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. 2021 Apr 28;16(4):e0250797. doi: 10.1371/journal.pone.0250797

Potential impact of introducing vaccines against COVID-19 under supply and uptake constraints in France: A modelling study

Laurent Coudeville 1,*, Ombeline Jollivet 1, Cedric Mahé 1, Sandra Chaves 1, Gabriela B Gomez 1,2
Editor: Yury E Khudyakov3
PMCID: PMC8081204  PMID: 33909687

Abstract

Background

The accelerated vaccine development in response to the COVID-19 pandemic should lead to a vaccine being available early 2021, albeit in limited supply and possibly without full vaccine acceptance. We assessed the short-term impact of a COVID-19 immunization program with varying constraints on population health and non-pharmaceutical interventions (NPIs) needs.

Methods

A SARS-CoV-2 transmission model was calibrated to French epidemiological data. We defined several vaccine implementation scenarios starting in January 2021 based on timing of discontinuation of NPIs, supply and uptake constraints, and their relaxation. We assessed the number of COVID-19 hospitalizations averted, the need for and number of days with NPIs in place over the 2021–2022 period.

Results

An immunisation program under constraints could reduce the burden of COVID-19 hospitalizations by 9–40% if the vaccine prevents against infections. Relaxation of constraints not only reduces further COVID-19 hospitalizations (30–39% incremental reduction), it also allows for NPIs to be discontinued post-2021 (0 days with NPIs in 2022 versus 11 to 125 days for vaccination programs under constraints and 327 in the absence of vaccination).

Conclusion

For 2021, COVID-19 control is expected to rely on a combination of NPIs and the outcome of early immunisation programs. The ability to overcome supply and uptake constraints will help prevent the need for further NPIs post-2021. As the programs expand, efficiency assessments will be needed to ensure optimisation of control policies post-emergency use.

Introduction

With the risk of continuous transmission of SARS-CoV-2 and the disruption of global economy, expectations and investments in research and development of vaccines to control the COVID-19 pandemic have been unprecedented. In just over a year, almost 100 candidates have started clinical testing, with 20 ongoing phase III trials globally [1, 2]. Of these, four vaccines have been approved for use after showing critical efficacy results [3–6]. Regulatory bodies have adapted approval processes, which in turn have shortened timelines from months to weeks, as shown by the fast-track reviews of the European Medicines Agency and the Federal Drug Administration in the USA [7, 8]. Under these accelerated timelines, vaccines have become available late 2020, with implementation starting end 2020 beginning 2021 [9]. However, in the presence of global demand, even with scaled-up production taking place before trials completion, supply is likely to be constrained in this first year of implementation.

In parallel to clinical trials, policy makers’ efforts have been geared towards planning immunisation programs to maximise societal benefits and achieve an equitable distribution of limited vaccines. Previous modelling studies have explored the potential population impact of immunisation programs depending on vaccines and programs characteristics, such as efficacy, coverage, duration of protection elucidated by vaccines or whether these are effective in preventing symptomatic disease alone or preventing infection as well [10–14]. Authors have shown that a vaccine will need to be highly effective and the immunisation program will need to achieve high coverage to be able to obviate the need of non-pharmaceutical interventions (NPIs) to control the pandemic in the short term. Other studies investigated prioritisation strategies to optimise immunisation impact considering limited coverage [15, 16], including recent modelling by the Imperial College COVID-19 Response Team. In this study, the authors showed that the optimal allocation strategy (i.e. groups to prioritise and relative coverage achieved) within country will likely depend on the level of supply constraint of vaccines being introduced in 2021 [17].

In addition, vaccine hesitancy limiting the impact of an eagerly awaited immunisation program should not be underestimated [18, 19]. Surveys to date have shown a changing level of willingness to vaccinate as individuals’ perceptions of risk have evolved [19–21]. Populations have become less willing to vaccinate with first-come vaccines and may be increasingly more willing to wait for additional data on safety and effectiveness in real life conditions [22]. Immunisation programs will likely see successive candidates [23] becoming available during 2021, and later vaccine entrants may play a role improving supply and, depending on further data available, possible uptake.

Here, rather than focusing on optimal conditions for a vaccination program to be successful, we aimed at identifying plausible scenarios for the short to mid-term impact of an immunisation program in France, considering the uncertain vaccine profile and likely variation of supply and uptake.

Methods

Model structure and calibration

We built on a previously published age-stratified compartmental transmission model of SARS-CoV-2 to examine the short-term impact of an immunisation program starting January 2021 in France [24]. Briefly, we expanded a standard Susceptible-Exposed-Infectious-Recovered (SEIR) structure to account for seasonality of SARS-CoV-2 transmission, levels of disease severity, and possibility of reinfection with reduced level of severity compared to the primary infection. Reinfections are being defined as any infection to Covid-19 following a period with naturally-acquired or vaccine-induced immunity. This immunity period is assumed to have a median duration of one year in the base case. Future vaccination is modelled through dedicated compartments where duration of immunity can be modulated.

The model was calibrated using least-squares minimization to French surveillance data up to November 21, 2020. Three outcomes derived from two sources were used for calibration: number of symptomatic cases and deaths reported by the European Centre for Disease Prevention and Control and hospital admissions reported by Santé Publique France [25, 26]. Natural history parameters for SARS-CoV-2 infection were based on the U.S. Centers for Disease Control and Prevention best estimates [27], while parameters such as infection fatality ratio, hospitalization rates, and social contact matrices by age were locally sourced [28, 29]. Our base case scenario corresponds to a situation with moderate seasonality (20% amplitude in COVID-19 transmission with a peak transmission in January) and limited symptoms in case of reinfection (90% reduced symptom severity compared to primary infections). A full description of the model, parameterization, and calibration method is presented in S1 Text in S1 File.

Non Pharmaceutical Interventions (NPIs)

NPIs have been widely implemented across the globe with varying levels of stringency and compliance. As we enter the second year of the pandemic, countries are balancing a changing epidemiology of re-emerging cases with population signs of fatigue to adhere to mitigation measures. In this analysis, we do not explicitly model the effect of discrete NPIs but assume a reduction of the effective reproduction number due to a change in measures in place (e.g., social distancing, curfew, lockdown, contract tracing) triggered by a predefined threshold. This threshold, as well as the targeted effective reproduction number and timing of relaxation, differs between the three levels of NPI response we considered (see S2 Table in S1 File). Two of these scenario responses are based on the evolution of the incidence of hospitalization rates observed in France. The first and second wave thresholds are defined by the peak number of hospitalizations observed in the first and second waves. These thresholds are 100 and 70 hospitalizations per million population per day, respectively. The latter was used as our reference case. The third scenario is based on a hypothesized government response that could tolerate high level of disease rates and be triggered by a higher threshold of 200 hospitalizations per million population per day. In addition to the threshold-based response, we also accounted for a relative reduction of exposure to infection in the vulnerable population (elderly and people with comorbidities) compared to the rest of the population due to a better adherence of this part of the population to distancing measures. The relative reduction was derived from the calibration in our reference case at approximately 30% (more information in S1 Text in S1 File). We considered that the vulnerable population no longer maintain a lower exposure to infection compared to the rest of the population when the roll-out of the vaccination program is completed towards the end of 2021.

Vaccine profiles

Vaccines efficacy in clinical trials published to date has been measured for prevention of moderate to severe disease [3–6]. However, in addition to the reduction of symptomatic (mild, moderate and severe) disease, these vaccines could also protect against infection (and therefore preventing also asymptomatic disease and transmission). We considered both cases as there is evidence from the trials of prevention of disease and emerging (less definitive) real-world evidence of prevention of infection [30, 31]. In both cases, we considered that onset of protection starts one month after the administration of the first dose. In our reference scenario, a vaccine protecting against infection with an efficacy varying from 50% to 90% for individuals without prior exposure to COVID-19 and a median duration of protection of one year [32].

Immunisation programs

We characterised the government-driven immunisation programs across three dimensions: 1) implementation, 2) population’s willingness to be vaccinated, and 3) supply of vaccines. For the implementation of the program, we assumed the scale-up of such program to follow the French COVID-19 scientific and vaccine committees’ proposal and distributes the vaccine allotment into priority access categories [33]. High priority groups (i.e. HCW and people with professional risks) are prioritised in the first two months of the immunisation program, vulnerable adults (i.e. those with comorbidities and the elderly) follow in the roll-out over the next four months. After these groups are covered, the national program reaches other adults (i.e. 20–59 years without comorbidities). This stepwise scale up aims to consider other implementation constraints related to health system limitations such as availability of human resources, consumables among others.

With regards to uptake, an important constraint for a COVID-19 immunisation program pertains to the willingness of the population to get vaccinated. The uptake constraint, defined as the maximum achievable coverage with available doses for the whole target group, was set at 60% of any priority access group based on the surveys of willingness to vaccinate available for the French population. Namely, an early survey in France (end March 2020) showed a significant proportion (25%) of respondents being reluctant to accept vaccination [19]. This proportion increased to more than 30% of respondents late in April 2020 and to 40% by early August 2020 [21, 34]. We also considered scenarios where uptake constraints are relaxed from mid-2021, leading up to a maximum of 90% coverage in the adult population. In those scenarios, the relaxation is hypothesised to result from public experience in the use of vaccines in real-life conditions, further safety data becoming available, and/or additional vaccines approved with different efficacy and safety profiles.

Supply constraints are likely to play a role in 2021. To date, the European Commission has concluded contracts with companies covering a broad portfolio of vaccine candidates [35–40]. As communicated by the European Commission, allocation between countries will be on a population pro-rata distribution key [41]. However, not all vaccine candidates are expected to be successfully registered. We assumed in this study that one or more vaccines will be available during the first quarter 2021 (currently three vaccines have been approved by EMA). We also assumed that new supplies will become available mid-year 2021, either due to industrial scale-up of first vaccines or subsequent vaccines becoming available [42, 43]. Four supply constraint scenarios were defined depending on the number of doses available during the first and second half of 2021 (see S3 Table in S1 File). These scenarios aim to represent a range of supply possibilities, with a ‘strong supply constraint’ scenario assuming just under 18 million people could be vaccinated by end of 2021, and a ‘weak supply constraint’ scenario that allows the program to reach up to 37 million people by the end of 2021. As with uptake constraints, we considered additional scenarios where all constraints are relaxed from mid-2021 (due to availability of vaccine doses), which we called “relaxed weak supply and uptake constraint” and “relaxed strong supply and uptake constraints”, moving away from limitations set at the beginning of the roll-out of the vaccination program.

Analysis

Health benefits associated with the immunisation program were quantified as the reduction in COVID-19 events and events averted per 1000 vaccinations. We focused on hospitalizations averted in the main text because this is a locally relevant indicator to assess health system stress which guided policy decisions. However, it is not the only indicator available and we present results for symptomatic cases and deaths averted in S1 Text in S1 File. We also assessed the impact of vaccination on the number of days with NPIs in place. Three timeframes were considered in our analysis (2021, 2022, and 2021–2022) while we discuss the possible evolution of COVID-19 beyond 2022. In our impact analysis, we include an uncertainty range of main outcomes reflecting a variation in vaccine efficacy from 50 to 90%.

The analysis is structured as follows. First, we looked at the progression of the COVID-19 epidemic in the absence of vaccines for varying health policy strategies policies, i.e. here with various thresholds based on hospitalization rates for NPI initiation. In these scenarios, NPIs are maintained throughout 2021 and 2022. In S1 File, we considered alternative timing for NPIs discontinuation (S4 Table in S1 File). Secondly, we present the impact of implementation scenarios compared to the no vaccine counterfactual. This counterfactual use, as a reference, the second wave threshold for NPIs initiation maintained throughout 2021 and 2022. It represents a conservative assumption with regards to vaccine impact.

Thirdly, we explored five vaccination scenarios: one uptake constraint scenario, two scenarios with limited supply (strong supply constraint, weak supply constraint) and two scenarios relaxing these supply and uptake constraints during the second semester of 2021 (relaxed strong supply and uptake constraint, relaxed weak supply and uptake constraint). Description of the scenario definition and the coverages achieved in these scenarios is presented in Table 1. For those scenarios including an increase in the supply and uptake of vaccines in the second semester of 2021, we assessed their incremental benefits compared to scenarios without this increase.

Table 1. Vaccine coverage by June 2021 and December 2021 for three groups prioritised.

Coverage by end of June 2021 Coverage by end of December 2021
Scenario1 High priority2 Vulnerable adults3 Other adults All Adults High priority2 Vulnerable adults3 Other adults All Adults
No vaccine 0% 0% 0% 0% 0% 0% 0% 0%
Uptake constraint 60% 60% 0% 33% 60% 60% 60% 60%
Strong supply constraint 60% 9% 0% 12% 60% 38% 0% 24%
Weak supply constraint 60% 52% 0% 30% 60% 60% 26% 45%
Relaxed strong supply and uptake constraint 60% 9% 0% 12% 90% 90% 42% 68%
Relaxed weak supply and uptake constraint 60% 52% 0% 30% 90% 90% 88% 89%
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1Scenarios defined: Uptake constraint reflects limited coverage rate due to a low willingness to be vaccinated in the population. Strong supply constraint reflects a limited amount of vaccines doses made available to the national program. In this case, the program is severely limited. Weak supply constraint reflects a limited amount of vaccines doses made available to the national program, in this case the program is moderately limited. Relaxed strong supply and uptake constraints: in this scenario, while the program is severely limited during the first half of the year, vaccine supply is increased during the second half of the year (higher production or new vaccines availability) and the public is more likely to be willing to vaccinate as the program has been in place for half a year. Therefore, we ‘eased’ the limitations of the program in the second semester. Relaxed weak supply and uptake constraints: in this scenario, while the program is moderately limited during the first half of the year, vaccine supply is increased during the second half of the year and the public is even more likely to be willing to vaccinate as the program has been in place for half a year. Therefore, we ‘eased’ the limitations of the program to achieve maximum coverage.

2High priority includes healthcare workers and professions at risk.

3vulnerable adults include elderly and adults with comorbidities.

Finally, sensitivity analyses were performed on potential drivers of SARS-CoV-2 transmission (seasonality, severity of reinfection), level of public health response, and vaccine profile (vaccine that only reduces symptomatic disease instead of preventing infection).

Results

We modelled the evolution of the COVID-19 pandemic in France after fitting to observed data for reported deaths, hospitalizations, and symptomatic cases (S1 Fig in S1 File). In Fig 1, we present hospitalization incidence in the absence of vaccination for varying levels of NPIs response maintained until the end of 2022. The level of NPI response defines not only the magnitude of peak incidence but also the number of activation periods for the 2021–2022 period. This number of activation periods ranges from four to seven as evidenced by the number of times incidence exceeds the predefined threshold. It is also noteworthy than incidence remains at a high level at the end of 2022 indicating the possibility for waves further to 2022.

Fig 1. Daily hospitalization incidence (rate per million population per day) in the absence of vaccination for varying level of public policy response, 2020–2022.

Fig 1

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Based on reference scenario for seasonal variation in COVID-19 transmission (20%), severity of reinfection (90% less than primary infection), median duration of natural/vaccine immunity of one year and NPIs maintained until end of 2022. Black dotted lines correspond to the predefined hospitalization threshold of public health response. The black curve follows a scenario where the threshold for NPIs is based on the first wave (100 hospitalization per one million population). The blue curve represents a scenario where the threshold for NPIs is based on the second wave (70 hospitalizations per one million population). The red curve represents a scenario where the response is weak and the NPI threshold high (200 hospitalization per one million population).

Discontinuing NPIs during the scale-up of an immunisation program could lead to uncontrolled COVID-19 outbreaks. Stopping NPIs in January 2021 could lead to a peak incidence of hospitalizations seven times the peak incidence of the first wave. The impact of all vaccination scenarios would also be minimal in this case (from 5 to 12% over the 2021–2022 period), as individuals could be infected before having the opportunity to benefit from vaccine protection (S4 Table in S1 File).

Potential immunisation program impact under uptake and supply constraints

Vaccination programs with uptake and supply constraints are not expected to allow interrupting NPIs in the short term (Fig 2). In the absence of vaccination, it is expected that NPIs would be in place for most of 2021 (327 days), this number reduces respectively to 297 [268–308], 203 [149–270] and 155 [149–265] for the strong supply constraint, weak supply constraint and uptake constraint scenarios. The situation improves in 2022, notably for the uptake constraint scenario where we observe 11 [3–18] days with NPIs in place compared to 186 for the no vaccine counterfactual.

Fig 2. Number of NPI activation periods in 2021–2022 and peak hospitalization incidence in the absence of NPIs.

Fig 2

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Based on reference scenario for disease characteristics, NPI response (second wave threshold), and vaccine profile (protection against infection). The number of days and error bars corresponds respectively to reference, minimum and maximum values for an efficacy of 70% ranging from 50% to 90%.

In Table 2, we assessed the reduction in hospitalizations due to the immunisation programs compared to a no vaccine counterfactual assuming NPIs are discontinued after immunisation program scale-up (end of 2021). The corresponding evolution of daily hospitalization incidence is presented in Fig 3. In 2021, the median variation in hospitalizations is +0.8%, -9.4% and -13.9% if there is a strong supply constraint, a weak supply constraint, or an uptake constraint only, respectively. By the end of 2022, the variation in hospitalizations since the start of the program compared to no vaccine reaches 20.2%, 35.1%, and 39.8% for the same scenarios.

Table 2. Cumulative incidence of COVID-19 hospitalization per million population and percentage reduction in hospitalization rates for immunisation programs with and without relaxation of uptake and supply constraints compared to no vaccination, 2021–2022.

2021 2022 2021–2022
Incidence % Incidence % Incidence %
No vaccine 12,722 ref 14 901 ref 27,622 ref
Immunization program under constraints
Strong supply constraint 12,819 0.8% 9,436 -36.7% 22,053 -20.2%
[11993;13001] [-6;2] [8732;10163] [-41;-32] [21733;22053] [-21;-18]
Weak supply constraint 11,527 -9.4% 5,669 -62.0% 17,932 -35.1%
[11126;12573] [-13;-1] [5195;8659] [-65;-42] [16321;18737] [-41;-27]
Uptake constraint 10,960 -13.9% 5,270 -64.6% 16,626 -39.8%
[9812;11996] [-23;-6] [4932;7392] [-67;-50] [14744;17266] [-47;-33]
Immunization program with relaxed constraints
Relaxed strong supply and uptake constraint 11,630 -8.6% 3,181 -78.7% 14,811 -46.4%
[11294;12444] [-11;-2] [1826;4297] [-88;-71] [13846;14894] [-50;-44]
Weak supply and uptake constraint 9,606 -24.5% 1,702 -88.6% 11,497 -58.4%
[9240;11204] [-27;-12] [1590;2110] [-89;-86] [11053;11497] [-60;-52]
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Based on reference scenario for disease characteristics, level of NPI response (second wave threshold), vaccine profile (protection against infections) and NPIs maintained until end of 2022. Incidence is given per million population and the % of variation is calculated in reference to the no vaccine counterfactual. For each scenario, both values for our reference scenario and range are provided. The vaccine efficacy in the reference case is assumed to be 70% ranging from 50% to 90%.

Fig 3. Daily hospitalization incidence (rate per million population per day) with and without an immunisation program with varying uptake and supply constraints, 2020–2022.

Fig 3

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Based on reference scenario for disease characteristics, NPI response (second wave threshold), vaccine profile (protection against infection) and NPIs maintained until end of 2022. Panel A–No vaccination (dark blue curve) and vaccination scenario under uptake constraint (light blue), Panel B–No vaccination (dark blue curve) and vaccination scenarios with strong supply constraint under two assumptions for relaxation of such constraints: the constraints not being eased during the second half of the year (light blue) or the constraints being eased during the second half of the years (orange), Panel C–No vaccination (dark blue curve) and vaccination scenarios with weak supply constraint under two assumptions for relaxation of such constraints: the constraints not being eased during the second half of the year (light blue) or the constraints being eased during the second half of the years (orange). The variation in impact due to the range of vaccine efficacy considered is shown as the area of the vaccine impact curves.

Potential immunisation program impact if uptake and supply constraints are relaxed

In 2021, the level of additional health benefits associated to the relaxation of constraints remains moderate: the median reduction in hospitalization compared to no vaccination (Table 2) reaches 8.6% for the relaxed strong supply constraint scenario and 24.7% for the relaxed weak supply constraint scenarios. However, in 2022, the relaxed constraints scenarios are associated with further reductions in COVID-19 hospitalizations compared to no vaccination: respectively 78.7% for the relaxed strong supply constraint and 88.6% for the relaxed weak supply constraint. Similarly, to the no vaccine counterfactual scenario, the incidence remains significant at the end of 2022 for all scenarios with vaccination and even on the rise for most of them.

When assessing the incremental benefit of relaxing constraints, we observed an additional reduction in hospitalizations ranging respectively from 30 to 36% for the strong supply constraint scenario and 32 to 39% for the weak supply constraint scenarios (Table 3). This incremental benefit is associated with a decrease in the number of hospitalizations averted per 1,000 vaccinated people (respectively from 30.6 to 22.4 and from 28.5 to 20.5 for scenarios with strong or weak supply constraints before July). However, this apparent decrease in efficiency is compensated by a further decrease in the time with NPIs in place that is significant for the strong supply constraint scenarios (from 393 days without relaxation to 269 days with relaxation). The main benefit observed in scenarios with relaxation is their ability to prevent the needs for NPIs in 2022 (Fig 2).

Table 3. Number of COVID-19 hospitalizations averted with and without relaxation of constraints in July 2021, 2021–2022.

  Without relaxation in July1 With relaxation in July2
Median Range Median Range
Strong supply constraint
Hospitalizations averted 5,569 [4,966;5,889] 7,664 [6,565;7,887]
Vaccinated subjects 181,719 [181,677;181,739] 341,464 [341,427;341,490]
Hosp averted/1,000 vaccinated subjects 30.6 [27.3;32.4] 22.4 [19.2;23.1]
Variation in incidence (%) -20.2% [-21; -18] -34.6% [-36;-30]
Days with NPIs 393 [387;498] 269 [207;285]
Weak supply constraint
Hospitalizations averted 9,690 [7,435;11,301] 6,990 [5,268;7,240]
Vaccinated subjects 340,574 [340,524;340,578] 341,535 [341,512;341,564]
Hosp averted/1000 vaccinated subjects 28.5 [21.8;33.2] 20.5 [15.4;21.2]
Variation in incidence (%) -35.1% [-41;-27] -35.0% [-39;-32]
Days with NPIs 208 [149;377] 203 [149;212]
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Based on reference scenario for disease characteristics, NPI response (second wave threshold), vaccine profile (protection against infection) and NPIs maintained until end of 2022.

1: Compared to the no vaccine counterfactual.

2: Compared to the corresponding constrained scenario. Hospitalizations averted: hospitalizations averted are per million population; Vaccinated subjects: people vaccinated per million population; Hosp averted/1,000 vaccinated subjects: Hospitalizations averted per 1,000 vaccinated people. For each scenario, both values for our reference scenario and range are provided. The vaccine efficacy in the reference case is assumed to be 70% ranging from 50% to 90%.

Finally, in Fig 4, we present sensitivity analyses assessing the impact of uncertainty related to vaccine and disease characteristics, on the reduction of hospitalization incidence. In S1 File, we also present sensitivity analyses on the number of days with NPIs in 2022 (S6 Fig in S1 File). We used as a reference the relaxed strong supply and uptake constraints scenario and present results for the uptake constraint scenario in supplementary material (S7 Fig in S1 File). The variation in vaccine profile (from protecting against infection to only protecting against symptomatic disease) reduces the program impact from -46% in our reference case to -34%. This reduction has a larger impact than the one associated to a low efficacy (-44% if vaccine efficacy is 50%) and is also associated with a significant number of days with NPIs in 2022 (69 days).

Fig 4. Tornado diagram on the impact of a variation of vaccine and disease characteristics on the reduction in hospitalization in 2021–2022 associated to vaccination (relaxed strong supply and uptake constraints scenario).

Fig 4

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All outcomes presented corresponds to univariate sensitivity analysis of the reference case for key disease and vaccine characteristics. The figure shows the change in number of hospitalizations (as %) for the 2021–2022 period compared to no vaccination counterfactual for different vaccine and disease characteristics. The red bars correspond to factor with the largest impact, figures next to the bars to the impact on COVID-19 hospitalizations compared to no vaccination and bars are oriented right or left depending of if the figure is smaller or higher than base case (first row).

Among uncertainties related to disease characteristics, duration of natural immunity and severity of reinfection have the largest impact. A median duration of natural immunity of two years is associated to a broader vaccination impact (-53%). On the opposite side, if reinfections are as severe as primary infections, the period with NPIs is predicted to exceed 100 days in 2022 (118 days) and the impact of vaccination drops to -27%. Therefore, if reinfections are as severe or even 50% less severe than initial infections, NPI activations would still be required in 2022 with the vaccination scenarios considered in our analysis.

Discussion

We explored the short-term impact of an immunisation program with supply and uptake constraints changing over time. Our analysis confirmed that an adult immunisation program, even with limited supply and uptake, could significantly mitigate the health consequences of COVID-19, albeit not obviating the need for NPIs in the short term. This analysis is timely in the context of implementation and supply constraints faced by countries at the time of revised version writing (February 2021). It also helps contextualising the important of public messages on mitigation measures that are needed as the program is rolled out, and the challenges vaccine hesitancy represent to the success of local immunisation programs.

Our results are in accordance with previously published results of vaccine impact where coverage, the rate of vaccination, and efficacy play key roles in the government’s ability to reduce social distancing measures [10, 12, 14, 17, 44–46]. Our analysis adds to previous literature in that it provides a detailed analysis of the likely implementation constraints and timing of benefits of a future immunisation program. In addition, we assessed the potential impact on the number of NPIs days, as an indicator of economic performance recovery. Assuming NPIs are maintained throughout until the end of 2022, a constrained immunisation program could result in 20% to 40% reduction in COVID-19 hospitalizations depending on the level of constraints compared to no vaccination over two years. Furthermore, NPIs may be avoided post-2021 depending on the extent of the constraints in place during roll-out. Relaxing both supply and uptake constraints towards mid-2021 increases the overall health impact and limits the risk of outbreaks once the program is completed and NPIs discontinued. The benefits of relaxing supply and uptake constraints start to be observed during the last quarter of 2021 and enable to a significant reduction in hospitalizations compared to the no vaccine counterfactual in 2021(exceeding 75%). However, to be successful, relaxation of such constraints requires achieving high vaccination coverage rates (from 68% to 89% of the adult population).

Our results on the incremental benefits associated to scenarios with relaxation of supply and uptake constraints indicate that lifting these constraints changes the value of the program over time as measured by the number of hospitalizations averted per 1000 people vaccinated (technical efficiency). However, this observation is the product of a trade-off: while it reduces the number of hospitalizations prevented per vaccination performed, it also reduces the need for NPIs and even prevents the need for them post-2021.

The insights on technical efficiency provided by our analysis are clearly only indicative. We do not account for the additional resources required to increase coverage nor do we capture the whole period for which vaccinations can impact COVID-19 outcomes. Given the scale and scope of societal impact of the COVID-19 pandemic and the urgency of the response, policy has been focused on alleviating health burden and curtailing societal and economic disruption. Quantifying the impact of an immunisation program focusing on hospitalizations averted and the need for NPI continuation in the short term allowed us to address both dimensions in an emergency response. While conceptually immunisation and social restriction responses could benefit from trade off analyses independently of the emergency of the response, our study emphasises that, after the initial public health response, expansions of immunisation programs will benefit from conventional assessments (such as cost-effectiveness assessments) of health, economic, and social welfare to optimise further policy responses [47].

With regards to the vaccine profiles explored, our primary analysis assumed vaccines available would protect against infection (and therefore against symptomatic disease) that can be seen as the most likely scenario. However, if any initially available vaccines only protect against symptomatic disease, although such vaccines would remain beneficial, we expect a reduced ability to prevent the need for NPI or outbreak occurrence after NPI discontinuation. We limited our analysis to vaccines offering a one-year protection. With such duration, the evolution of COVID-19 hospitalizations observed at the end of our period of analysis, at a time when most vaccine-conferred protection has waned, points to a need for revaccination to maintain disease control post-2022. Data on duration of protection, from immunity afforded by natural infection or vaccination, are starting to appear but it is early to know whether immunity will last longer than one year [48].

Among disease characteristics, severity of reinfection can also have a significant influence on the ability to control the disease not only in the long run but also in the next two years as considered here. To date, limited information is available on the severity of reinfection but our results indicate that, even with a broad vaccination program, NPIs would be still needed in 2022 to prevent a major COVID-19 outbreak if reinfection are as severe as primary infection. Finally, another aspect of uncertainty not addressed in our manuscript relates to changes in the virus to scape host immunity and/or improve its transmissibility [49]. Also, some mutations observed in the viruses suggest an ability to escape antibody immunity that could affect the success of vaccination programs in the short term [50] reinforcing the need for mitigation measures to be considered during 2021.

As with any modelling study, our work has limitations due to several simplifications and our results should be interpreted with caution. First, our characterisation of uncertainty remains limited. There are still many unknowns in the future evolution of COVID-19, public policy response, natural history and, importantly, the characteristics of vaccines to be approved. In this uncertain context, rather that assessing all possible scenarios including the most optimistic and pessimistic ones, we aimed at identifying the main drivers that could impact our conclusions. We proceeded to integrate and assess uncertainty in our analysis in several ways. We calibrated to several outcomes (hospitalizations, deaths, and cases reported), included uncertainty ranges linked to vaccine efficacy, and used scenario and sensitivity analyses. Secondly, even if we account for a reduced exposure to infection of vulnerable people and a prioritisation in access to vaccination, our modelling framework do not account fully for the possible correlation between risk associated to COVID-19 and willingness to accept vaccination. Previous research on the profile of people reluctant to accept vaccination showed to include low-income people and people aged older than 75 years [19]. Therefore, our results may have overestimated the impact of vaccination in the presence of self-selection out of a program by individuals at higher risk of infection or complications. Vaccines have been introduced in France during January as modelled. However, there have been supply and implementation challenges in the program roll out. A successful roll out of vaccines in 2021 will allow for a significant impact over the 2021–2022 period. Our results showing a possible increase in COVID-19 activity later in 2022 results from the assumption that the immunisation program only lasts one year. The timing and magnitude of subsequent raises in activity in the long term will depend on other variable such as the duration of vaccinal and natural immunity, presence of routine immunisation programs or the severity of reinfection. Our results also might not apply directly to all settings as significant differences exist across the globe in terms of mitigation strategy and management of constraints. We did not explore the longer term as there is significant uncertainty on these different drivers or the impact of virus mutation. Finally, we do not formally assess the economic value of vaccines but present a proxy for programmatic (technical) efficiency. Our approach in this regard is deliberately conservative as it pertains to the use of vaccines in the short term to mitigate the pandemic effects.

This research has implications for vaccine research and development as well as policy. While a vaccine introduced in limited supply and uptake could positively impact the COVID-19 epidemic, additional doses or vaccines made available later in 2021 will help reduce the health burden further and prevent the need for NPIs post-2021. It is expected that uncertainty around vaccine characteristics will resolve as vaccination programs are implemented and data become available, yet there is a need to monitor the severity of reinfection in trials and post-regulatory approval commitments both in those people vaccinated and non-vaccinated, and for each vaccine in use. Experience gained on vaccines and their use in real conditions could improve vaccine acceptance in the population. Finally, immunisation is expected to play a central role in helping societies move on from this pandemic. Yet the efficiency of an immunisation program is likely to change as programs expand. A continuous assessment of the future value of vaccination within a comprehensive response to the pandemic will be needed to ensure optimal post-emergency use.

Supporting information

S1 File

(DOCX)

Click here for additional data file. (559.9KB, docx)

Acknowledgments

We would like to recognize our colleagues from Sanofi Pasteur medical and R&D for insightful discussions about specific aspects of vaccination challenges. Their deep knowledge of industry, research and development, and modelling was invaluable when shaping our thinking.

Data Availability

The model code used is available at GitLab: https://gitlab.com/SPMEGModels/covid-model.

Funding Statement

Sanofi provided financial support to authors in the form of salaries but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The specific roles of the authors are articulated in the ‘Contributors’ section of the manuscript.

References

Decision Letter 0

Yury E Khudyakov

Transfer Alert

This paper was transferred from another journal. As a result, its full editorial history (including decision letters, peer reviews and author responses) may not be present.

8 Feb 2021

PONE-D-20-37719

Potential impact of introducing vaccines against COVID-19 under supply and uptake constraints in France: a modelling study

PLOS ONE

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Reviewer #1: The study is a statistic model of the vaccine effect on public health. the study adds to previous literature analysis on timing of benefits of future immunization program. The study is published when there are already preliminary data on the efficacy of the vaccine and therefore it is published a little too late (After the horses are already out of the barn). there is still benefit in publishing as the model predicts the morbidity in the next two years.

The study claim that the vaccine will need to be highly effective and to achieve high coverage to be able to obviate the need of non-pharmaceutical interventions and to control the pandemic. The data support the claim but there are some major comments:

Introduction:

1. Line 4- the numbers should be updated (for example there are more than 20 ongoing phase III trials and not 11).

2. Line 8- the number of vaccine candidates should be updated (there are at least 3 authorized vaccines already).

3. Line 23- please add reference to the study that was mentioned (modelling by the imperial college…).

4. Line 23- references 13 and 14 are actually a survey results about vaccine hesitancy and less about strategies to optimize immunization. Please add relevant reference.

5. Line 25- reference 15 is a study about the willingness of the population to be vaccinated. I couldn't find any support in the authors claim about supply constraint. Another reference would be more suitable.

Methods:

1. All the references should be checked. For example hospital admission reported by sante was specified as Ref 24 when it is actually Ref 25.

2. The definitions of uptake constrains and supply constrains are confusing and not intuitive. For example the phrase 'Relaxed uptake constraints' is confusing and not intuitively understood as high compliance. I suggest change 'uptake constraints' to more simple definition like 'vaccine compliance', and supply constrains to vaccine supply or quantity.

3. Line 43- please mention what period was taken.

4. Line 79- the association of other vaccines, such as influenza vaccine, have been proved to reduce COVID-19 infection(doi: 10.1080/21645515.2020.1852010). It can therefore be assumed that a dedicated vaccine will prevent disease and not only reduce symptoms. I suggest discuss it and take it into account when assuming vaccine efficacy.

5. Line 83- the authors mentioned efficacy of 50-90%. Previous studies mentioned 95% efficacy of the vaccine (for example: DOI: 10.1056/NEJMoa2034577). Such a large variation in the efficacy data of the vaccine may alter the results of the statistical model.

6. Line 99- the vaccine uptake was set as 60%. On what was the assessment based? There are published surveys on compliance that the author can rely on (for example: DOI: 10.1016/j.vaccine.2020.08.043).

7. Line 109 -the details are not accurate. There are already a few available vaccines. Assumption is not needed.

8. Line 130- the sentence is to complicate and long. Please simplify.

Results:

1. To my point of view, mean and C.I instead of median and range will be more appropriate.

2. Line 184- reduction in hospitalization range is not presented in table 3. Please clarify.

3. The effect of the vaccine compliance and supply was measured as hospitalization incidence. I think that number of infected patients is more appropriate. Please explain why did you choose that variable.

4. Previous study has demonstrated that hemoglobin A1C is a predictor of COVID‐19 Severity (doi: 10.1002/dmrr.3398 ). Has a connection between adherence to diabetes treatment and infectivity (R) and response to the vaccine been taken into account?

5. Currently, there is a growing evidence of side effects of the vaccine. Was it taken into account in calculating hospitalization rates and compliance rates?

Tables:

1. Table 2- please rechecked the numbers (hospitalization rates are higher under 'vaccine strong constraints' than under 'no vaccine' at all).

Reviewer #2: In this manuscript the authors present an analysis of the COVID-19 spreading dynamics in France after the initiation of vaccination drive. The incorporation of constraints from both the supply and demand side adds realism to the model. Some statements from the results section drew my attention however. They are : (a) that even with the uptake constraint i.e. maximal vaccine distribution, there would be NPIs being applied in 2022, (b) that with discontinuation of NPI at the end of 2021, there would be +0·8 percent, -9·4 percent and (presumably negative although this has not been indicated by authors) 13·9 percent variation in hospitalizations in 2021 with the three vaccine constraints relative to the no vaccine case, and (c) that the incidence of COVID-19 remains significant at the end of 2022 with all situations of vaccination and even on the rise for most of them. These statements are counter-intuitive and a bit pessimistic – most people are hoping for a return to normalcy by this fall or at least by the end of the year. I would like the authors to recognize and discuss this fact in detail.

The authors could consider several major and minor revisions. Some major revisions are given below:

1 There are certain modeling studies of vaccination dynamics which present a more optimistic view than the authors’ work. A key example is

Shayak B, Sharma MM and Mishra AK, “Impact of immediate and preferential relaxation of social and travel restrictions for vaccinated people on the spreading dynamics of COVID-19 : a model-based analysis,” available at

https://www.medrxiv.org/content/10.1101/2021.01.19.21250100v1

The references by Alvarez et. al. and Betti et. al. in the above manuscript are also optimistic. While I am aware that all these works were written after the authors’ manuscript, they must now be cited. It must be explained why the authors’ results differ from these analyses.

2 What is the role of the temporary immunity in generating the authors’ case trajectories ? In other words, if the vaccine immunity had been 2 years or 5 years, then what would the trajectories have been like ? Authors should perform simulations to demonstrate this.

3 What is the role of the bang-bang NPI control strategy in generating the authors’ bleak predictions ? Instead of this strategy, if a continuous NPI were applied or NPI gradually relaxed over time then what would the trajectories have looked like ? Simulations should be performed to analyse these questions.

4 Why there is an increase in hospitalization in 2021 with strong supply constraint relative to no vaccination ? Surely this is a surprising result. In continuation of the above, the authors should explore the solution space in much greater detail. They should clearly identify the scenarios where the outbreak ends in a reasonable time-frame instead of continuing on into 2023 and beyond. This should be used to motivate a discussion of effective vs ineffective vaccines and good vs bad policy decisions during the vaccination drive.

Apart from the above major concerns, there are several minor issues as well, as given below.

5 The population of France should be mentioned so that the supply constraints can be understood in terms of percentage population.

6 The introduction should be updated to reflect the current situation of vaccination drives. EUA granted to Pfizer, Moderna, Oxford/ Astra Zeneca, ICMR/ Bharat Biotech and Sputnik vaccines should be mentioned.

7 In Tables 1 and 2, the phrases “relaxed strong/weak supply and uptake constraint” is not clear to me. By relaxing a constraint one typically understands that the constraint does not exist any longer. However this does not seem to be what the authors imply.

8 Figure 4 is barely legible; moreover, it is difficult to understand the point attempted to be conveyed by the authors. The authors must improve the clarity of presentation here.

9 Factors like governmental support have not been considered.

10 Currently there are several viral strains such as B1.1.7 and B1.351 that might interfere with the effectiveness of vaccinations. It would be really impactful if the authors would mention about these variants as well.

11 Another important variable is the availability of required man-power which was not mentioned in the paper which might influence the supply and uptake constraints.

12 Altough it is a modelling study, but as the core topic was vaccination, some concepts on involvement of antibodies or other physiological concepts could have made the story more interesting. Not required though.

In summary, the Article as written presents a very strong claim without basing it on a sufficiently solid foundation. It also suffers from avoidable defects of presentation. Hence I recommend the authors to revise the manuscript along the lines indicated above and resubmit the revised version.

**********

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Attachment

Submitted filename: Decision Letter.pdf

Click here for additional data file. (125.2KB, pdf)
PLoS One. 2021 Apr 28;16(4):e0250797. doi: 10.1371/journal.pone.0250797.r002

Author response to Decision Letter 0

23 Feb 2021

We would like to thank the editor and reviewers for their thorough review of our manuscript and insightful comments. In this revised version, we aimed at addressing each of the comments as indicated in our point-by-point response below.

Reviewer #1: The study is a statistic model of the vaccine effect on public health. the study adds to previous literature analysis on timing of benefits of future immunization program. The study is published when there are already preliminary data on the efficacy of the vaccine and therefore it is published a little too late (After the horses are already out of the barn). there is still benefit in publishing as the model predicts the morbidity in the next two years.

� We agree with the reviewer that other modelling studies have addressed the issue of impact of future immunization programs. These studies have explored the parameter space of vaccine efficacy. As the reviewer points out, efficacy trials have been published and we are now in the process of expanding vaccination coverage. An analysis placing the constraints (supply and uptake) we are having in program expansion is timely and needed to inform the current discourse. Currently, demand is outstripping supply, governments and health systems are facing challenges in implementation of what is arguably the biggest immunization program in history. In addition, uptake constraints (for example a reluctance to be vaccinated) could potentially pose serious challenges to programs in countries such as France. Therefore, our message can reinforce the need of programs to tackle these issues sooner rather than later. We tried to reinforce this message (of timeliness) for the benefit of readers in the first paragraph of the discussion.

The study claim that the vaccine will need to be highly effective and to achieve high coverage to be able to obviate the need of non-pharmaceutical interventions and to control the pandemic. The data support the claim but there are some major comments:

Introduction:

1. Line 4- the numbers should be updated (for example there are more than 20 ongoing phase III trials and not 11).

� we updated these numbers – it is indeed a rapidly evolving field. If accepted, we will also ensure these number are up to date in the proofs.

2. Line 8- the number of vaccine candidates should be updated (there are at least 3 authorized vaccines already).

� we updated these numbers. If accepted, we will also ensure these number are up to date in the proofs.

3. Line 23- please add reference to the study that was mentioned (modelling by the imperial college…).

� Apologies to the reviewers and editor – we experienced a glitch when generating the reference list and the numbers do not correspond to the references meant. We have verified all references.

4. Line 23- references 13 and 14 are actually a survey results about vaccine hesitancy and less about strategies to optimize immunization. Please add relevant reference.

� same as above

5. Line 25- reference 15 is a study about the willingness of the population to be vaccinated. I couldn't find any support in the authors claim about supply constraint. Another reference would be more suitable.

� same as above

Methods:

1. All the references should be checked. For example hospital admission reported by sante was specified as Ref 24 when it is actually Ref 25.

� same as above

2. The definitions of uptake constraints and supply constraints are confusing and not intuitive. For example the phrase 'Relaxed uptake constraints' is confusing and not intuitively understood as high compliance. I suggest change 'uptake constraints' to more simple definition like 'vaccine compliance', and supply constrains to vaccine supply or quantity.

� we have five scenarios of varying constraints. The terminology aims to reflect the programmatic evaluation literature and we want to highlight the limitation of programs as well as the dynamic aspect of the limitations. To clarify, we have added the following explanations to table 1.

� Uptake constraint reflects a limited coverage rate due to a limited willingness to be vaccinated in the population.

� Strong supply constraint reflects a limited amount of vaccines doses made available to the national program. In this case, the program is severely limited.

� Weak supply constraint reflects a limited amount of vaccines doses made available to the national program, in this case the program is moderately limited.

� Relaxed strong supply and uptake constraints. In this scenario, while the program is severely limited during the first half of the year, vaccine supply is increased during the second half of the year (higher production or new vaccines availability) and the public is more likely to be willing to vaccinate as the program has been in place for half a year. Therefore, we ‘eased’ the limitations of the program in the second semester.

� Relaxed weak supply and uptake constraints. In this scenario, while the program is moderately limited during the first half of the year, vaccine supply is increased during the second half of the year and the public is even more likely to be willing to vaccinate as the program has been in place for half a year. Therefore, we ‘eased’ the limitations of the program to achieve maximum coverage.

3. Line 43- please mention what period was taken.

� we have added the duration of such immunity period – Median duration of one year.

4. Line 79- the association of other vaccines, such as influenza vaccine, have been proved to reduce COVID-19 infection(doi: 10.1080/21645515.2020.1852010). It can therefore be assumed that a dedicated vaccine will prevent disease and not only reduce symptoms. I suggest discuss it and take it into account when assuming vaccine efficacy.

� We agree with the reviewer that given experience gathered on other vaccines, the ability for vaccines to impact COVID-19 infections and hence reduce transmission is a likely scenario. We besides considered for our reference case a vaccine that prevents infection. This has however not been fully demonstrated to date even if some preliminary evidence exists (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3777268, https://doi.org/10.1101/2021.02.08.21251329)

Regarding the link between COVID-19 and influenza vaccination, even if the publication mentioned by the reviewer indicates positive impact of previous influenza vaccination, other studies have not found this association (https://academic.oup.com/occmed/article/70/9/665/6029444 and https://onlinelibrary.wiley.com/doi/10.1111/irv.12839).

In this revised version, we indicate that a vaccine preventing infection is the most likely scenario and acknowledged remaining uncertainties. We however did not discuss the link between COVID-19 vaccination and previous influenza vaccination we considered is beyond the scope of our analysis.

5. Line 83- the authors mentioned efficacy of 50-90%. Previous studies mentioned 95% efficacy of the vaccine (for example: DOI: 10.1056/NEJMoa2034577). Such a large variation in the efficacy data of the vaccine may alter the results of the statistical model.

� We have rephrased the paragraph on vaccine’s profiles modelled to reflect current knowledge available for already approved vaccines. The results are presented for a vaccine efficacy of 70% with shaded areas representing a variation from 50-90%. While efficacy in clinical trials with short follow up has been shown to be 95% for some of the vaccines, we wanted to provide a range that represents the mix of vaccine effectiveness (real life estimates) likely to be available, representing scenarios and not necessarily guessing actual estimates. Moreover, we are still uncovering results of vaccine effectiveness on reduction of infection (i.e., asymptomatic and symptomatic infections). We have added text to the figures, so that ranges of efficacy are clearly represented.

6. Line 99- the vaccine uptake was set as 60%. On what was the assessment based? There are published surveys on compliance that the author can rely on (for example: DOI: 10.1016/j.vaccine.2020.08.043).

� We based the 60% uptake on published surveys of willingness to vaccinate attitudes similar to the one suggested by the reviewer but specific to France. We have reworded the text to reflect the inclusion of this evidence.

7. Line 109 -the details are not accurate. There are already a few available vaccines. Assumption is not needed.

� we have reviewed the statements on vaccine availability in Europe to include further exploratory talks started mid-January and the authorizations to date. Our scenarios reflect supply constraints that are not only related to the authorization of vaccines but also the industrial capacity of companies to deliver at the scale needed. In fact, despite initial projections of vaccine dose availability, most countries in Europe and in North America are facing supply constraints due to production limitations (similar to the constraint scenarios assumptions). We added text to the methods to back up our assumptions.

8. Line 130- the sentence is to complicate and long. Please simplify.

� We have simplified the text to clarify what is present in the main text as opposed to the additional results.

Results:

1. To my point of view, mean and C.I instead of median and range will be more appropriate.

� we present the values for our reference case, a vaccine efficacy of 70% and the range represents the variation in results of our range of efficacy considered. We have clarified this in each figure., table and the results.

2. Line 184- reduction in hospitalization range is not presented in table 3. Please clarify.

� The range mentioned line 184 (30 to 39) corresponds respectively to the lower and upper values of the confidence intervals corresponding to the two vaccination scenarios with constraint we considered in our manuscript. To clarify this point, we modified the sentence to indicate explicitly the two confidence intervals reported Table 3.

3. The effect of the vaccine compliance and supply was measured as hospitalization incidence. I think that number of infected patients is more appropriate. Please explain why did you choose that variable.

� we chose to present hospitalizations in the main text as it is a locally relevant indicator of the stress COVID-19 is putting on the health system which leads to government decisions on implementing mitigation measures. However, we acknowledge this is not the only relevant indicator. We present additional indicators such as number of days with NPIs in place in the main text, while cases and deaths are presented in the appendix. We have clarified this in the methods section and discussion.

4. Previous study has demonstrated that hemoglobin A1C is a predictor of COVID‐19 Severity (doi: 10.1002/dmrr.3398 ). Has a connection between adherence to diabetes treatment and infectivity (R) and response to the vaccine been taken into account?

� There may be an association between hemoglobin A1C and COVID-19 severity as pointed out by the reviewer and which is still explored by some researchers. However, the relevance of such predictor in the context of our analysis is accounted for by using broader risk categories driven by local literature on fatality ratio, hospitalization rates and social contact matrices. Moreover, our analysis did not aim to account for the effect of every individual risk factor, varying individual immune response and all the angles of constraints associated with rollout of vaccination programs for COVID-19. Our manuscript demonstrates scenarios driven by uncertainties and discuss the importance of considering such uncertainties when planning public health interventions.

5. Currently, there is a growing evidence of side effects of the vaccine. Was it taken into account in calculating hospitalization rates and compliance rates?

� Currently, the hospitalization rates and uptake are based on the reported rates for France and the willingness to vaccinate on surveys, respectively. As both pieces of evidence are pre-vaccine, the hospitalization rates or uptake rates do not account for changes since the start of the program. However, the program started 3 weeks ago and there is no data available. We added this as a limitation to the discussion.

Tables:

1. Table 2- please rechecked the numbers (hospitalization rates are higher under 'vaccine strong constraints' than under 'no vaccine' at all).

� The result for the strong supply constraint scenario indeed indicates a potential slight increase in hospitalization in 2021 (range: -6 to +2%) but not for the 2021-2022 period (range : -18 to -21%) and not for all other scenarios. This rather counterintuitive result stems from the fact that the vaccination program indirectly impacts the level of NPI in our analysis which remains an important driver for the overall COVID-19 burden in 2021 (lower NPIs are associated with a larger number of hospitalizations). As it corresponds to a rather extreme scenario and is no longer observed when a more adequate time horizon for assessing vaccination benefits is considered (i.e. 2021-2022), this result should not be overstated. Nevertheless, it reinforces the message in our manuscript around the need for a combination of vaccination and NPI in 2021.

Reviewer #2: In this manuscript the authors present an analysis of the COVID-19 spreading dynamics in France after the initiation of vaccination drive. The incorporation of constraints from both the supply and demand side adds realism to the model. Some statements from the results section drew my attention however. They are : (a) that even with the uptake constraint i.e. maximal vaccine distribution, there would be NPIs being applied in 2022,

(b) that with discontinuation of NPI at the end of 2021, there would be +0·8 percent, -9·4 percent and (presumably negative although this has not been indicated by authors) 13·9 percent variation in hospitalizations in 2021 with the three vaccine constraints relative to the no vaccine case,

and (c) that the incidence of COVID-19 remains significant at the end of 2022 with all situations of vaccination and even on the rise for most of them.

These statements are counter-intuitive and a bit pessimistic – most people are hoping for a return to normalcy by this fall or at least by the end of the year. I would like the authors to recognize and discuss this fact in detail.

� In this analysis, we focused in the short-term impact of a vaccination program taking place during 2021 with a specific focus on the role of supply and uptake constraints. Even if some our conclusions might appear pessimistic to the reviewer, our conclusions around the need to maintain NPIs alongside vaccination are actually consistent with several other recent pre-publications see e.g. https://doi.org/10.1101/2021.01.06.21249339 , https://doi.org/10.1101/2020.12.30.20248888 . In any case, our analysis can contribute to the debate around the need to tackle issues related to programmatic issues associated to vaccination programs

With regards to COVID-19 activity observed post 2021, our results notably reflect assumptions on duration of immunity and the fact that we did not specifically consider the implementation of routine vaccination in 2022 as it is beyond the scope of the analysis presented in our manuscript.

We however acknowledge that there are clearly remaining issues with regards to the future evolution of COVID-19. In this revised version, we expanded the discussions notably the limitations of the study to hopefully clarify our conclusions and put them in regards with the current knowledge on COVID-19.

We also thank the reviewer for identifying the missing minus sign before 13.9, this was corrected in main text (already accurate in table 2).

The authors could consider several major and minor revisions. Some major revisions are given below:

1 There are certain modeling studies of vaccination dynamics which present a more optimistic view than the authors’ work. A key example is

Shayak B, Sharma MM and Mishra AK, “Impact of immediate and preferential relaxation of social and travel restrictions for vaccinated people on the spreading dynamics of COVID-19 : a model-based analysis,” available at

https://www.medrxiv.org/content/10.1101/2021.01.19.21250100v1

The references by Alvarez et. al. and Betti et. al. in the above manuscript are also optimistic. While I am aware that all these works were written after the authors’ manuscript, they must now be cited. It must be explained why the authors’ results differ from these analyses.

� thank you for pointing these papers out. We have referenced and added a commentary in the discussion to place our results in the context of these other studies.

2 What is the role of the temporary immunity in generating the authors’ case trajectories ? In other words, if the vaccine immunity had been 2 years or 5 years, then what would the trajectories have been like ? Authors should perform simulations to demonstrate this.

� We made the choice in this manuscript to focus on programmatic constraints without necessarily exploring in detail the duration of immunity, especially as our period of analysis is relatively short (2 years including one year of vaccination). This is the topic of other papers in the field (see e.g. https://doi.org/10.1126/science.abd7343) and in a context where the short-term evolution of COVID-19 remains mainly driven by the primary infections and level of NPIs this does not necessarily significantly impact our conclusions even if a longer duration of immunity improved expected vaccination benefits.

Below, we illustrate the evolution in the absence of vaccination for a duration of immunity varying from 1 to 5 years. For a 2 years duration of naturally immunity, it is still expected to have a significant COVID-19 circulation in 2022.

In the revised version, we updated Figure 4 to include a scenario with a media duration of immunity of 2 years and also added discussion on this point.

3 What is the role of the bang-bang NPI control strategy in generating the authors’ bleak predictions ? Instead of this strategy, if a continuous NPI were applied or NPI gradually relaxed over time then what would the trajectories have looked like ? Simulations should be performed to analyse these questions.

� We considered in our analysis two types of NPIs: threshold-based NPIs i.e. more stringent measures implemented when incidence exceeds a predefined threshold but also risk-based NPIs i.e. reduced exposure to infection for vulnerable people compared to the rest of the population. Contrary to the first one, this second one is continuous throughout the roll-out of the vaccination program.

The threshold-based NPIs, that can be seen as a stop-and-go approach however account for a gradual relaxation of measures over time. Time-varying measures are also in fact consistent with actual measures implemented in a number of countries including France. Fully constant NPIs will not necessarily represent reality (even if authorities do not enforce any change in their policy a more active virus circulation can impact individual behavior). Besides, one of the main expected outcomes of vaccination is the ability to stop NPIs and the impact of vaccination on NPIs is part of the analysis we performed.

We however agree with the reviewer that more constant NPIs could have been considered in our analysis (e.g. longer period for relaxation of NPIs after an outbreak) but this won’t have changed our main conclusion. In this revised, we explicitly mention as a limitation that we did not account for all possible evolutions of NPIs over time.

4 Why there is an increase in hospitalization in 2021 with strong supply constraint relative to no vaccination ? Surely this is a surprising result.

� (similar response to reviewer 1): The result for the strong supply constraint scenario indeed indicates a potential slight increase in hospitalization in 2021 (range: -6 to +2%) but not for the 2021-2022 period (range : -18 to -21%) and not for all other scenarios. This rather counterintuitive result stems from the fact that the vaccination program indirectly impacts the level of NPI in our analysis which remains an important driver for the overall COVID-19 burden in 2021 (lower NPIs are associated with a larger number of hospitalizations). As it corresponds to a rather extreme scenario and is no longer observed when a more adequate time horizon for assessing vaccination benefits is considered (i.e. 2021-2022), this result should not be overstated. Nevertheless, it reinforces the message in our manuscript around the need for a combination of vaccination and NPI in 2021.

In continuation of the above, the authors should explore the solution space in much greater detail. They should clearly identify the scenarios where the outbreak ends in a reasonable time-frame instead of continuing on into 2023 and beyond. This should be used to motivate a discussion of effective vs ineffective vaccines and good vs bad policy decisions during the vaccination drive.

� We focused our scenarios in the next 2 years due to the substantial uncertainties of a long-term modelling. The increase seen post-2022 is driven by the assumption that both natural and vaccine induced immunity last on average 1 year. This assumption comes from (population based and challenge) studies of human coronaviruses in the 80s and later. There are yet limited data to support long lasting assumptions (i.e., longer than 1 year). This is particularly relevant as we consider changes in the human antibody immune response to variant viruses already circulating. We have added this discussion to the manuscript more explicitly and indicated how the various constraint scenarios can affect the impact of vaccination in curtailing the pandemic effect, addressing reviewer’s concern.

Apart from the above major concerns, there are several minor issues as well, as given below.

5 The population of France should be mentioned so that the supply constraints can be understood in terms of percentage population.

� the percentage coverage of the total population for all scenarios are presented in table 1, as well as for the subgroups. We added a reference to the total population for clarity as suggested.

6 The introduction should be updated to reflect the current situation of vaccination drives. EUA granted to Pfizer, Moderna, Oxford/ Astra Zeneca, ICMR/ Bharat Biotech and Sputnik vaccines should be mentioned.

�We have updated the text to reflect advances in the pipeline, the authorizations as well as implementation to date.

7 In Tables 1 and 2, the phrases “relaxed strong/weak supply and uptake constraint” is not clear to me. By relaxing a constraint one typically understands that the constraint does not exist any longer. However this does not seem to be what the authors imply.

� (similar response to reviewer 1): we have five scenarios of varying constraints. The terminology aims to reflect the programmatic evaluation literature and we want to highlight the limitation of programs as well as the dynamic aspect of the limitations. To clarify, we have added the following explanations to table 1.

� Uptake constraint reflects a limited coverage rate due to a limited willingness to be vaccinated in the population.

� Strong supply constraint reflects a limited amount of vaccines doses made available to the national program. In this case, the program is severely limited.

� Weak supply constraint reflects a limited amount of vaccines doses made available to the national program, in this case the program is moderately limited.

� Relaxed strong supply and uptake constraints. In this scenario, while the program is severely limited during the first half of the year, vaccine supply is increased during the second half of the year (higher production or new vaccines availability) and the public is more likely to be willing to vaccinate as the program has been in place for half a year. Therefore, we ‘eased’ the limitations of the program in the second semester.

� Relaxed weak supply and uptake constraints. In this scenario, while the program is moderately limited during the first half of the year, vaccine supply is increased during the second half of the year and the public is even more likely to be willing to vaccinate as the program has been in place for half a year. Therefore, we ‘eased’ the limitations of the program to achieve maximum coverage.

8 Figure 4 is barely legible; moreover, it is difficult to understand the point attempted to be conveyed by the authors. The authors must improve the clarity of presentation here.

� As there is still a large number of uncertainties on COVID-19 evolution, we used a tornado diagram approach for assessing separately the potential impact of important uncertainty factors that is presented Figure 4.

To facilitate the readability of this figure, in the revised version, we only kept in the main text the panel A (univariate sensitivity analysis on reduction over the 2021-2022 period) and added panel B to supplementary material). In response to the comment on duration of immunity, we also added a sensitivity analysis on this topic.

9 Factors like governmental support have not been considered.

� Governments have supported vaccine development by providing push and pull incentives – these include financing of R&D and production at risk as well as the streamlining of regulatory processes. We touch upon these in the introduction. Once the vaccine has been developed, in France, the design and implementation of the immunization program is government driven and thus, it is intrinsically supported by the national public health and health systems. We added some background around this narrative to the program description.

10 Currently there are several viral strains such as B1.1.7 and B1.351 that might interfere with the effectiveness of vaccinations. It would be really impactful if the authors would mention about these variants as well.

� We agree with the reviewer that the emergence of new variants with reported increased transmissibility and/or severity and threats for vaccine-induced immunity is a critical factor for the future evolution of COVID-19. However, the evidence gathered around these new variants is very recent and a complete analysis of their consequences is beyond the scope of our manuscript.

In this revised version, we added the discussion a paragraph of the potential consequences of these new variants that actually reinforces our conclusion around the need for NPIs alongside vaccination

11 Another important variable is the availability of required man-power which was not mentioned in the paper which might influence the supply and uptake constraints.

� The programs we modelled included assumptions on the ability of the health system to scale up, especially in the first half of 2021. The rate of vaccination is influenced by the availability of human resources, building space and consumables among others. We added this explanation to the methods.

12 Although it is a modelling study, but as the core topic was vaccination, some concepts on involvement of antibodies or other physiological concepts could have made the story more interesting. Not required though.

� Thank you for your comment. Although we agree with the reviewer, it is difficult to extrapolate and expand on aspects of immunity in a manuscript that used modeling to discuss uncertainties related to the evolution of the pandemic in a broad population sense. However, we have added to the discussion on the aspects of vaccine response to give more depth to the paper.

In summary, the Article as written presents a very strong claim without basing it on a sufficiently solid foundation.

� our conclusion is that a limited immunization program may not be sufficient in the short term to avoid further spread of SARS-CoV-2. If the constraints of such an immunization program are addressed in the second half of the year, the impact increases and more control over the epidemic is realized. With this conclusion we aim to highlight the importance of considering vaccination impact in realistic contexts which includes implementation and supply constraints and vaccine hesitancy in the short term. We hope with the additional text included in the methods, results and discussion we have addressed this concern.

It also suffers from avoidable defects of presentation.

� we have addressed these defects as well as issues with the reference list. Thank you

Hence I recommend the authors to revise the manuscript along the lines indicated above and resubmit the revised version

� To the best of our ability we have addressed both reviewers’ comments. Thank you

Attachment

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Click here for additional data file. (113.5KB, docx)

Decision Letter 1

Yury E Khudyakov

22 Mar 2021

PONE-D-20-37719R1

Potential impact of introducing vaccines against COVID-19 under supply and uptake constraints in France: a modelling study

PLOS ONE

Dear Dr. coudeville,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

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Your revised manuscript was reviewed by 2 experts in the field who reviewed the original version. Although one reviewer was completely satisfied with your modification of the manuscript, the other still identified many important issues and produced a very strong recommendation. Please consider carefully the attached comments and provide point-by-point responses

==============================

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Academic Editor

PLOS ONE

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Reviewer #2: (No Response)

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Reviewer #2: Manuscript ID : PONE-D20-37719

Revision stage : First revision

Title : Potential impact of introducing vaccines against COVID-19 under supply and uptake constraints in France : a modeling study

Authors : Coudeville L et. al.

I thank the authors for revising their manuscript in response to the reviewers’ feedbacks. However, upon detailed reviewing of the revised manuscript, I am still not convinced about the utility of authors’ conclusions in a practical scenario.

My specific concern had been regarding the authors’ prediction that even with vaccination drive, COVID-19 would be a significant presence as late as 2023. To this end, I had asked the authors to consider various situations such as longer-lasting immunity of the vaccines and different pattern of NPIs so that we could get a much clear idea of the circumstances where COVID-19 continued for a long time and those where the disease got eliminated. I appreciate the fact that this analysis has indeed been performed by the authors. However, they have found high caseload of COVID-19 in 2023 in all situations, even with the most effective vaccine, the most relaxed constraint, and the longest immunity.

I am afraid that an epidemic model which can only produce solutions of one class is fundamentally limited or flawed. A versatile model must be able to show different kinds of solutions for different parameter values. One example is the model in

Shayak B, Sharma MM and Mishra AK, “COVID-19 spreading dynamics in an age-structured population with selective relaxation of restrictions for vaccinated individuals : a mathematical modeling study” (2021) available at https://www.medrxiv.org/content/10.1101/2021.02.22.21252241v1

In this Article it will be seen that the disease is getting contained above a threshold vaccine efficacy and perpetuated below that efficacy. I would like to remind the authors that full or near-total containment of COVID-19 without vaccination has already been achieved in New Zealand, Australia and Taiwan, so vaccine-aided elimination of the disease is not entirely a utopian concept. Hence, a model which cannot exhibit this solution in any case is not a very accurate description of reality. Just to be clear, I am not predicting that COVID-19 will definitely get contained by year-end. It is indeed possible that it will continue into 2023 like the authors predict. However, in my perspective a good mathematical model must be able to generate both classes of solutions and not just one of them. Thereafter, one can have a discussion regarding the situations which lead to the two different outcomes.

My confidence in the authors’ model is further dented by their prediction that vaccination under strong constraints would lead to greater number of hospitalizations in 2021 than no vaccine at all. I would have believed that even if one thousand people were to be vaccinated all over France then overall there would be several hundred less hospitalizations than if the vaccine were not administered.

In conclusion, the authors have apparently used an imperfect mathematical model to predict a dystopian scenario with COVID-19 continuing at full force into 2023. I am not confident of approving for publication such a pessimistic prediction that did not consider other possibilities in the trajectory. Hence, I must recommend that the manuscript be rejected. Perhaps, a suggestion would be to work on models with greater predictive power having more realistic applications.

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PLoS One. 2021 Apr 28;16(4):e0250797. doi: 10.1371/journal.pone.0250797.r004

Author response to Decision Letter 1

29 Mar 2021

Reviewer #1:

Apologies for the delay in reviewing the submitted article. after reading the author's comments, all required questions have been answered and all responses met formatting specifications.

� We are pleased to read that the reviewer is satisfied by the responses we gave to his previous comments

Reviewer #2:

I thank the authors for revising their manuscript in response to the reviewers’ feedbacks. However, upon detailed reviewing of the revised manuscript, I am still not convinced about the utility of authors’ conclusions in a practical scenario.

My specific concern had been regarding the authors’ prediction that even with vaccination drive, COVID-19 would be a significant presence as late as 2023. To this end, I had asked the authors to consider various situations such as longer-lasting immunity of the vaccines and different pattern of NPIs so that we could get a much clear idea of the circumstances where COVID-19 continued for a long time and those where the disease got eliminated. I appreciate the fact that this analysis has indeed been performed by the authors. However, they have found high caseload of COVID-19 in 2023 in all situations, even with the most effective vaccine, the most relaxed constraint, and the longest immunity.

I am afraid that an epidemic model which can only produce solutions of one class is fundamentally limited or flawed. A versatile model must be able to show different kinds of solutions for different parameter values. One example is the model in

Shayak B, Sharma MM and Mishra AK, “COVID-19 spreading dynamics in an age-structured population with selective relaxation of restrictions for vaccinated individuals : a mathematical modeling study” (2021) available at https://www.medrxiv.org/content/10.1101/2021.02.22.21252241v1

In this Article it will be seen that the disease is getting contained above a threshold vaccine efficacy and perpetuated below that efficacy. I would like to remind the authors that full or near-total containment of COVID-19 without vaccination has already been achieved in New Zealand, Australia and Taiwan, so vaccine-aided elimination of the disease is not entirely a utopian concept. Hence, a model which cannot exhibit this solution in any case is not a very accurate description of reality. Just to be clear, I am not predicting that COVID-19 will definitely get contained by year-end. It is indeed possible that it will continue into 2023 like the authors predict. However, in my perspective a good mathematical model must be able to generate both classes of solutions and not just one of them. Thereafter, one can have a discussion regarding the situations which lead to the two different outcomes.

� Models exploring all parameter space to identify the ideal optimal combination of vaccine efficacy and coverage have been published (as referenced in our introduction). This type of approaches, that can be qualified as normative, are very useful in an initial phase of thinking through how to introduce technologies. They have been invaluable to define prioritisation policies ensuring societies aim to minimise deaths while maximising transmission reduction later in the pandemic.

Currently, we are introducing vaccines in real programs and implementation of these programs is undeniably constrained. Our intent is to highlight the impact of the implementation constraints faced in France (as an example for EU countries). Therefore, rather than assessing all possible scenarios and identify optimal ones we selected a positive rather than normative approach which consists in identifying plausible scenarios given realistic situation and expected constraints. We see our approach as complementary to existing publications.

The comparison performed by the reviewer between our results for France and the situation in Australia, New Zealand and Taiwan does not seem to us as the most relevant. First, the geographic and insular situation of these countries is very different from the one of France. Secondly, the near containment obtained under strict NPI measures cannot be really compared with the situation that could be observed later in France without such measures.

Failure to account for constraints during the priority setting process/implementation planning in mathematical modelling can result in unfeasible health interventions being recommended, theoretically optimal but practically unreasonable expectations of impact and, ultimately, in evidence being disregarded by decision-makers and public wariness. The need for a diversity of approaches in modelling analyses including accounting for constraints has been evident for years in resource limited settings, especially when introducing large intervention programs – such as a global vaccination campaign (see e.g. https://doi.org/10.1371/journal.pmed.1002240) The measurement, inclusion and analysis of impact of constraints in mathematical modelling is a change in paradigm in model-based policy recommendations as well described by Bozzani et al. in recent publication, quote, “Common objectives of model-based analyses incorporating constraints are to assess real-world feasibility or allocate resources efficiently” (see e.g. https://doi.org/10.1016/j.epidem.2021.100450)

We believe this perspective is needed in the literature, as we are facing a complicated set of constraints to scale up vaccination.

To clarify this point in the revised version of the manuscript, we specifically indicate that our objective in this manuscript was not to identify optimal conditions for a vaccination program to be successful (line 23), that we did specifically assessed all possible scenarios including the most optimistic and pessimistic ones (line 286) and that our results are not directly applicable to all settings (line 304).

It is also noteworthy to mention that the situation we described actually reflects the current situation in France and in other countries (e.g. Germany, Belgium, Spain) where despite the initiation of the vaccination program, supply and uptake constraints are still very much present and has not prevented the need for lockdown measures which are currently being extended in most European countries.

The conclusion in our manuscript is similar to that reported for other settings described in recent publications (e.g. Makhoul et al. [2021] that notably state “:Despite 95% efficacy, actual vaccine impact could be meager in such countries if vaccine scale-up is slow, acceptance is poor, or restrictions are eased prematurely.” https://doi.org/10.3390/vaccines9030223

My confidence in the authors’ model is further dented by their prediction that vaccination under strong constraints would lead to greater number of hospitalizations in 2021 than no vaccine at all. I would have believed that even if one thousand people were to be vaccinated all over France then overall there would be several hundred less hospitalizations than if the vaccine were not administered.

�The correct way to interpret the result mentioned by the reviewer, is actually more a neutral impact of vaccination (range: -6 to +2%). It certainly does not mean that vaccination has no impact.

It rather indicates that the implementation of a vaccination program also impacts the NPIs in place (we report a reduction in NPI of 30 days in 2021 for the strong supply constraint scenario, see Figure 2). The overall impact is, therefore, a combination of vaccination effect and changes in NPIs measures. If the vaccination coverage is too low, changes in NPIs might have a stronger impact on hospitalizations than the vaccination itself. As it corresponds to a rather extreme scenario, is no longer observed when a more appropriate time horizon is considered (i.e. 2021-2022), the importance of this result is not to be overstated but it would be incorrect to dismiss it as a ‘wrong’ result – the peril of early relaxation of NPIs with suboptimal vaccination coverage is real and has been highlighted by others, notably Moore et al ‘For all vaccination scenarios we investigated, our predictions highlight the risks associated with early or rapid relaxation of NPIs. ( https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(21)00143-2/fulltext)

Therefore, It does not seem for us that this result invalidates the quality of the model. Moreover, as we observed earlier, the impact of low vaccine uptake and supply constraints have led EU nations to extend their mitigations measures and/or initiate lockdowns after short period of relaxation – similar to what we discussed in our paper.

In conclusion, the authors have apparently used an imperfect mathematical model to predict a dystopian scenario with COVID-19 continuing at full force into 2023. I am not confident of approving for publication such a pessimistic prediction that did not consider other possibilities in the trajectory. Hence, I must recommend that the manuscript be rejected. Perhaps, a suggestion would be to work on models with greater predictive power having more realistic applications.

� We agree with the reviewer on the imperfectness of our model which is in fact a common trait to all models. However, we disagree on two aspects of the statement made by the reviewer:

• Our scenarios are not dystopian. Implementation constraints are being reported daily and the risk of suboptimal vaccination in combination with early relaxation of control measures has been highlighted by several modelling groups to date in other settings.

• We do not predict ‘COVID-19 will continue in full force in 2023’. Our results indicate in most scenarios a limited need for NPIs in 2022 (e.g. 0-11 NPI days for most vaccination scenarios in 2022 except the “strong supply constraint” scenario) and this also applies to 2023. This cannot be compared to the 2020-2021 when significant outbreaks are observed despite the implementation of significant NPI measures. We still do not know the duration of natural or vaccine-afforded immunity. Based on experience with human coronaviruses, immunity from natural infection may last 1-2 years. We also do not know the level of severity expected in those re-infected. Therefore, we focused our model and discussion to a mid-term situation.

Each model is designed to fit the ability to answer a precise question and to the available information to fuel it and to validate it. We built a model aiming to be able to be sufficiently precise to be able to compare conditional scenario – ‘what if’ scenario – of public policies, with the most up-to-date knowledge of realistic constraints. Scenario planning is useful in considering alternative futures – so that policy makers can assess the opportunity costs of inaction. To consider scenario planning as prediction modelling has been a recurrent misinterpretation during this pandemic – leading to misplaced suspicion of modelling results.

Finally, we are confident that our manuscript constitutes a positive addition to the scientific debate on the topic. It has, of course, to be put in perspective with other publications, which we hope we did.

Decision Letter 2

Yury E Khudyakov

14 Apr 2021

Potential impact of introducing vaccines against COVID-19 under supply and uptake constraints in France: a modelling study

PONE-D-20-37719R2

Dear Dr. coudeville,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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Kind regards,

Yury E Khudyakov, PhD

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

Acceptance letter

Yury E Khudyakov

19 Apr 2021

PONE-D-20-37719R2

Potential impact of introducing vaccines against COVID-19 under supply and uptake constraints in France: a modelling study

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    Data Availability Statement

    The model code used is available at GitLab: https://gitlab.com/SPMEGModels/covid-model.

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