Background
Prior to December 2020, implementation of nonpharmaceutical interventions (NPIs), including school/business closures, physical distancing, and mask-wearing, was the main tool to control the spread of SARS-CoV-2. However, with the development of effective vaccines against SARS-CoV-2, in December 2020 many countries were able to initiate vaccination campaigns [
1‐
3]. The most recommended strategy was prioritizing the elderly and high-risk populations, followed by essential workers, and then the general public [
4‐
6]. At the initial stage of vaccine distribution, strict NPIs were kept in place to avoid potential virus resurgence. After almost six months of immunization, the focus shifted in establishing an optimal vaccination strategy in order to safely lift NPIs while avoiding virus resurgence.
There have been numerous mathematical models aiming to identify the best vaccination strategy [
7‐
16]. Earlier models focused on reducing the disease spread and identifying priority groups for receiving their first doses. For example, Matrajt et al. [
16] developed a deterministic model with age structure to determine which age group should be vaccinated first. They showed that with low coverage, the elderly (60 + years) must be prioritized to reduce the number of deaths. Bubar et al. [
9] showed that prioritizing younger ages (20–49 years) can reduce cumulative cases independently from rollout speeds and coverages. In Fall 2020, new, more transmissible, and virulent, variants of concern (VOCs) were discovered [
17‐
20]. In many areas of the world, VOCs cases increased rapidly in the following months and the VOCs became dominant over SARS-CoV-2 wildtype [
20‐
23]. Giordano et al. [
8] investigated the impact of mass vaccination campaigns and NPI lifting while considering increased transmission due to VOCs. They found that NPIs implementation is crucial even after the rollout of a vaccine. Moore et al. [
11] also introduced VOCs in their age-structured model as well as vaccination and different levels of reopening. They similarly confirmed that relaxing NPIs too early will result in virus resurgence and noted the infeasibility of reaching herd immunity through vaccination. While vaccination of young children was approved much later, some previous studies still considered younger age groups when defining the best vaccine rollout for minimizing infections, hospitalizations, and deaths [
9,
24,
25]. Meehan et al. [
24], for example, showed that prioritizing individuals aged 30–59 reduces the transmission, while prioritizing ages 65 + reduces deaths. They also found that when coverage is close to levels required for herd immunity, vaccinating middle-aged adults should be prioritized, since vaccinated young teenagers and children appear to have minimal impact. Shim et al. [
25] conducted an optimization analysis on vaccination strategies, considering age groups and vaccine efficacy. They found that for a vaccine with at least 70% efficacy, targeting ages 20–49 is best for reducing infections, while targeting ages 50 + is best for reducing mortality. Although existing studies provide important information for decision making, they do not capture the nuances around the impact of VOCs on vaccination efforts by age group in terms of both transmission and virulence, as well as vaccine effectiveness, in order to assess scenarios for the safe lifting of NPIs at various timepoints.
In this paper, we aimed to determine an optimal vaccination strategy to enable the safe lifting of NPIs while avoiding virus resurgence, using Toronto, Canada as a case study. We have extended the basic SIR compartmental model to reflect a variety of infectious and recovered states and incorporated age structure and vaccine status. We further included two strains of the virus, differentially affecting transmission, virulence, and vaccine effectiveness. We then assessed different reopening strategies given varying degrees of vaccine coverage by age group aiming to reduce infections, hospitalizations, and deaths.
Discussion
We developed an age-structured compartmental model which captures the transmission dynamics of COVID-19. The SLAIHDR model considers vaccination and waning processes and an infectious compartment that captures both symptomatic and asymptomatic cases. Hospitalizations and deceased individuals are also included. The population is divided into six age groups and assumes that children aged 0 to 9 years are not immunized against the SARS-CoV-2 virus. Given the emergence of new variants, the growth of cases deriving from variants of concern (VOC) was captured using a time-dependent sigmoidal function. This needed to be included in the model to better predict the course of the infection and effectiveness of vaccines. This approach can identify severity differences between strains for outcomes such as death and hospitalization rates.
Our analysis shows that while prioritizing ages 10–19 years for vaccination rollout will not have a large impact, reaching 80% vaccine coverage in ages 20–39 and 40–59 by mid June 2021 will maximize reductions of cases, deaths, and hospitalizations. Sensitivity analysis confirms this result. Our results also confirm, as expected, that a late partial and total reopening will reduce the infection outcomes by roughly 57%; we still observe that the more adults aged between 20 and 59 years are vaccinated, the lower increase of cases and deaths is reported. However, even if delayed, a complete reopening, with the number of pre-pandemic contacts, will result in a visible spread of infection, also with the highest vaccine coverage.
As of June 14, 2021, the coverage in Toronto of adults is 76.12% and 72.9% for the age groups 20–39 and 40–59 years, respectively [
39]. Over summer 2021 a strong immunization campaign was conducted, allowing more citizens to become fully immunized over a short period of time. However, after the reopening stages in August, a new wave, although smaller than the previous ones, was reported in the City of Toronto [
26], followed by a much larger wave reported in late 2021 and early 2022 (Figure SI
9). Our results suggest that with more relaxed NPIs in August or September, cases will increase towards the end of 2021, even with the highest vaccine coverages, and this confirms the visible increase in severe outcomes reported in Toronto after the reopening.
With new variants circulating, vaccine efficacy plays an important role in rollout strategies. Our analysis on the vaccine distribution and reopening strategies shows that with a lower efficacy against the virus, regardless of the reopening levels, the number of cases, deaths and hospitalizations reported increase. These results are confirmed in the new wave in December 2021 that resulted from the low efficacy of vaccine against the new variant Omicron and its higher transmissibility. Our result suggests that a prompt response of public health in increasing the immunization level is crucial if new variants circulate in the population. Moreover, our model suggests that even with a lower efficacy, it is important to vaccinate elderly and adults to minimize severe outcomes and infections.
The time at which NPIs are lifted has a substantial impact on the control of the infection. Our results show that in general, a late reopening, is more beneficial. In fact, with partial reopening in September rather than August, cases, deaths and hospitalizations are reduced.
Since the second vaccine dose increases efficacy, faster distribution of vaccine to reach full immunization can control the spread more quickly. Our analyses examining the impact of administering second doses after 21 or 50 days, show a higher reductions in case counts if full immunity is provided 3 weeks following the first dose. This result is expected from the formulation of our model, since a shorter period between doses will increase the number of individuals who are fully immunized faster.
Our study has some limitations. Firstly, we assumed that all the VOC cases are coming from B1.1.7 and the efficacy against the virus is the same for wildtype variants and VOC. However, as new variants emerge, with a much lower vaccine efficacy, it will be important in future work to consider multiple strains to better capture the role of efficacy and vaccine rollout. Secondly, we assumed that recovered individuals from any variant are not susceptible to other variants, but with more transmissible variants emerging, infection-acquired immunity might protect individuals only partially. Thirdly, while we assumed that all individuals vaccinated with the first dose will eventually receive the second dose, a fraction of people might opt not to receive the second dose. Lastly, we assumed that vaccination is effective from the day it is received, however individuals are considered fully immunized after 14 days from their last inoculation [
40]. This study was motivated by the emergence and persistence of the first VOC, alpha. However, since our initial study the delta variant and later omicron variant emerged. Furthermore, additional doses of vaccine began being offered beyond the two-dose regiment considered in our model. The evolving nature of the virus and our societal response make it difficult to produce rapid real-time modelling that is both reflective of current realities and has accurate predictive power. Instead, this study considers how to effectively distribute vaccines between age groups when two strains of a virus are circulating. Though focused on alpha, the increased transmissibility of other variants and their increasing evasiveness of vaccine impact all ages and therefore the relative differences in disease impact between age groups is generally agnostic to variant. Nevertheless, we have compared our cases predictions with real cases data up to December 2021 in Figure SI
9 which shows comparable qualitative trends between model and data. In fact, we observe that some of our predictions on cases, with low efficacy, high vaccine coverage and different reopening degrees, and hence higher transmission, reflect the level of cases reported at the end of 2021. We further note that the actual case data falls within our precited case counts for different reopening strategies. While the late surge in 2021 was due to omicron, a variant not considered in this model, the bounding from our model suggests that a re-parameterization of the model as new variants emerge can extend its validity and applicability.
Conclusions
In conclusion, our model reflects the course of COVID-19 infection in Toronto considering infection from the VOC and original wildtype strain. We were able to capture, through data, the different infection outcomes such as transmission, hospitalizations, and deaths, generated by different variants of the virus. Our results show that it is imperative to direct our efforts towards individuals aged between 20 and 59 years, showing similarities with previous works [
6,
22,
23] In fact, these are the age groups with higher contacts, social activity, and population size. Moreover, we showed that a complete return to the number of pre-pandemic contacts will result in an immediate virus resurgence, even with the highest vaccine coverages reached by mid June 2021. The situation may be even worse if there are new more transmissible variants. Also, we showed that the introduction of new variants, the vaccine efficacy against them, and the reduced time to obtain full immunity play an important role in the vaccination rollout aimed to reduced new infections and severe outcomes. A reduction in vaccine efficacy will lead to a higher spread of the infection, and if, additionally, the second dose is delayed too much, the risk of having a re-emergence of the infection is possible.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.