key: cord-0875498-iwo9itd9
authors: Swan, D. A.; Goyal, A.; Bracis, C.; Moore, M.; Krantz, E.; Brown, E. R.; Cardozo-Ojeda, F.; Reeves, D. B.; Gao, F.; Gilbert, P. B.; Corey, L.; Cohen, M. S.; Janes, H.; Dimitrov, D.; Schiffer, J. T.
title: Vaccines that prevent SARS-CoV-2 transmission may prevent or dampen a spring wave of COVID-19 cases and deaths in 2021
date: 2020-12-14
journal: nan
DOI: 10.1101/2020.12.13.20248120
sha: 5d12b196bc052dd914e0f07872005c1fab66080a
doc_id: 875498
cord_uid: iwo9itd9

Ongoing SARS-CoV-2 vaccine trials assess vaccine efficacy against disease (VEDIS), the ability of a vaccine to block symptomatic COVID-19. They will only partially discriminate whether VEDIS is mediated by preventing infection as defined by the detection of virus in the airways (vaccine efficacy against infection defined as VESUSC), or by preventing symptoms despite breakthrough infection (vaccine efficacy against symptoms or VESYMP). Vaccine efficacy against infectiousness (VEINF), defined as the decrease in secondary transmissions from infected vaccine recipients versus from infected placebo recipients, is also not being measured. Using mathematical modeling of data from King County Washington, we demonstrate that if the Moderna and Pfizer vaccines, which have observed VEDIS>90%, mediate VEDIS predominately by complete protection against infection, then prevention of a fourth epidemic wave in the spring of 2021, and associated reduction of subsequent cases and deaths by 60%, is likely to occur assuming rapid enough vaccine roll out. If high VEDIS is explained primarily by reduction in symptoms, then VEINF>50% will be necessary to prevent or limit the extent of this fourth epidemic wave. The potential added benefits of high VEINF would be evident regardless of vaccine allocation strategy and would be enhanced if vaccine roll out rate is low or if available vaccines demonstrate waning immunity. Finally, we demonstrate that a 1.0 log vaccine-mediated reduction in average peak viral load might be sufficient to achieve VEINF=60% and that human challenge studies with 104 infected participants, or clinical trials in a university student population could estimate VESUSC, VESYMP and VEINF using viral load metrics.

Ongoing SARS-CoV-2 vaccine trials assess vaccine efficacy against disease (VEDIS), the ability of a vaccine to block symptomatic COVID-19. They will only partially discriminate whether 45 VEDIS is mediated by preventing infection as defined by the detection of virus in the airways (vaccine efficacy against infection defined as VESUSC), or by preventing symptoms despite breakthrough infection (vaccine efficacy against symptoms or VESYMP). Vaccine efficacy against infectiousness (VEINF), defined as the decrease in secondary transmissions from infected vaccine recipients versus from infected placebo recipients, is also not being measured. Using 50 mathematical modeling of data from King County Washington, we demonstrate that if the Moderna and Pfizer vaccines, which have observed VEDIS>90%, mediate VEDIS predominately by complete protection against infection, then prevention of a fourth epidemic wave in the spring of 2021, and associated reduction of subsequent cases and deaths by 60%, is likely to occur assuming rapid enough vaccine roll out. If high VEDIS is explained primarily by reduction in 55 symptoms, then VEINF>50% will be necessary to prevent or limit the extent of this fourth epidemic wave. The potential added benefits of high VEINF would be evident regardless of vaccine allocation strategy and would be enhanced if vaccine roll out rate is low or if available vaccines demonstrate waning immunity. Finally, we demonstrate that a 1.0 log vaccine-mediated reduction in average peak viral load might be sufficient to achieve VEINF=60% and that human 60 challenge studies with 104 infected participants, or clinical trials in a university student population could estimate VESUSC, VESYMP and VEINF using viral load metrics.

The endpoint for SARS-CoV-2 vaccine efficacy trials targeting licensure is vaccine efficacy against disease (VEDIS) which is defined by a reduction in symptomatic disease, confirmed with polymerase chain reaction (PCR) testing for viral RNA, in vaccine recipients relative to placebo recipients (1, 2). The FDA benchmark for licensure is a point estimate of VEDIS>50% with lower alpha-adjusted 95% confidence limit exceeding 30% (3) . Two mRNA 70 vaccines have shown high levels of protection (>90%) at interim analyses (4, 5).

Once VEDIS is established and a vaccine is licensed, mathematical modeling is useful for projecting a roll out strategy that affords maximal reductions in deaths and cases, and to prevent the need for future lockdowns (6-8). Yet VEDIS does not provide sufficient information to fully inform these models. High VEDIS is determined by a combination of two distinct phenomena 75 which will only be partially captured in these trials: vaccine efficacy against susceptibility (VESUSC) which is defined as the vaccine-induced reduction in the rate of infection -as evidenced by detection of virus by PCR -and vaccine efficacy against symptoms (VESYMP) which is defined as the reduction in the presence of symptoms conditional on infection under vaccine versus placebo (Table 1, Figure 1 ) (1, 2, 9) . If a vaccine mediates VEDIS primarily 80 through reduction in symptoms, the extent to which people, who convert from symptomatic to asymptomatic infection as a result of receiving the vaccine, can still transmit the virus, remains unknown. A vaccine that achieves high VEDIS via VESYMP could theoretically contribute less to overall herd immunity than a vaccine that achieves high VEDIS via VESUSC, as the former may not block ongoing chains of transmission from vaccine recipients. 85

A third vaccine effect, efficacy against infectiousness (VEINF) is defined as reduction in secondary transmissions from either symptomatic or asymptomatic infected vaccine versus placebo recipients and could also have significant effects on the trajectory of viral epidemics (10) . Reduced VEINF anticipates that symptomatic breakthrough infections in vaccine recipients may be associated with fewer secondary transmissions than in placebo recipients, and that people 90 who develop asymptomatic rather than symptomatic infection due to vaccination (VESYMP) may also be less likely to transmit. This latter observation would be expected if a vaccine mediates reduction in both symptoms and secondary transmission potential by lowering the quantity of viral shedding (11) . While high VEDIS guarantees a high likelihood of individual benefit, protection of unvaccinated members of the population will also depend on VESUSC and VEINF, as 95 well as the velocity of a vaccination roll out program (8, 12) .

SARS-CoV-2 serology is being used in the Pfizer and Moderna trials to capture asymptomatic infections and thereby estimate VESUSC and VESYMP (1). Yet, waning SARS-CoV-2 humoral responses could limit the sensitivity of this approach. Results from the ChAdOx1 vaccine trial show a trend towards lower protection against infection by viral nucleic acid 100 detection than against symptomatic COVID-19, highlighting the potential importance of this approach, though low frequency of sampling could limit the accuracy and precision of these estimates (13) . VEINF is also not being directly assessed in ongoing vaccine trials. While all current studies will ultimately measure viral load at presentation among symptomatic infected persons only, this approach misses all asymptomatic people who may or may not continue to 105 secondarily transmit SARS-CoV-2. It also does not capture the critical pre-symptomatic phase of symptomatic infection when viral load and transmissibility are highest (14-16).

The inability to fully discriminate VESUSC from VESYMP, and to directly measure VEINF, in the current slate of promising vaccines limits our ability to forecast vaccine impacts in the population. Specifically, there is uncertainty regarding the threshold of vaccinated people 110 required to achieve herd immunity, where the effective reproductive number (Reff) is maintained below 1 and new cases contract. It is similarly challenging to optimize vaccine allocation to different sectors of the population. For instance, it may be best to target a vaccine with high VESUSC or VEINF, which breaks secondary chains of transmission, towards essential workers and young people. Alternatively, a vaccine with high VESYMP but limited effects on secondary 115 transmission may be best prioritized towards populations with highest risk of severe disease, such as the elderly (8) .

Several possible methods exist to estimate VEINF. One is to measure secondary attack rate among household contacts of infected vaccine recipients versus infected placebo recipients (17) .

Alternatively, cluster randomized trials can assess for indirect protection of unvaccinated persons 120 in vaccinated versus unvaccinated communities (18). While both of these trial designs are attractive, they have high operational complexity and will need to be implemented and completed rapidly to impact the course of the pandemic.

Another option is to use a viral load metric as a surrogate endpoint. VEINF is likely to be mediated via a reduction in viral load among recipients of vaccine versus placebo, particularly 125 early during pre-symptomatic or asymptomatic infection when nasal and saliva viral loads are highest (16, [19] [20] [21] . It is possible that VESYMP is also driven by viral load reduction, though it has yet to be proven beyond association whether any specific viral load metric predicts development of symptoms or severe COVID-19 (22) . Moreover, only a few studies captured critical early peak viral load kinetics, and in too few people to perform correlate analyses (20) . Viral load in 130 infected vaccine versus placebo recipients could be measured in large clinical trials in which enrolled participants undergo frequent self-sampling after enrollment, or in smaller highly controlled human challenge studies (23) .

Here we use a mathematical modeling approach using data from King County Washington to demonstrate the potential effects of VEINF at the population level given multiple 135 vaccine profiles. In contrast to existing models of vaccine prioritization (7, 8) , including our own (24) , the model accounts for the likely need for recurrent lockdowns once cases and hospitalizations exceed a certain threshold. We next estimate reduction in peak viral load required to achieve various VEINF and outline animal viral graded challenge experiments required to verify the relationship between viral load and likelihood of transmission. Finally, we 140

propose human challenge study design, and describe a potential clinical trial in university students, to rapidly estimate VESUSC, VESYMP and VEINF for a vaccine.

Overview. We use a mathematical model of COVID-19 in King County Washington to project the impact of different vaccine profiles on incident cases, hospitalizations and deaths throughout 2021. Our goal is to identify vaccine efficacy profiles under which high VEINF would or would not reduce a large number of infections and deaths, as well as the need for prolonged lockdowns.

Because we identify that VEINF could determine whether or not a large fourth wave of infections 150 occurs in the region during the spring of 2021, and because VEINF has not yet been measured for vaccines under study, we next focus on approaches to rapidly estimate its value. Using an intrahost transmission model (14, 25, 26) , we consider reduction in peak viral load as a potential surrogate endpoint for VEINF, discuss graded challenge studies in animal models to validate these predictions, and provide human viral challenge study designs which might provide actionable 155 VEINF estimates within relevant timeframes for the pandemic.

Vaccine efficacy definitions. We include vaccines defined by four different types of efficacy (Table 1) . VEDIS is the primary endpoint in all ongoing phase 3 vaccine trials and is defined as the proportion of vaccine versus placebo recipients who do not develop symptomatic COVID-19 160

(1). VEDIS represents a composite of efficacy against infection (VESUSC) and disease (VESYMP).

VESUSC is the proportion of people in a vaccine arm relative to the placebo arm of a trial who are fully protected against both asymptomatic and symptomatic virologically confirmed SARS-CoV- conditional on infection and is defined as the proportion of people in the vaccine arm relative to . CC-BY-NC 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) preprint the placebo arm of a trial who remain asymptomatic despite being infected. A vaccine in which VEDIS is mediated entirely by VESYMP will not lower the absolute number of people infected Fig 1) .

The proportion of secondary contacts who are symptomatically or asymptomatically 170 infected (red and orange figures respectively in Fig 1) Notably, the addition of VEINF=50% prevents a much larger number of secondary infections in a 175 scenario where high VEDIS is mediated entirely by VESYMP (Vaccine 4) versus a scenario where high VEDIS is mediated entirely by VESUSC (Vaccine 2).

The possible relevance of this concept for the Moderna and Pfizer vaccines is evident by comparing extreme scenarios in which VEDIS=90%. A vaccine with VEDIS=90% due to VESUSC=90% / VESYMP=0% / VEINF=0% would have very similar population level effects as a 180 vaccine with VESUSC=0% / VESYMP=90% / VEINF=100%. In the latter scenario, all vaccinated and subsequently infected people would be asymptomatic and could also not secondarily transmit the virus. On the other hand, a vaccine with VESUSC=0% / VESYMP=90% / VEINF=0% would protect vaccinated people against symptoms but have no impact on downstream transmissions. 185

assuming no vaccine. We modified a previously developed compartmental model to reproduce the ongoing COVID-19 epidemic in King County Washington (24) . The model includes uninfected, exposed, asymptomatic infected, pre-symptomatic infected, symptomatic infected, 190 diagnosed asymptomatic, diagnosed symptomatic, hospitalized, dead and recovered compartments, all stratified into four age cohorts (Sup fig 1) . We calibrated the model to daily cases (Sup fig 2a) , daily hospitalizations (Sup fig 2b) , daily deaths (Sup fig 2c) , age-stratified cases (Sup fig2d), age-stratified hospitalizations (Sup fig2e), age-stratified deaths (Sup fig2f), cumulative cases (Sup fig 2g) , and cumulative deaths (Sup fig 2h) through November, 2020. Extending beyond the calibration period, we attempt to capture realistic approximations of local pandemic management to date. First, based on experience in other U.S. states and current Washington state policies, we assume that in the absence of a vaccine, numbers of cases 200 and hospitalizations are likely to fluctuate due to the community response to the epidemic (27, 28) . When number of new infections remains below a certain threshold, physical distancing measures are assumed to relax allowing greater contact between susceptible and infected people.

The effective reproductive number (Re) eventually exceeds one and cases start growing in number. Eventually a threshold is surpassed that necessitates reinforcement of physical 205 distancing restrictions: Re drops below one and cases contract. Based on timing of Washington state reinforcement of social distancing (29), we set this threshold at a 2-week daily case average of 300 new cases per 100,000. Physical distancing is set on a scale of 0 to 1 where 0 represents the level of pre-pandemic interactivity in the population and 1 implies no physical interactions. Fig 2) , we projected the ongoing recurrent third wave 210 (numbered in top row) of infections (Fig 2a) , diagnosed cases (Fig 2b), hospitalizations (Fig 2c) and deaths (Fig 2d) between 11/2020 and 3/2021 (Fig 2, top row) . We also anticipated the need . CC-BY-NC 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) preprint

The copyright holder for this this version posted December 14, 2020. ;

to re-enforce physical distancing to achieve 40% interactivity relative to pre-pandemic levels (Fig 2e) , in order to lower Re below 1 (Fig 2f) . The model projects that this third wave would have a significantly higher number of infections, diagnosed cases and hospitalizations then the 215 first wave in the spring of 2020 and the second wave in the summer of 2020. Daily deaths were projected to peak at similar levels to the first wave due to a higher proportion of younger individuals becoming infected with lower death rates. By January 2021, despite physical distancing, ~15% of the population was projected to have been infected with ~7000 hospitalizations and ~1500 deaths (Fig 2, middle row) . 220

In the absence of a vaccine, our model projected a substantial fourth wave of infections (Fig 2a) , diagnosed cases (Fig 2b) , hospitalizations (Fig 2c) and deaths (Fig 2d) between April and October 2021, necessitating a fourth cycle of increased physical distancing (Fig 2e) . At the end of this fourth wave, we forecast that ~25% of the population will have been infected and ~5% diagnosed with ~10,000 hospitalizations and ~2000 deaths (Fig 2, middle row) . We initially assumed 5000 vaccinations per day with the goal of covering 50% of the population of 2.2 million people with a start day for vaccination on January 1, 2021 allowing 220 days until completion in mid-August. In our simulations, both susceptible and recovered persons were vaccine eligible. We assumed that the vaccine start date represented timing of the second shot for the mRNA vaccines such that efficacy accrues at the defined time of vaccination. 245

Initially, we imputed no loss of vaccine efficacy over time.

In one scenario (Fig 2) , we assumed disproportionate initial targeting of the cohorts aged > 70 initially (80% of vaccines with 20% to those older than 20 years old). In a second scenario (Sup fig 3) , we first vaccinated the age cohorts with greatest inter-connectivity (20-45 and 45-69 years old received 80% of vaccines). We also imputed slow relaxation of social distancing 250 during the vaccination program when cases remained below a certain threshold.

cases, deaths, and lockdown in spring 2021. We first considered scenarios in which elderly cohorts were vaccinated first and VEDIS was mediated mostly by VESUSC rather than VESYMP 255 (VESYMP=10%). Vaccines with high VESUSC (90%, blue lines) or VEINF (90% darkest blue, green and red lines) resulted in the greatest reduction in peak (Fig 2 top row) and cumulative (Fig 2 middle row) infections (Fig 2a) , diagnosed cases (Fig 2b) , hospitalizations (Fig 2c) and deaths . CC-BY-NC 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) preprint

The copyright holder for this this version posted December 14, 2020. ; (Fig 2d) . All vaccines with VESUSC = 50% (green lines) or 90% (blue lines), or VEINF = 50% (medium blue, green and red) or 90% (dark blue, green and red), prevented a large fourth wave 260 of infections and deaths and allowed 20% physical distancing starting in April 2021 (Fig 2e) while maintaining Re less than 1 (Fig 2f) . Notably, only VESUSC=90% vaccines (blue lines) are compatible with Moderna and Pfizer results and VEINF had little impact on these projections.

All vaccines with at least 90% VESUSC or VEINF, or both 50% VESUSC and 50% VEINF, lead to a reduction in approximately 200,000 infections, 45,000 diagnosed infections, 3500 265 hospitalizations and 600 deaths since the start of the vaccination period (Fig 2 bottom row) , though fewer deaths were prevented than would have already occurred by April 2021 (~1500). A vaccine with VESUSC = 10%, VEINF = 10% and VESYMP = 10% (pink line) was predicted to only delay the peak of infections, hospitalizations and deaths (Fig 2 top row) with a small percentage reduction in these outcomes over time (Fig 2 bottom row) and a requirement for a fourth phase 270 of increased physical distancing (Fig 2e) .

Nearly equivalent results were noted when younger and middle-aged cohorts with higher inter-connectivity were vaccinated with higher priority (Sup fig 3) .

and lockdown in spring 2021 for low VESUSC, high VESYMP vaccines. We next considered a scenario in which VEDIS was mediated mostly by VESYMP rather than VESUSC (10%) with vaccine prioritization to the elderly. Once again, for all conditions with VEINF = 90% (darkest purple, darkest orange lines), we observed a substantial decrease in infections (Fig 3a) , diagnosed cases (Fig 3b) , hospitalizations (Fig 3c) and deaths (Fig 3d) with no large fourth wave observed (Fig  280   3, top row) , a levelling off in cumulative incidence of all outcomes (Fig 3, middle row) , and a . CC-BY-NC 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) preprint

The copyright holder for this this version posted December 14, 2020. ; https://doi.org/10.1101/2020.12.13.20248120 doi: medRxiv preprint 60-70% reduction in all outcomes starting at the time of vaccination (Fig 3, bottom row) . There were no visible effects of increasing VESYMP when VEINF = 90%.

Under the high VESYMP, low VEINF scenario compatible with the Moderna and Pfizer vaccine trial results (light purple line), a fourth protracted wave of ~60,000 infections and ~200 285 deaths lasting from April 2021 through January 2022 occurred which did not meet a threshold that necessitated further resumption of lockdown measures (Fig 3e,f) . At moderate VEINF (50%, medium purple and medium orange) and in particular at lower VEINF (10%, light purple and light orange), we observed a beneficial effect of increased VESYMP (Fig 3) with further reduction in all outcomes at high (90%, light purple) versus moderate (50%, light orange) VESYMP. This result 290 likely relates to the fact that VESYMP converts symptomatic to asymptomatic infection which in our model is predicted to be associated with a 44% decrease in overall infectivity.

VEINF. We explored the impact of varying VEINF under several plausible vaccine scenarios with 295 VEDIS = 90%. We generated heat maps for total post-vaccine diagnosed cases (Fig 4a) and deaths (Fig 4b) and identified that for scenarios when VEDIS =90% is mediated mostly by VESYMP (90%, black circles), increasing VEINF from 10% to 90% resulted in substantial further reductions in diagnosed cases (~20,000) and deaths (~60). When VEDIS=90% was mediated entirely (90%, white circles) or mostly (70%, grey circles) by VESUSC, then increasing VEINF 300 from 10% to 90% resulted in very limited further reductions in diagnosed cases and or deaths.

We next identified that VESUSC and VEINF had nearly equivalent effects on number of post-vaccine diagnosed cases (Sup fig 4a) and deaths (Sup fig 4b) . For VESYMP = 10% and 50% (Sup fig 4, left and middle columns) , at values of VESUSC<50%, increases in VEINF lead to . CC-BY-NC 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) preprint

The copyright holder for this this version posted December 14, 2020. ; https://doi.org/10.1101/2020.12.13.20248120 doi: medRxiv preprint further reductions in cases and deaths. However, at high values of VESUSC, increases in VEINF 305 added little benefit. There was moderate effect modification by VESYMP: particularly for deaths, there was less added benefit of increasing VEINF, when VESYMP = 90% (Sup fig 4, right column) highlighting that VESYMP prevents deaths more efficiently than infections.

The distribution and acceptability of vaccines to the public remains uncertain. We therefore simulated the vaccine scenarios in Nevertheless, at slower roll out, a fourth wave of infections (Fig 5a) , diagnosed cases (Fig 5b) , 315 hospitalization (Fig 5c) and deaths (Fig 5b) occurred among all scenarios. The peak (Fig 5 top row) was blunted and delayed under scenarios with VESUSC=90% (blue lines) or VEINF=90% (dark red, green and blue) with ~100,000 fewer cumulative cases and ~300 fewer deaths (Fig 5 middle and bottom rows) indicating that VEINF would take on added importance under less optimal roll out scenarios with low VESUSC. Only the scenario with limited effects on secondary 320 transmission VESUSC=10% and VEINF=10% allowed a severe enough wave to necessitate another round of physical distancing (Fig 5e,f) .

Vaccine uptake at 5000 per day resulted in Reff<1 in April to June at 20% social distancing relative to pre-pandemic conditions (SD=0.2), a rough proxy for herd immunity assuming some degree of residual social distancing and masking (Fig 6a) . Vaccine uptake at 325 2500 per day achieved Reff<1 in August to September (Fig 6b) . The more rapid roll out scenario achieved this functional herd immunity before occurrence of the fourth wave whereas under the . CC-BY-NC 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) preprint

The copyright holder for this this version posted December 14, 2020. ; https://doi.org/10.1101/2020.12.13.20248120 doi: medRxiv preprint slower roll out scenario, a surge in cases in July contributed to development of Reff<1 (Fig 6, bottom row). Under both roll out rate scenarios, vaccines that had both low VESUSC and VEINF (light green and pink), had a one-to-two month delay to reach Reff<1, thereby allowing more 330

infections. eventually occurred among all vaccine scenarios, but was delayed under scenarios with VESUSC=90% (blue lines) or VEINF=90% (dark red, green and blue) indicating that VEINF may 340 also take on critical importance in the event of waning vaccine efficacy.

The above results suggest that the potential severity of a fourth wave can only be estimated with accurate estimates for VESUSC, VESYMP and VEINF among relevant vaccines, as well as rates of vaccine roll out and duration of 345 protection. It is therefore a priority to identify the true values for these vaccine characteristics.

Based on experience from multiple other viruses that exposure dose predicts transmission (30, 31) , we hypothesize that VEINF is likely to be mediated by reduction in viral load among infected people (Fig 7) . We therefore employed our existing intra-host model described in the Methods that links SARS-CoV-2 viral load dynamics in an infected person with the potential for 350 . CC-BY-NC 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. 

We next considered methods to estimate VEINF using viral load as a potential surrogate. To simulate the effect of a vaccine on 360 viral load, we assumed the presence of a tissue-resident population of immune cells with rapid ability to recognize and kill infected cells, as well as proliferate in situ, as a necessary condition to lower peak viral load in infections such as SARS-CoV-2 with rapid initial growth kinetics (34) . We first established a relationship between the initial number of tissue resident immune cells and peak viral load (Fig 8a, b) during individual simulated infections. We then assumed 365 vaccination trials consisting of 1000 people in which vaccine recipients generated a certain number of these immune cells while placebo recipients did not. By estimating the reduction in number of transmissions, we then were able to estimate VEINF for each vaccine. The model predicted a sigmoidal relationship between reduction in peak viral load and VEINF: a 0.6 log or 4fold reduction in peak viral load resulted in VEINF =50% and a 2.5 log or ~300-fold reduction 370 resulted in VEINF = 90% (Fig 8c) .

. CC-BY-NC 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) preprint

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load could serve as a surrogate endpoint for VEINF requires experimental validation. While a 375 transmission dose response relationship has been demonstrated for SARS-CoV-1 in mice (35) , and infection of SARS-CoV-2 between golden hamsters occurred with direct viral load exposure at 10 11 RNA copies but not 10 9 viral RNA copies (36, 37) . CC-BY-NC 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) preprint

The copyright holder for this this version posted December 14, 2020. ; https://doi.org/10.1101/2020.12.13.20248120 doi: medRxiv preprint

vaccines trials with viral load as endpoints. One method to directly assess VESUSC and VESYMP, and to indirectly estimate VEINF, using projections from our model (Fig 8c) is a human challenge study in which healthy participants are challenged with SARS-CoV-2 one month after receiving a final dose of a vaccine or placebo schedule in a blinded fashion. Following challenge, viral load would be sampled daily for 2 weeks to capture true peak. If VEDIS is mediated entirely by VESYMP, then vaccine recipients will shed virus as in Fig   7 and useful comparisons can then be made between infected vaccine and placebo recipients. We demonstrate that with this approach, 80% power can be achieved to detect differences in peak 410 log10 viral load between vaccine and placebo arms with as few as 10 infected participants per arm if peak viral reduction is 2.5 log10 (model estimated VEINF~90%), 52 participants per arm if peak viral reduction is 1.0 log10 (model estimated VEINF~60%), and 143 participants per arm if peak viral reduction is 0.6 log10 (model estimated VEINF=50%) (Sup fig 6) .

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The copyright holder for this this version posted December 14, 2020. ; https://doi.org/10.1101/2020.12.13.20248120 doi: medRxiv preprint

An optimal vaccine program would prevent the maximum numbers of cases and deaths, without the need for further lockdown periods. The first component of such a program will be 420 testing and licensing of vaccines that provide at least partial protection from symptomatic disease (VEDIS). Initial data from the Pfizer and Moderna trials suggest that these products may have 90% or higher VEDIS. The second step is to consider the proportion of the population that will need to be vaccinated in order to provide herd immunity. This threshold will depend critically on indirect effects that protect unvaccinated members of the population. Indirect effects occur when 425 VEDIS is mediated by VESUSC rather than VESYMP, but may also be augmented by a vaccine product with high VEINF in the scenario where VESUSC is low. Given rapid enough roll out, our results suggest that vaccines with either high VESUSC or high VEINF, or both moderate VESUSC and moderate VEINF, could prevent a fourth wave of cases and deaths in the spring and summer.

Unfortunately, VESUSC can only be partially discriminated from VESYMP in current 430 clinical trials using serologic assays which may miss infection due to waning humoral responses (38) . Moreover, VEINF is not being directly assessed. While viral load is being compared between symptomatic infected vaccine and placebo recipients, in most cases, sampling will occur several days after the peak viral load when transmission risk is highest (1). Viral load in asymptomatic cases also will not be captured. Overall, VESUSC, VESYMP and VEINF are 435 particularly challenging to measure, leaving policy makers with incomplete information for projecting the impact of a given vaccine.

We identify that under any scenario in which VESUSC is low, a vaccine with VEINF >50% would add substantial protection at the population level. A vaccine with this profile would exert maximal benefit whether given to younger or elderly cohorts first if rolled out quickly enough. If 440 . CC-BY-NC 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) preprint

The copyright holder for this this version posted December 14, 2020. ;

VESYMP is driving observed results, then high VEINF would be vital for preventing thousands of cases and saving hundreds of lives in King County, with much larger benefits when considered across the larger US population. In scenarios where a fourth spring wave is inevitable, such as slow vaccine roll-out or waning vaccine induced protection, VEINF could potentially delay and blunt the peak number of cases and deaths, thereby preventing the need for re-enforcement of 445 physical distancing while also preventing many deaths.

Therefore, it is an urgent research priority to identify reasonable estimates for VESUSC, VESYMP and VEINF for vaccines that will be given to the population at large. Trial strategies which attempt to directly measure secondary infections in households (39, 40), or to assess the degree of protection afforded to unvaccinated members of communities with partial vaccination 450 relative to communities with less vaccination, would potentially be conclusive. They will need to be performed quickly to obtain actionable results prior to spring 2021.

Our analyses suggest that peak viral load could serve as a surrogate endpoint for secondary transmission and allow for rapid, complementary studies. We estimated the relationship between viral load and transmission probability for SARS-CoV-2 based on model 455 fitting to observed serial intervals and individual R0 values (14). The emergent transmission response curve took on a similar sigmoidal shape to empirically derived curves for SARS-CoV-1 in a controlled set of murine experiments (35) , and also resembled the relationship between quantitative viral PCR and probability of culture positivity in humans infected with SARS-CoV-2 (41). 460

As a first step, it is necessary to formally test the hypothesis that exposure viral load is predictive of transmission risk (42). A valid viral load surrogate cannot currently be inferred from human cohorts as the exposure viral load is never documented between transmission pairs, . CC-BY-NC 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) preprint

The copyright holder for this this version posted December 14, 2020. ; though formal surrogate endpoint analysis will ultimately be necessary if sufficient data emerges.

We suggest that animal models of infection are ideal for this purpose and that necessary 465 transmission dose can be inferred with a relatively small number of non-human primates or mice.

Human trials using reduction in peak viral load or viral area under the curve as correlates for reduction in VEINF could take one of two forms. The first would involve prospective nasal sampling of virus in all enrolled participants with virologic endpoints compared between those who become infected in vaccine and placebo arms. An ideal study population would be 470 university students due to their high incidence rate and low overall infection morbidity. The . CC-BY-NC 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) preprint

The copyright holder for this this version posted December 14, 2020. ; https://doi.org/10.1101/2020.12.13.20248120 doi: medRxiv preprint Our approach has limitations. We combine several scales of models which reflect population conditions unique to King County Washington and virologic findings from across the globe. The models are not equipped to make precise vaccine schedule assessments for different locations and are not meant as predictions. Rather, we intend to make the conclusion that VEINF could theoretically provide substantial population level benefits and to provide a framework for 490 most rapid evaluation of this metric. The scope of the ongoing third wave is difficult to forecast and will depend on changes in human behavior over the next several weeks. The number of cases and deaths during a possible fourth spring wave may be somewhat dependent on current events.

In conclusion, in the situation where observed high VEDIS is predominately due to reduction in symptoms rather than absolute protection against infection, VEINF will be vital to 495 measure as it may determine whether a severe fourth wave of cases and deaths is imminent in the spring. Using peak viral load as a proxy measure in human challenge studies is an efficient way to complement other clinical trial designs to assess VEINF.

. CC-BY-NC 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. In our main scenario we assume that 20% of infections are asymptomatic and that 510 asymptomatic people are as infectious as symptomatic individuals but missing the highly infectious pre-symptomatic phase. As a result, the relative infectiousness of individuals who never develop symptoms is 56% of the overall infectiousness of individuals who develop symptomatic COVID-19. This conservative estimate falls between the 35% relative infectiousness estimated in recent review based on 79 studies (44) and the current best estimate 515 of 75% suggested by the CDC in their COVID-19 pandemic planning scenarios (45).

The forces of infection, representing the risk of the susceptible individuals to acquire infection (transition from susceptible to exposed), are differentiated by age of the susceptible individual, the contact matrix (proportion of contacts with each age group), infection and treatment status (asymptomatic, pre-symptomatic, symptomatic, diagnosed and hospitalized 520 cases) of the infected contacts as described in the Supplement.

. CC-BY-NC 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) preprint

The copyright holder for this this version posted December 14, 2020. ; https://doi.org/10.1101/2020.12.13.20248120 doi: medRxiv preprint

The model is parameterized with local demographic and contact data from King County, WA and calibrated to local case and mortality data using transmission parameters ranges informed from published sources (15, (46) (47) (48) .

A critical parameter in the model is the social distancing metric which estimates the 525 amount of potential infection contacts between members of the population. This parameter is intended to capture physical contact reduction due to physical distancing policies, but also decreased number of transmission contacts due to masking. The parameter varies between 0, which represent pre-pandemic level of interactivity, and 1, which represents complete physical distancing with no interactivity. 530

In the current version, we incorporate fluctuating values of this parameter retrospectively to calibrate the model to observed infection, hospitalization and death data through the end of October 2021, as well as prospectively to capture likely enhanced physical distancing in response to present and future cases. Our benchmarks for increasing physical distancing to 0.6 was when 2-week average number of cases exceeded 300 per 100,000. We allowed relaxation of the 535 parameter to 0.2 when 2-week average number of cases fell below 100 per 100,000. For elderly populations, we assume greater restrictions to 0.8 and lessen relaxation to 0.4. This approach reproduces the waves of infection which have defined the United States pandemic to date.

We consider several vaccine efficacy 540 profiles as described in the Results with different efficacies as defined in Table 1 .

Implementation of these efficacies is described in the Supplement.

. CC-BY-NC 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) preprint

The copyright holder for this this version posted December 14, 2020. ; https://doi.org/10.1101/2020.12.13.20248120 doi: medRxiv preprint

CoV-2 infection from our previous study to generate viral loads to assess transmission risk (21) .

Intra-host transmission model. We employed our previously described model linking transmitter viral load with probability of transmission (21) . The details of this model are described in the Supplement.

We simulated the impact of the vaccination by assuming that a vaccine generates a certain number of SARS-CoV-2 specific acquired immune cells that are ready to proliferate (with no need for precursor compartments ! ! and ! " ) and act to quickly eliminate the ongoing infection. We thereby modify our intra-host model in the Here, ) $% denotes the level of infected cell that allows proliferation of immune cells at 50% 560 maximal. We assume it to be 10 cells/mL. We further fix / = 2 days -1 cells -1 and + = 0.01 days -1 cells -1 .

. CC-BY-NC 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 this version posted December 14, 2020. ; https://doi.org/10.1101/2020.12.13.20248120 doi: medRxiv preprint Each vaccine trial consists of selecting a starting condition of parameter E (E0) that leads to a predictable reduction in peak viral load (Fig 6b) . We simulate individual trials with 1000 vaccine participants and 1000 placebo recipients, and then assess the relative reduction in 565 transmissions to estimate VEINF as in Table 1 .

We assume that the dose response model is given by

is the infectiousness based on viral loads V (dose) at the time t of viral challenge, λ is the infectivity parameter that represents the viral load that 570 corresponds to 50% infectiousness and α is the Hill coefficient that controls the sharpness in the dose-response curve.

We consider the trial design given this initial estimation of parameters: α = 0. We simulate the data from the two-parameter dose-response model and use the function 'drm' in 580 the R package 'drc' to fit the model.

We consider sensitivity analysis when ID 50 is poorly specified, especially if ID 50 is smaller than expected. We also we consider a dynamic sample size allocation procedure.

Particularly, we first allocate n1 = N/5 animals to V1 and determine the following dose allocation based on the number of infections in this V1 dose group, denoted as m1. If more than half of the 585 . CC-BY-NC 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 this version posted December 14, 2020. ; https://doi.org/10.1101/2020.12.13.20248120 doi: medRxiv preprint animals allocated to V1 are infected, i.e., m1 ≥ n1/2, we set λ * = V1 and assign the rest of the animals equally to the doses V2 * =1pfu, V3 * =2pfu, V4 * =18pfu and V5 * =100pfu, which reflect this new λ * . Based on this dynamic sample size allocation procedure, the proportion of replicates that fail to produce an estimate is smaller and we are able to identify the values of α and ID 50 with increased accuracy. 590

Human challenge study sample size estimates. Sample size calculations were based on a 2sample t-test to compare mean peak log10 viral load between the vaccine and placebo arm with 80% power. We conservatively assumed a common standard deviation of 1.8 log10 for the peak log10 viral load in both arms, which is based on estimates from natural infection (49), and likely 595 an upper limit for our proposed human challenge trial where the challenge dose and anatomic site would be equivalent. We also assumed equal number of participants in each arm, and a 2sided type I error of 0.05. We considered a range of values for the difference between peak log10 viral loads in the vaccine and placebo arm that corresponded to projected values of VEINF ranging from 30% to 100%. 600 . CC-BY-NC 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 top row is number of vaccinated people (y-axis) and date (x-axis) at which Re decreases below 1. Middle row is cumulative number of infected people (y-axis) and date (x-axis) at which Re decreases below 1. Bottom row is the projected 4 th wave at these scenarios demonstrating that ongoing cases contribute to herd immunity with slower roll out only. VESYMP=90% is assumed for each of the nine vaccines. The most rapid time to achieve herd immunity is associated with either high VESUSC or VEINF. Of note, these simulations occur at 20% social distancing. 

Simulated virologic trajectories with higher imputed initial number of vaccine-generated tissue-resident immune cells (E0) demonstrate lower peak viral loads. b. Varying number of tissue-resident immune effector cells generated by a vaccine (x-axis) predicts peak viral load (y-axis) in individual infection simulations each denoted with a dot. The red line indicates a correlation line. c. Reduction in viral load (x-axis) predicts VEINF (y-axis) in vaccine simulations. Each black dot is a simulation of 1000 vaccine recipients given a vaccine which generates a fixed E0 versus 1000 placebo recipients. VEINF=50% is achieved with a 0.6 log10 reduction in peak viral load. VEINF=90% is achieved with a 2.5 log10 reduction in peak viral load. The relationship between change in peak viral load (x) and VEINF is captured with the formula: VEINF = (log10 x) 1.6 / (IV50) 1.6 + (log10 x) 1.6 where IV50=0.6. 

King County model parameters. Model parameters are listed as follows with values listed in the 755 Supplementary Table 1: pi -proportion of the infections which become symptomatic by age in absence of a vaccine γ1, γ2-progression rates from exposed (E) to infectious (A and P) to symptomatic (I) The forces of infection (λ , ), representing the risk of the susceptible individuals by age to acquire infection (transition from susceptible to exposed), are differentiated by age of the susceptible individual, a contact matrix (proportion of contacts with each age group), infection and treatment status (asymptomatic, pre-symptomatic, symptomatic, diagnosed and hospitalized cases) 

where βa, βp, βs, βd, βh are the transmission rates from contacts with asymptomatic, presymptomatic, symptomatic, diagnosed and hospitalized infections (before the start of COVID 790 measures at t= δ1), cij is contact matrix (proportion of the contact with other age groups), Ni is population size by age, va is vaccine efficacy in reducing the acquisition risk (reduction of susceptibility), vt is vaccine efficacy in reducing the transmission risk (reduction of infectiousness).

measures which is applied uniformly to all age groups. It is scaled up linearly from 0 to R ./ 708 between t= δ1 and t= δ2). Later it is calibrated monthly to match the King County epidemic through October of 2020 and then controlled dynamically based on the bi-weekly case rates per 100k of the population. For age groups 1-3 the highest value of R ./ 708 is 0.6 (i.e. interactions at 40% of pre-COVID levels) and the lowest allowed is 0.2 (social interactions at 80% of pre-800 COVID levels). These limits are each 0.2 higher for the oldest age group. The triggers for increasing or decreasing social distancing levels are given in the parameter table.

King County model calibration. The model is calibrated to 3 "targets" based on local data (Supplementary fig 2) , namely: the age-wise number of confirmed daily cases (S2d), daily 805 deaths (S2e) and daily hospital admissions (S2f) reported in King County over time since the start of the epidemic outbreak through October 31 st , 2020. We used the BFGS optimization algorithm to estimate the best parameter values for the time period being fitted. We defined thresholds for each parameter and proceeded with the best set reported by the routine.

Calibration was divided into multiple periods. The first was from the start of the epidemic 810 through the initial lockdown period ending in early May. Subsequent fits were by month, but sharde the initial fits for start date, β* (overall infectivity) and βd (adjustment to infectivity for diagnosed individuals). our previously proposed within host model and estimates (2) . X is the infectivity parameter that represents the viral load that corresponds to 50% infectiousness and 50% contagiousness, and Y is the Hill coefficient that controls the slope of the dose-response curve. Our transmission model assumes that only some contacts of an infected individual with viral load dependent infectiousness are physically exposed to the virus (defined as exposure contacts), that only some 845 exposure contacts have virus passaged to their airways (contagiousness) and that only some exposed contacts with virus in their airways become secondarily infected (successful secondary infection). Contagiousness and infectiousness are then treated as viral load dependent multiplicative probabilities with transmission risk for a single exposure contact being the product. Contagiousness is considered to be viral load dependent based on the concept that a 850 transmitter's dispersal cloud of virus is more likely to prove contagious at higher viral load, which is entirely separate from viral infectivity within the airway once a virus contacts the surface of susceptible cells.

We assumed that the total exposed contacts within a time step (Z E % ) is gamma distributed, i.e. Z E %~\ ] F G , _`Δ & , using the average daily contact rates (b) and the dispersion 855 parameter (_). To obtain the true number of exposure contacts with airway exposure to virus, we multiply the contagiousness of the transmitter by the total exposed contacts within a time step We further assume that upon successful infection, it takes j days for the virus to move within-host, reach the infection site and produce the first infected cell. To calculate serial interval 870 (time between the onset of symptoms of transmitter and secondarily infected person), we sample the incubation period in the transmitter and in the secondarily infected person from a gamma distribution (4, 5). In cases in which symptom onset in the newly infected person precedes symptom onset in the transmitter, the serial interval is negative; otherwise, serial interval is nonnegative. 875

The model was fit to distributions of individual R0 (secondary transmissions per person) and serial interval as previously described (6-10). We then arrived at parameter estimates for X, j, Y and b and identified that a skewed distribution of daily exposure contacts explains the virus super-spreader property. This model was used to obtain baseline levels of secondary transmission for simulated placebo recipients. 1% per month 5% per month a.

b. 10% per month c.

Supplementary figure 6. Required study size for human challenge studies to achieve 80% power. a. The relationship between mean peak viral load change and required sample size demonstrates that if a vaccine induces a >1.0 log10 reduction in peak viral load, then required sample size is much lower. b. The relationship between projected VEI and required sample size demonstrates that if a vaccine induces VEINF>60%, then required sample size is much lower. 

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Model structure captures transition from susceptible (S) to exposed (E) to asymptomatic infection (A), or to pre-symptomatic (P) and then symptomatic infection (I) followed by recovery (R), hospitalization (H) or death (F). A similar potential pathway is also shown for a vaccinated cohort (V). Diagnosed (D) and diagnosed asymptomatic (DA) is an intermediate step for a proportion of people.

Model fit is to a. daily cases, b. daily hospitalizations, c. daily deaths, d. age-stratified cases, e. age-stratified hospitalizations, f. age-stratified deaths, g. cumulative cases, and h. cumulative deaths through the end of October 2021. b.

For unvaccinated (black lines) and each vaccine cohort (colored lines, legend), we project daily diagnosed cases (top row) and daily deaths (bottom row). Columns are a. 1% (left), b. 5% (middle) and c. 10% (right) of of persons with vaccine induced immunity reverting to susceptible per month. Waves of infection are numbered 1-4. Nine combinations of VESUSC and VEINF are considered while VESYMP is fixed at 90%. High VESUSC (90%) simulations are blue and have similar outcomes to one another. Moderate VESUSC (50%) simulations are green. Low VE SUSC (10%) simulations are red / pink. Dark lines are high VE INF (90%) and have similar outcomes to one another. Moderate darkness lines are medium VEINF (50%). Light lines are low VEINF (10%). The largest reduction in cases is associated with either high VESUSC or VEINF though slow rebound occurred with VESUSC or VEINF 50%. 5000 vaccines are given per day starting January 1, 2021 (yellow square) until 50% are vaccinated. Case threshold for reinstituting physical distancing to 0.6 is 300 per 100,000 and for relaxation is 100 per 100,000. 80% of vaccines are initially allocated to the elderly with the remaining 20% to middle-aged cohorts. 

No vaccine