Immunological model

The immunological model is as described in Hogan and colleagues [31]. Briefly, we followed the approach in Khoury and colleagues [25], in which neutralising antibody titre is assumed to be a correlate of protection against SARS-CoV-2 infection, severe disease, and death over time. Such a model does not necessarily exclude other immune mechanisms playing a role in protection—including T cell-mediated immunity—but rather makes the underlying assumption that the patterns of protection over time can be related to the trends observed in the neutralising antibody titre. We therefore define these underlying dynamics of immunity as an individual’s immunity level (IL) [31]. We further assume that an individual’s IL decays according to a biphasic exponential decay function, where an initial faster period of decay is followed by a longer period of slow decay [24,25]. We then assume logistic relationships between IL and effectiveness to capture time-varying vaccine protection against mild disease (infection) and hospitalisation over time, with the logistic function parameterisation capturing higher protection against severe outcomes [25]. We use model parameters against the Delta and Omicron variants for 2 vaccine products—the Oxford/AstraZeneca AZD1222 vaccine and the Moderna mRNA-1273 vaccine (Table A in S1 Text). The resulting pattern of IL and vaccine effectiveness over time are shown in Hogan and colleagues [31]. To capture loss of immune recognition against Omicron and future variants, we estimate a multiplicative scaling factor (referred to as the variant fold reduction, VFR) to reflect the reduced neutralization of a given variant for each modelled vaccine. This VFR for the ancestral vaccines is based on our estimates of the degree of immune escape obtained by fitting the immunological model to vaccine effectiveness data against the Delta and Omicron (BA.1/2) variants [31].

We use the same approach to capture infection-induced immunity and its interaction with vaccine-induced immunity, where each infection is assumed to generate a boost to IL of 1, i.e., equivalent to that measured in convalescents [25]. In our model, this corresponds to a mean protection against reinfection of 80% over 180 days, similar to estimates obtained in a recent study of infection-induced protection against Omicron BA.4 and BA.5 subvariants which found 76.2% [95% CI 66.4%, 83.1%] protection against symptomatic reinfection [32]. This level of boost is higher than that observed under primary vaccination, potentially representing a broader and longer-lasting immune response and resulting in higher infection-induced protection. We additionally performed sensitivity analyses to this assumption exploring boosts to IL of 0.75 and 1.25, corresponding to protection against reinfection over 180 days of 65% and 89%, respectively. In the absence of definitive data to suggest otherwise [33], the infection-induced IL is assumed to decay at the same rate as following booster vaccination. We include a sensitivity analysis to this assumption by reducing the rate at which immunity is lost by either 75% or 50% (i.e., increasing the durability of protection). Each infection or vaccine dose results in an additive increase in IL, with an upper limit on the total level of vaccine- or infection-induced IL for each individual [34].

We assume that following the emergence of a variant, the infection-induced IL developed through exposure to previous variants is reduced by the VFR in the same way that vaccine-induced protection is reduced. However, subsequent infections with the new variant are assumed to match and therefore are not reduced by the VFR. The degree of matched protection is set to capture strain-specific protection against infection without explicitly modelling each variant (see S1 Text).

We capture the additional benefit of variant-adapted vaccines by increasing the immunogenicity generated upon vaccination (so as to reduce the impact of the VFR once variant-adapted vaccines are introduced). Khoury and colleagues estimated a 1.61-fold [95% CI 1.5, 1.8] relative neutralization titre for variant-adapted compared to ancestral vaccines based on the vaccines available at the end of 2022 [24]. To capture the initial variant-adapted vaccines (i.e., the bivalent vaccines against BA.1/2 and BA.4/5), we therefore apply an increase to the vaccine-induced IL from dose 4 onwards. This partially counteracts the impact of immune escape (the VFR) of the circulating SARS-CoV-2 strain in 2022. This increase to the IL is calculated as the central estimate of the Omicron VFR divided by the relative neutralization titre of 1.61. In our first set of scenarios, we assume that this remains the primary vaccine and that no further updates are introduced. We refer to this schedule as “variant-adapted” vaccination.

We further explore the benefits of introducing a vaccine that is updated each year. To do so, we assume that the vaccine is matched to the variant that is circulating 1 year earlier. In the model, at the time point that a new dose is scheduled to be rolled out to the eligible population, we obtain the level of immune escape (i.e., the value of the VFR) at exactly 1 year earlier. We then multiply the vaccine-induced IL by this prior VFR to obtain an increase in the level of vaccine protection, and apply this process from dose 5 onwards, for the applicable scenarios. We refer to this schedule as “yearly updated” vaccination.

Population model and vaccine allocation

To explore the population impact of vaccines, we developed a stochastic, individual-based model of SARS-CoV-2 transmission and vaccination (open-source at https://mrc-ide.github.io/safir/) [35]. The main transmission model captures the infection status of individuals as being in one of the follow states: susceptible; exposed, infectious with mild symptoms; infectious and asymptomatic; infectious requiring hospitalisation; hospitalised in a general ward; hospitalised in an intensive care unit (ICU); cases in recovery from ICU; and cases that have died (Fig 1). Within the model, each individual is assigned a 5-year age bin, with the bin sizes corresponding to the demographics of the population.

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Fig 1. Schematic representation of the compartmental epidemiology of the stochastic individual-based model.

The green circle denotes the IL, which increases in response to both exposure to infection and to vaccination and wanes over time (see section on the Immunological Model). The IL is tracked for each individual in the model and influences the probability of being infected (from susceptible S to exposed E) and of developing disease requiring hospitalisation (Icase) given a breakthrough infection. I_mild denotes mild symptomatic disease, I_asymp asymptomatic infection, I_hosp disease requiring hospitalisation (which is comprised of people requiring mechanical ventilation, people requiring oxygen, and people requiring neither), I_ICU disease requiring ICU admission, I_rec stepdown from ICU, and D death. ICU, intensive care unit; IL, immunity level.

https://doi.org/10.1371/journal.pmed.1004195.g001

Vaccine-derived and infection-induced immune dynamics follow the immunological model described above. The model structure and epidemiology broadly mirror a previously published compartmental model, but these processes are instead implemented at the individual level [36]. This allows for immunity to be implemented at the individual level, capturing both vaccine- and infection-induced immunity, individual variation in this immunity, decay over time, and allowing for individual-level tracking of vaccine and infection history. Each individual’s level of immunity, or IL, can be boosted by infection or vaccination, and wanes over time according to the dynamics of the immunological model described above. This IL determines an individual’s risk of becoming infected and the subsequent risk of disease progression and hospitalisation. Transitions between epidemiological states are summarised in Fig 1 and Table B in S1 Text. The model was parameterised using published literature and was not explicitly fitted to data. Model parameters include those determining the natural history for SARS-CoV-2 infection (i.e., progression from infection to symptomatic and severe disease and infectivity), age-stratified probabilities of requiring hospital care, and the infection fatality ratio. These were obtained from Hogan and colleagues [36] and are reproduced in Table C in S1 Text. The model additionally captures differences between countries in demography, age-mixing patterns, and access to hospital facilities, using the parameterisation from Hogan and colleagues and Walker and colleagues [36,37].

The model structure also allows for a high degree of flexibility in dose and age-based vaccine prioritisation strategies. However, only 1 vaccine type can be modelled across the population; the results presented here are generated using the parameters from Hogan and colleagues [31] for the AZD1222 and mRNA-1273 vaccines. Vaccines are allocated according to an algorithm accounting for available stock, the age groups that are prioritised for each dose, minimum time delays between the receipt of subsequent doses, and coverage targets for each dose and age group following the approach taken in Hogan and colleagues [36]. This is described in further detail in S1 Text Section 1.5 and illustrated in Fig A in S1 Text.

Settings and transmission

We consider 2 representative income settings—high-income countries (HICs) and lower-middle-income countries (LMICs)—and characterise each setting by contact patterns and demography [36,37]. In LMICs, we assume healthcare system capacity is limited; once modelled hospitalised cases exceed a threshold in these settings, infected individuals who require hospital care experience worse outcomes [37]. In HICs, we assume no limit to healthcare capacity due to surge provisions.

We further stratify the current epidemiological state of countries into 3 categories. “Category 1” represents countries that have experienced substantial past transmission (and hence have a substantial level of infection-induced immunity) alongside a high level of access to vaccines. Many high- and upper-middle-income countries fall into this category—including countries in North America, Central/South America, the Middle East, and Europe. We created a representative epidemic profile for such countries, with a first wave occurring between March and May 2020, a second wave during the northern hemisphere winter of 2020/21, and transmission gradually increasing (interventions being relaxed) from mid-2021 (Fig B in S1 Text). This broadly characterises a northern hemisphere setting but does not include seasonality. “Category 2” are countries that have experienced substantial prior transmission and have had limited distribution of vaccines. Many low- and lower-middle-income countries fall into this category (although we note that several LMICs have successfully limited transmission). For these countries, we model a similar background epidemic to that in Category 1 (Fig B in S1 Text) but with fewer interventions in place during 2021. “Category 3” countries are those that successfully interrupted transmission for a substantial time period (“zero-COVID” countries, mostly in east Asia and the Pacific) and therefore have more limited infection-induced immunity, alongside high vaccine uptake. For these, we assume a gradual lifting of restrictions (Fig B in S1 Text) from late 2021. These scenarios, alongside our transmission parameters, are informed by fits of a similar compartmental model to the global pandemic in 2020–2021 [1].

In all settings, we assume that the Omicron variant (BA.1 and BA.2 subtypes) gradually replaces Delta over 1 month from end-November 2021. This replacement impacts infection- and vaccine-induced immunity, transmissibility, and severity (see S1 Text). Following the emergence of the Omicron variant, we then assume that the virus continues to evolve or “drift” over time, with a new variant regularly replacing the dominant variant. This can be considered to represent the gradual drift that is now being observed with the Omicron subvariants. In our model, we implement this by increasing both the level of transmission and the VFR (relative to Delta) every 4 months, to represent small increases in transmissibility and gradual immune escape. Antigenic cartography studies have shown continued evolution with substantial jumps within the Omicron variant [38–40]. However, translating these antigenic maps into the degree of immune escape (and hence our VFR parameter) remains challenging given the widespread exposure to SARS-CoV-2 that has now occurred. We therefore explore a range of values for the degree of both transmission and immune escape. We use a central value of 5% for the main analysis and include a sensitivity of the model outcome to values between 0% and 20% in S1 Text.

Vaccine dose strategies

The maximum population-level coverage for each income setting is based on the current WHO-reported coverage by income setting, which on 20 June 2023 reported 75% and 48% for the primary series and booster doses, respectively, in HIC settings, and 61% and 19%, respectively, in LMIC settings [41]. For our analysis, in HIC settings we assume total maximum population-level coverage of 80% and 53% for the primary series and booster doses, respectively. In LMIC settings, we assume a maximum coverage of 75% in all age groups >10 years that translates in our average demography to 56% for the primary series. This is slightly lower than the WHO reported statistic but is representative of age-based patterns in these settings. In LMIC settings, given that the rollout to date of booster doses has been limited to date, but is still underway, for our simulations we assume a maximum 60% uptake of booster doses relative to the primary series, equating to 39% population-level coverage. This is higher than the current WHO-reported level to reflect ongoing expansion of booster programmes in these settings [41]. In all settings, we prioritise the oldest individuals with vaccines delivered sequentially to consecutive 5-year age groups until the target age group is vaccinated, and we assume that uptake is highest in older age groups, with age-based uptake informed by various WHO and country-level sources [42–46]. We undertook an additional scenario as a sensitivity analysis where 70% population-level coverage of the primary series is achieved in LMIC settings, based on WHO policy targets [47]. As we assume that only individuals 10 years and older (10+) are eligible for vaccination, this total population-level coverage corresponds to higher uptake within targeted groups and zero coverage within ineligible groups; the within-age group uptake for each setting is shown in Table D in S1 Text.

Vaccine distribution strategies are implemented as follows. For Categories 1 and 3 (HICs), vaccines are administered at a constant rate of 5% of the population receiving 1 dose per week, starting 1 January 2021, assuming the mRNA-1273 vaccine for the primary 2-dose series and booster to those 10+. After the primary doses and first booster dose, we then either cease to administer any additional doses, or administer at the same pace, one of the following strategies with a variant-adapted vaccine: annual or 6-monthly booster doses to the 75+ population; annual or 6-monthly booster doses to the 60+ population; or annual booster doses to the 10+ population. We additionally consider the outcome if all doses from dose 4 onwards are the ancestral mRNA-1273 vaccine instead of a variant-adapted product.

For Category 2 (LMICs), vaccines are administered at a maximum constant rate of 2% of the population immunised per week starting 1 April 2021. We assume the first 2 doses are the AZD1222 vaccine, the first booster (third dose) is with the mRNA-1273 vaccine, and subsequent doses are either with a variant-adapted vaccine (default) or the ancestral mRNA-1273 vaccine. We assume the primary series and first booster is administered to those aged 10+ according to the levels of uptake in Table D in S1 Text. We then either cease to administer any additional doses, administer annual booster doses to the 60+ population at the same pace, boost the 40+ population annually, or boost the 10+ population annually.

For Category 2 (LMICs), we additionally model a separate scenario where we consider the relative impact of administering doses to vaccinate the younger working-age population with their primary series, versus diverting those doses to vaccinate the older population with a booster dose. We commence vaccination with the AZD1222 vaccine from April 2021, delivering the primary 2-dose series to the 40+ population. Once the target coverage is achieved, vaccination is paused until the delay between the second and booster doses (12 months) is complete. We then construct the following scenarios. For the first, we vaccinate the 40+ population with booster doses, beginning with the oldest (80+) age group. For the second, we take the same number of doses that would be required to give boosters to 40+ years, and instead deliver these doses to individuals younger than 40 years (2 doses per person). We construct these rollout scenarios such that the daily doses delivered is equivalent between scenarios. We compare these outputs with the scenario where no additional doses are delivered beyond 2 doses to the 40+ population.

Setting characteristics and vaccine rollout assumptions are summarised in Table E in S1 Text. The scenarios in each of the 3 settings are illustrated in Fig 2.

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Fig 2. Summary of the scenarios explored.

Key assumptions relating to the level of transmission, the timing of vaccine dose delivery, the vaccine product delivered, and the level of immune escape, are illustrated for each category. Category 1 represents high-income settings with historically high levels of SARS-CoV-2 transmission, Category 2 represents lower-middle-income settings with historically high levels of transmission, and Category 3 represents high-income settings with initially lower levels of transmission. Additional assumptions are summarised in Table D and E in S1 Text. SARS-CoV-2, Severe Acute Respiratory Syndrome Coronavirus 2; VFR, variant fold reduction.

https://doi.org/10.1371/journal.pmed.1004195.g002

Variant scenarios

In addition to our baseline scenario in which we mimic the continued gradual antigenic drift within the Omicron clade that is captured in the main scenarios, we explored the impact of the emergence of a more antigenically distant dominant variant. This was chosen to reflect a “worst-case scenario” given the ongoing uncertainty in the future evolution of the virus. We assume that this new variant emerges and replaces the Omicron variant between 1 and 31 October 2023 and that thereafter this new variant continues to gradually drift (as for the Omicron variant) for the remainder of the simulation time period (i.e., to end-2024). We consider 3 possible new variants with the following characteristics: (1) severity increased to that of Delta (“increased severity”); (2) VFR relative to Delta increased to 10 (“additional immune escape”) and hence an additional 2-fold reduction relative to Omicron (an antigenic shift away from Omicron of a similar magnitude to the shift from Delta to Omicron); and (3) both severity increased to Delta and VFR increased to 10 (“increased severity and immune escape”). These 3 scenarios represent a range of plausible scenarios (since they are based on what has been observed with previous variants) and also generate a reasonable worst-case scenario.

Forward simulations

For each scenario, we repeat the model simulation across 50 random seeds, with a simulation population size of 1 million, and summarise the outputs by the median over these stochastic realisations. As the runs are based on a single model, we were unable to capture uncertainty in model structure. Furthermore, given the high degree of uncertainty in the future evolution of the virus and hence epidemic trajectories, we did not sample parameter uncertainty as these would give a sense of precision that is misleading. Instead, we evaluate the value of different vaccination strategies against a range of epidemic scenarios and address parameter uncertainty through sensitivity analyses. This is in line with the longer-term scenario methods used to support policy in situations of high uncertainty [48].

We use these outputs to calculate the daily infections and hospitalisations from 1 February 2020 to 31 December 2024, as well as the total infections, hospitalisations, and deaths from 1 July 2022 to the end of the simulation window. Given the high degree of uncertainty in the future course of the pandemic, these numerical values should be interpreted as indicative guides rather than predicted estimates.

Impact and cost-effectiveness

The model outputs include infections, hospitalisations, and deaths over time alongside the number of vaccine doses that have been delivered. These outputs are used to estimate the number of vaccine doses required to avert X hospitalisations and deaths (where X is specified). We further estimate the incremental cost per hospitalisation and death averted of the vaccine strategies by calculating the total number of additional vaccine doses delivered, relative to the “3 doses only” (HIC) or “no additional doses” (LMIC) scenarios. These values are divided by the additional hospitalisations or deaths averted compared to the baseline scenario and multiplied by the assumed cost of each dose to obtain the incremental cost-effectiveness. We use 3 illustrative costs for the vaccine unit price (US $2, $20, or $50 per dose) as this price is known to vary between countries and it not available in the public domain. While vaccine prices may differ between products, as this information is not publicly available, we assume no difference in price between the different vaccine types [49]. These illustrative unit costs per dose are assumed to incorporate delivery and wastage.