuals do not revert to pre-pandemic contact rates, and if non-vaccinated individuals remain compliant with physical distancing measures. Both require convincing, clear and appropriately targeted communication strategies by public health authorities.

Significance Statement SARS-CoV-2 vaccination campaigns are in progress in many countries around the world. As the vaccination coverage increases, the compliance with physical distancing measures aimed at reducing virus transmission may decline. Using a socio-epidemiological model we identify factors that are the drivers of increased transmission when SARS-CoV-2 prevalence is higher than the projected prevalence without vaccination. To maximize the benefits of vaccination campaigns, compliance in vaccinated and non-vaccinated groups should be targeted prioritizing one group over the other depending on the vaccination rate, the efficacy of vaccine in blocking the infection, and the circulating variant.

vaccination coverage is still low. 94 We developed a socio-epidemiological model ( Figure - a susceptible-exposed-infectious-recovered (SEIR) framework. 100 The vaccine works as all-or-nothing conferring perfect protec-101 tion to a fraction of susceptible individuals who receive it. The 102 vaccine delivered to individuals in other disease stages has no 103 effect. 104 We assume that the vaccination rollout takes place during a 105 government-imposed lockdown, whereupon many public venues 106 are closed or operate at a reduced capacity, thus limiting the 107 average number of contacts. Additionally, the government 108 may issue a set of recommendations with respect to physical 109 distancing. Compliance with these recommendations is cap-110 tured by a reduction in the daily number of contacts relative 111 to the pre-pandemic level of contacts. The non-vaccinated 112 population is divided into individuals who can be more compli-113 ant (henceforth referred to as "compliant") and less compliant 114 ("non-compliant") to measures. The reduction in contacts is 115 larger for compliant and smaller for non-compliant populations. 116 On the other hand, we assume that vaccinated individuals 117 perceive themselves protected from COVID-19 and therefore, 118 are no longer compelled to comply with physical distancing 119 measures. Thus they are not affected by the compliance 120 acquisition-loss process and increase their contact rate above 121 that of non-compliant individuals, thereby returning to nearly 122 pre-pandemic level of contacts. Non-vaccinated individuals 123 can move between compliant and non-compliant modes, and 124 the rates of moving depend on the state of the epidemic and 125 on vaccination coverage. Specifically, more individuals become 126 compliant with physical distancing measures as the incidence 127 of SARS-CoV-2 infection cases increases and lose compliance 128 faster as the proportion of vaccinated individuals grows (see 129 Methods). 130 We considered a baseline scenario without vaccination and 131 several vaccination scenarios. To observe the full spectrum of 132 possible scenarios, we sampled vaccination rate on a wide range, 133 which was based on the observations during the first six months 134 of the vaccination rollout in European countries and Israel (38) . 135 Further, we considered scenarios for three types of SARS-CoV-136 2 variants. The first variant has the transmission potential of 137 the original variant that was circulating in Europe prior to fall 138 2020. The second variant is a more transmissible, Alpha-like 139 variant (B.1.1.7), that spread in many European countries 140 during the winter of 2020/2021 and became dominant in the 141 spring of 2021 (44). Finally, we also considered the dynamics 142 of a "hyper-contagious" Delta-like variant (B.1.617.2), which, 143 as of August 2021, became the dominant strain in Europe 144 (10). We investigated the impact of compliance with physical 145 distancing measures on the numbers of infected, vaccinated and 146 compliant individuals over the course of the vaccination rollout. 147 We also compared the cumulative numbers of new infections 148 after three and six months into the vaccination programme to 149 the numbers without vaccination. We tested the robustness of 150 our findings to the values we chose for the initial conditions 151 and parameters by performing multivariate sensitivity analyses 152 (see Figure 5 and Supplementary materials). The values for 153 initial conditions and parameters were sampled continuously. 154 Next, we considered the potential effects of two interventions 155 aimed at improving compliance. The first intervention is tar-156 geted at people who have not been vaccinated yet and aims 157 at keeping their compliance with physical distancing at the 158 level of prior to vaccination rollout. The second intervention 159 is targeted at people who have been vaccinated and aims at 160 keeping their contact rates low. We also considered a com-161 bined intervention where both interventions are implemented 162 simultaneously. 163 Finally, we considered the possibility that in the case of a 164 sharp rise in prevalence which may occur due to the decline of 165 outcomes that we collected to the assumed initial conditions. 195 We have assumed that the baseline epidemiological dynamics Henceforth, these rates are referred to as "slow" and "fast", reproduction number for the Alpha-like variant was 1.65, i.e. 226 50% higher than for the original variant (6) . We have set 227 the basic reproductive number for the Delta-like variant using 228 the estimate of 4.92 (50), which makes it approximately 2 229 times more transmissible as the original variant. Therefore, 230 the effective reproductive number for the Delta-like variant 231 was approximately equal to 2.2 at the start of the vaccina-232 tion rollout. The contact rate of vaccinated individuals was 233 assumed to be close to the pre-pandemic rate and 1.5 times 234 higher than the contact rate of non-compliant individuals (51). 235 We explored sensitivity of the outcomes to this parameter.

In our model, individuals become compliant if there are in-237 fectious individuals in the population. The per capita rate of 238 switching to the compliant state is proportional to the inci-239 dence of infectious cases (see Methods, Table 1 ). The rate of 240 moving to the compliant state was fixed in the main analysis. 241 The sensitivity analyses for this parameter are shown in the 242 Supplementary materials. Furthermore, the compliance which 243 has an intrinsic natural decay rate, wanes more rapidly as the 244 vaccination coverage increases. The proportion of compliant 245 population for a constant incidence of infection is shown in 246 Figure 2b where we used slow and fast vaccination rates from 247 Figure 2a . We used incidence of 16,062 cases per day, based on 248 the number of infectious people in the Netherlands which was 249 approximated by RIVM using hospital admissions and data 250 from the Pienter Corona study (47) in the period used for the 251 model calibration (4). For slow vaccination, three months after 252 the start of vaccination, approximately 89% of the population 253 is compliant with physical distancing measures and after six 254 months, 84% is compliant. For fast vaccination, the compliant 255 population decreases more rapidly, with only approximately 256 54% and 32% of individuals being compliant after three and 257 six months, respectively. Interventions targeting compliance. To investigate how inter-386 ventions may improve the impact of vaccination rollout, we 387 considered an intervention that targets compliance of those 388 who are not yet vaccinated and an intervention targeted at the 389 vaccinated population. We assume that the first intervention 390 targets non-vaccinated individuals and is successful in keeping 391 the duration of compliance at the pre-vaccination length (30 392 days) as vaccination coverage grows. The second intervention, 393 targeted at vaccinated individuals, succeeds in convincing vac-394 cinated individuals to abstain from increasing the contact rate 395 above that of the contact rate of non-compliant individuals. 396 Our model predicts that a successful implementation of either 397 of these interventions reduces the cumulative number of new 398 infections after vaccination rollout and can get this number 399 below the level of the no-vaccination scenario. The effective-400 ness of these interventions depends on the circulating variant 401 and the vaccine uptake rate. We summarize our findings in 402 

The original variant of the virus circulates. All panels show relative difference in the cumulative number of new infections as compared to the no-vaccination scenario. a and b Vaccination rollout not supplemented with compliance interventions three and six months into the vaccination rollout, respectively. c and d Vaccination rollout supplemented with compliance interventions targeting non-vaccinated individuals three and six months into the vaccination rollout, respectively. e and f Vaccination rollout supplemented with compliance interventions targeting vaccinated individuals three and six months into the vaccination rollout, respectively. g and h Vaccination rollout supplemented with compliance interventions targeting both vaccinated and non-vaccinated individuals three and six months into the vaccination rollout, respectively. Magenta curves mark boundaries between parameter regions with different sign of the cumulative number of new infections. The scale of x-axis is not linear since the axes were obtained by conversion of the vaccine uptake rate to the vaccination coverage following three and six months after the start of the vaccination rollout.

we also see mixed results. For the combination of the vac- Six months after start of the vaccination rollout, the situation 456 is similar (Figure 5f ). Given a slow vaccination rate, the 457 minimum of vaccine efficacy where the relative increase of 458 infections can be avoided is higher than in the scenario where 459 the vaccination rollout is not supplemented with the interven-460 tion. But if the vaccination rate is fast, than the respective 461 vaccine efficacy minimum is lower than it was without the 462 intervention.

The dynamics for different regions of the vaccine efficacy and For the ranges used in Sensitivity analysis see Table 1 . 

We observe that there is an excess of infections relative to the 544 no-vaccination scenario for the whole range of values for the 545 contact rate of non-compliant individuals that we considered 546 (Figure 13 in Supplementary materials). The largest relative 547 increase in the cumulative number of infections happens when 548 the contact rate of non-compliant individuals is close to the pre-549 pandemic levels and the contact rate of compliant individuals 550 is significantly lower. Therefore since the growing vaccination 551 coverage causes modifications of the compliance distribution, 552 the average contact rate in the non-vaccinated individuals 553 increases significantly.

The cumulative number of new infections and the relative 555 difference in the cumulative number of new infections (as com-556 pared to the no-vaccination scenario) are very sensitive to 557 variations of the rate of moving to the compliant state and 558 the duration of the compliant state (Figures 14 and 15 in 559 Supplementary materials). The cumulative number of infec-560 tions is the highest when individuals move to the compliant 561 state at a slow rate but the duration of the compliant state 562 is low (Figure 14) . As the rate of moving to compliant state 563 and the duration of being compliant increase the, cumulative 564 number of infections decreases. The relative difference in the 565 cumulative number of infections has the opposite relationship 566 with the two parameters (Figure 15 ). Such that, the differ-567 ence is largest when the rate of moving to compliant state 568 is fast and the average duration of staying of compliant is 569 long. We observe that the duration of compliant state has 570 little effect on the possibility of excess infections as compared 571 to the no-vaccination scenario. However, if the rate of moving 572 to compliant state is sufficiently high, the cumulative number 573 of infections will exceed the no-vaccination scenario level. Supplementing vaccination rollout with a lockdown 577 Our simulations indicated that due to compliance waning as 578 the vaccination coverage grows, it is possible that an addi-579 tional prevalence peak appears. So far, in our simulations no 580 centralized intervention triggered by a steep increase in the 581 number of new cases was modeled. Here we consider such an 582 intervention, whereupon if during the vaccination rollout the 583 prevalence of new infectious cases exceeds a certain threshold, 584 the government tightens the lockdown, further restricting the 585 D R A F T average contact rate. Once the prevalence falls bellow the 586 threshold, the lockdown is being relaxed to its prior state. We 

Our main finding is that, if compliance decays as the vacci-669 nation coverage grows, the speed of vaccination rollout has 670 a strong impact on whether the cumulative number of new 671 infections can be decreased three and six months after the start 672 of vaccination below the level that would have been expected 673 without vaccination. If vaccination rollout is slow, its positive 674 effects on the incidence will be counteracted by fading compli-675 ance and increasing contact rates in the population. This may 676 lead to an increase in the prevalence exceeding the prevalence 677 in a situation without vaccination and, in the short term, we 678 may even see an additional epidemic peak. If vaccination is 679 rolled out faster, these detrimental effects can be avoided. The 680 outcome will depend on the vaccine efficacy. If the efficacy 681 is high, then the cumulative number of new infections will 682 decrease relative to the no-vaccination scenario. If the vaccine 683 efficacy is low and the vaccination rate if fast, an excess of 684 infections is possible in the first six months of the vaccination 685 rollout. Generally, given a low vaccine efficacy, our model pre-686 dicts that after the first six months of the vaccination rollout, 687 the cumulative number of new infections is higher for a faster 688 vaccination uptake rate. This effect happens due to the loss of 689 compliance by vaccinated individuals. Note that, since among 690 the excess infections a certain proportion of infected people 691 will have been vaccinated, they will have a low probability of 692 developing severe disease or death. Finally, as a result of our 693 comprehensive analysis of the effect of the vaccination rate and 694 vaccine efficacy on the cumulative number of new infections, 695 we derived threshold curves which separate parametric regions 696 where the relative difference in the cumulative number of in-697 fections as compared to the no-vaccination scenario changes 698 sign. We observed, that if the vaccine has a high efficacy, then 699 the excess of infections can be avoided for a relatively low 700 vaccination uptake rate. As the vaccine efficacy decreases, the 701 uptake rate increases. Our results are based on some simplifying assumptions, one 769 of them that physical distancing measures remain in place 770 throughout the time period of analysis (six months). While 771 this would be advantageous for preventing transmission of the 772 virus, it might not be feasible out of societal and economic 773 reasons. Therefore, compliance rates may wane even faster 774 in real populations and contact rates may be up to higher, 775 possibly pre-pandemic values during the rollout of vaccination. 776 We do not expect that this would change our results much, as 777 our results are obtained relative to the no-vaccination scenario, 778 which would similarly be affected by a change in physical dis-779 tancing measures. We expect therefore that the relative effects 780 of vaccination would remain similar as in our simulations. We 781 also assumed that the speed of vaccination rollout stays con-782 stant over the time period of six months, which is not the case 783 in reality. In the Netherlands for example, vaccination rates 784 have increased substantially after a slow start in January 2021 785 (38). These rates will depend on many factors, nevertheless 786 large differences will remain between countries. Finally, we 787 have captured the dependence of rates of becoming compliant 788 and non-compliant on the incidence of new infectious cases 789 and vaccination coverage, respectively, using linear functions. 790 As the vaccination in many countries continues and the popu-791 lation response data is collected, a more precise formulation of 792 the response functions can be obtained. However, our results 793 predominantly depend on the assumed monotonicity of these 794 functions.

795 Furthermore, our model is relatively simple, not taking into 796 account age structure and heterogeneity in contact patterns. 797 Therefore, we do not attempt to make quantitative predictions 798 on the impact of vaccination, but we provide qualitative in-799 sight into possible effects of waning compliance with physical 800 distancing in the face of increasing vaccination coverage.

A number of studies/reports estimated the bounds for vac-802 cine efficacy for the original variant in terms of reducing 803 the infection for some vaccines approved for use in Europe 804 (21, 22, 24, 25). As Alpha (B.1.1.7) and Delta (B.1.617.2) 805 variants emerged and, in turn, became dominant in many 806 European countries, the first estimates for vaccine efficacy for 807 reducing the infection became available (30, 31, 58). Whether 808 the reduction in infection comes in the guise of reduction of 809 susceptibility or transmissibility of vaccinated individuals is 810 not known. Therefore, in this work we modeled the vaccination 811 to be all-or-nothing and vaccine efficacy was given in terms 812 of probability of conferring full protection from becoming in-813 fected. Our sensitivity analyses ( Figure 5 and Figures 1, 2, 4 , 814 and 5 in Supplementary materials) show that the effect of a 815 vaccination campaign and of individual interventions is highly 816 sensitive with respect to this parameter. However, we observed 817 that if no compliance-targeting interventions accompany the 818 vaccination rollout, the range of efficacies for which a surplus 819 of new infections as compared to no-vaccination is possible 820 three and six months following the vaccination rollout falls 821 within the vaccine efficacy boundaries that were reported for 822 different vaccines (22, 24-27, 29-31, 59) . To implement the 823 most efficient vaccination rollout it is important to know the 824 boundaries of vaccine-conferred reduction of transmission. 825 Finally, in this work we have considered dynamics of circulation 826 of three SARS-CoV-2 virus variants, the original variant and 827 two mutations, whose transmission potential is similar to the 828

Alpha and Delta variants. For all three variants, we modeled tially detected in the UK and became dominant in many 890 European countries in the spring of 2021; and finally, the 891 "hyper-contagious" Delta (B.1.617.2) variant, which became 892 dominant in Europe in summer 2021. We parameterized the 893 differences between these variants by using different probabil-894 ities of transmission per contact, . We assumed that in all 895 other respects the variants have the same properties. We inves-896 tigated model dynamics where only one of the three variants 897 circulates in the population.

To model vaccination, the population was stratified into vac-899 cinated and non-vaccinated classes. While for some vaccines 900 authorised for use in Europe (BioNTech/Pfizer, Moderna and 901 AstraZeneca, (17)), two vaccine doses, as well as a certain 902 time period passing after the second dose are required for full 903 immunisation, we modelled vaccination as a single event that 904 confers protection instantaneously. We assumed that indi-905 viduals do not obtain a diagnostic or antibody test prior to 906 vaccination, and therefore infected and recovered individuals 907 also get vaccinated. Thus, individuals in all epidemiological 908 compartments can get vaccinated, but only those who were 909 susceptible (S) at the time of vaccination may become immu-910 nised (V ). The vaccination rate of susceptible, exposed, and 911 recovered individuals is denoted by υ. We introduced a pa-912 rameter k1, 0 ≤ k1 ≤ 1, such that k1υ denotes the vaccination 913 rate for individuals in the infectious compartment, to reflect 914 that a fraction of infectious individuals (who have symptoms) 915 might not be eligible for or might decide against vaccination. 916 In the main analysis we considered the case where infectious 917 individuals get vaccinated at the same rate as individuals in 918 other compartments (k1 = 1). We explored sensitivity of the 919 dynamics to variation of k1 and observed little effect of changes 920 in this parameter (the Supplementary materials). We assumed 921 that the vaccine works as all-or-nothing, i.e. upon vaccination, 922 a proportion ω of susceptible individuals (S) is fully protected 923 (V ), while in a proportion 1 − ω of susceptible individuals the 924 vaccine has no effect. We refer to ω as "vaccine efficacy" in 925 the context of conferring sterilising immunity. Vaccination 926 does not confer protection to individuals, who were in other 927 infection compartments (E, I and R) at the time of vacci-928 nation, and their infection progression is identical to that of 929 non-vaccinated individuals. Individuals who were vaccinated 930 but did not obtain the protection are denoted by S V , E V , I V 931 and R V . individuals (S, S C , and S V ) become exposed (E, E C , and E V , respectively) with rates λ inf , λ C inf , and λ V inf through contact with infectious individuals (I, I C , and I V ). Exposed individuals become infectious (I, I C , and I V , respectively) at rate α. Infectious individuals recover (R, R C , and R V ) at rate γ. Compliance is gained with rate λ C and lost with rate µ. Individuals in any state of infection or compliance can get vaccinated. A proportion ω of susceptible individuals S, who were vaccinated are fully protected, V . Individuals who were vaccinated, but did not obtain protection, are denoted by S V , E V , I V and R V and are epidemiologically indistinguishable from their non-vaccinated counterparts.

(30). This estimate was supported by another report based 951 on the data in a highly vaccinated health system workforce of Rates In this section we define the transition rates that depend 991 on the incidence of infectious cases and on vaccination coverage: 992 rates of infection acquisition, and rates of acquisition and loss 993 of compliance. 994 We assumed that individuals become infected at a rate that 995 depends on the fractions of different types of infectious indi-996 viduals, as well as on the mixing of compliant, non-compliant 997 and vaccinated individuals. Therefore, infection acquisition 998 rates as well as infection transmission rates depend on com-999 pliance and vaccination status of susceptible and infectious 1000 individuals. We define the following matrix to summarize 1001 transmission rates between different types of susceptible and 1002 infectious individuals.

where 

We assumed that as individuals learn about new infections 1013 they become compliant with physical distancing measures, and 1014 therefore compliance is gained at a rate λC which is a positive 1015 increasing function of the incidence of infectious cases (equal 1016 to the rate with which individuals leave the exposed stage): 

Equations The system of ordinary differential equations (4) 1025 provides a full description of the model.

Dynamics of non-compliant individuals:

Dynamics of vaccinated individuals: To estimate the total number of exposed individuals E + E C 1054 at the start of the vaccination rollout, we assumed that, at the 1055 time, the epidemiological dynamics are in (pseudo) equilib-1056 rium, with the prevalence of infectious cases equal to 112,435 1057 individuals (4). Using the average duration of infectious pe-1058 riod equal to 7 days (64), we estimated that, at the start of 1059 the vaccination rollout, the daily incidence of new cases was 1060 16,062 individuals. Using the average duration of the exposed 1061 period of infection equal to 4 days (60, 61, 63), we obtained 1062 E + E C . Having fixed the size of susceptible (S + S C ), exposed 1063 (E + E C ), and recovered (R + R C ) compartments and using 1064 the total population size of the Netherlands, the size of the 1065 susceptible compartment (S + S C ) follows. 1066 We have set the initial proportion of compliant individuals 1067 to 65%. This was based on data on the compliance with 1068 maintaining a distance of 1.5m, from a study on behavioral 1069 measures and well-being conducted between November 11-15, 1070 2020 (48) in the Netherlands. 1071 We obtain

Using Eq. (6) and the percentage of compliant population , 1074 initial values for S, E, I, R, S C , E C , I C , R C follow.

Setting the total population size to be equal to approximately that of the Netherlands, 1.7 × 10 7 we obtain the initial data: The initial values for the remaining compartments are set to 1076 0.

Contact rates We defined a contact as an encounter with an-1078 other individual that is sufficiently long to have a conversation, 1079 or that involves physical interactions (51). The pre-pandemic 1080 contact rate in the Netherlands was reported to be equal to 1081 14.9 individuals per day (51). We assume that the population 1082 is in the state of a partial lockdown at the start and throughout 1083 the vaccination rollout. In addition to the lockdown-related 1084 Re = cS(0) γ(N (0) + N c (0)r1) + r1cSc(0) (µ0(α + γ + µ0) + αγr1) γ(α + µ0)(γ + µ0)(N (0) + N c (0)r1) .

[7]

The value Re = 1.1 is obtained for pairs of contact rates of individuals in the population is determined by the compliance 1125 acquisition rate δ and compliance loss rate µ. For the main 1126 analysis we fixed the duration of compliance when there is no 1127 vaccination, 1/µ0 to 30 days. We selected the per capita rate 1128 of moving to the compliant state, δ = 4 × 10 −5 so that given a 1129 constant daily incidence of 16,062 cases, 95% of the population 1130 is expected to be compliant. In the regime where the epidemic 1131 is seeded with the original variant in a population without any 1132 physical measures as much as 84% of the population can be 1133 compliant provided there were no compliant individuals at the 1134 start of the epidemic. This value denotes the case with high 1135 compliance acquisition rate. We investigated the sensitivity of 1136 the outputs to variation in per capita rate of moving to the 1137 compliant state and the compliance loss rate (Supplementary 1138 materials).

In the main analysis we considered a compliance decay sce-1140 nario where as the vaccination coverage grows, the duration 1141 of compliance decreases, in particular when 33% of the pop-1142 ulation is vaccinated the compliant state lasts on average 7 1143 days. In other words, for a daily incidence of 16,062 cases, 1144 which we used to initialize the model, and a slow vaccination 1145 rate, approximately 83% of the population is still compliant 6 1146 months after start of the vaccination rollout, while for a fast 1147 vaccination rate only 32% are compliant (Figure 2b ). These 1148 dynamics occur when the growth rate of compliant decay rate 1149 as the vaccination coverage increase is µ1 = 0.3 per day. 

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