Background: Since December 2020, public health agencies have implemented a variety of vaccination strategies to curb the spread of SARS-CoV-2, along with pre-existing Nonpharmaceutical Interventions (NPIs). Initial strategies focused on vaccinating the elderly to prevent hospitalizations and deaths, but with vaccines becoming available to the broader population, it became important to determine the optimal strategy to enable the safe lifting of NPIs while avoiding virus resurgence. Methods: We extended the classic deterministic SIR compartmental disease-transmission model to simulate the lifting of NPIs under different vaccine rollout scenarios. Using case and vaccination data from Toronto, Canada between December 28, 2020, and May 19, 2021, we estimated transmission throughout past stages of NPI escalation/relaxation to compare the impact of lifting NPIs on different dates on cases, hospitalizations, and deaths, given varying degrees of vaccine coverages by 20-year age groups, accounting for waning immunity. Results: We found that, once coverage among the elderly is high enough (80% with at least one dose), the main age groups to target are 20–39 and 40–59 years, wherein first-dose coverage of at least 70% by mid-June 2021 is needed to minimize the possibility of resurgence if NPIs are to be lifted in the summer. While a resurgence was observed for every scenario of NPI lifting, we also found that under an optimistic vaccination coverage (70% coverage by mid-June, along with postponing reopening from August 2021 to September 2021) can reduce case counts and severe outcomes by roughly 57% by December 31, 2021. Conclusions: Our results suggest that focusing the vaccination strategy on the working-age population can curb the spread of SARS-CoV-2. However, even with high vaccination coverage in adults, increasing contacts and easing protective personal behaviours is not advisable since a resurgence is expected to occur, especially with an earlier reopening.
Keywords: COVID-19; SARS-CoV-2; Mathematical modeling; Age structure; Nonpharmaceutical Interventions; Vaccine; Waning; Resurgence; VOC
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1186/s12889-022-13597-9.
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 [[
There have been numerous mathematical models aiming to identify the best vaccination strategy [[
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.
Our model is applicable to any geographical region where sufficiently detailed data are available. To study COVID-19 vaccination rollout and reopening strategies, we used data from Toronto, Canada between December 28, 2020 and May 19, 2021. To calibrate model parameters, we used data on cases, deaths, hospitalizations, and daily vaccine doses, publicly available at the City of Toronto website [[
As of May 5, 2021, the Canadian government approved the use of the Pfizer-BioNTech COVID-19 vaccine in teenagers aged 12 + years [[
Graph: Fig. 1 Flow diagram of COVID-19 transmission dynamics with two vaccination processes. Acronyms: i ∈ {1–6}Age groups: 0–9 (unvaccinated), 10–19, 20–39, 40–59, 60–79, 80+ ; In Age group i: Si (Susceptible), Li (Latently infected), Ai (Asymptomatic infected), Imi (Symptomatic mild infected), Hi (Hospitalized), Di (Deceased), Ri (Recovered), V1i (Vaccinated with first dose), V2i (Vaccinated with second dose). To capture the different infection severities coming from VOC or wildtype variant, each disease-state progression is variant-dependent (* = wildtype or VOC). Red arrows: vaccination process. Dashed lines: waning process. Model assumptions: • Only susceptible individuals, aged 10+ years, will receive the vaccine. Vaccine reduces susceptibility. Partially vaccinated people can become infected and infectious if the vaccine is not efficient. • Immunity follows two steps: partial (receiving 1 dose) and full (receiving 2 doses), with the second dose given after 112 days (in some predictive scenarios after 50 or 21 days). Immunity from one dose wanes in 120 days and from two doses after 365 days. Vaccination continues until 80% of the entire population receive at least one dose. • Vaccine efficacy is age-dependent (higher for teenagers and adults, 10% lower for elderly) and is the same against wildtype variant and VOC (all non-wildtype cases are assumed to be B.1.1.7 variant). • VOC and wildtype are both included in the transmission process, assuming that the proportion of VOC cases increases over time following a sigmoidal function, with transmission from VOC 1.5 times higher than wildtype. • Only individuals hospitalized might die from the infection. βO,βN: • probability of transmission; cij: contacts rate between individuals in age group i and individuals in age group j; ξ: proportion of infectious individuals not respecting isolation; λ: daily vaccine doses; ω1,ω2: waning rates, after one or two doses; σ: average time between doses; ρ: proportion of individuals developing symptoms; γH: hospitalization rate; μH: death rate; γaR,γmR,γHR: recovery rate of asymptomatic, infectious and hospitalized individuals
The infection dynamic is presented in Fig. 1. The susceptible compartment (S), with age-dependent susceptibility, can become infected with either the wildtype or VOC (indicated with O and N, respectively), with age-dependent transmission rate
The population is further structured by vaccination status (none, partial and full), with no possibility of reinfection. The vaccine we chose to model has the characteristics of Pfizer/Moderna in that it is delivered in two doses [[
With increasing vaccination rollout, public health has considered easing some NPI restrictions [[
For each reopening scenario, we examined the impact of vaccination by age group. We used vaccination data up to May 19 to estimate the vaccination rate required to reach specific coverages by June 14, 2021 (a plateau, or a 10%, 20% or 30% increase from current coverage for each age group), all the model permutations are given in Figure SI3. We then used the average daily doses from that day moving forward, until 80% of the population has received at least one dose. Since the vaccine coverage by May among ages 60 + was above 70%, we primarily focus on varying coverages in those under 60 years of age, assuming that by mid-June, ages 60–79 and 80 + might reach 80%-90% coverage with the first dose, ages 40–50 might reach 70%-90%, ages 20–39 might reach 60%-80%, and ages 10–19 might reach 20%-40%. Given guidelines on extended timeframes with limited vaccine supply [[
To explore the impact that vaccine- and infection- related parameters have on the model outcomes, we conducted a sensitivity analysis using the Latin Hypercube Sampling-Partial Rank Correlation Coefficient (LHS-PRCC) method. We generated 1000 samples using the LHS method with uniform distribution and investigated correlation between the samples and model outputs, such as cumulative cases and deaths. The scenario used is total reopening in September. PRCC values above 0 indicate that the parameter is positively correlated to the outcome, indicating that as the parameter value increases, the outcome increases. Conversely, PRCC values below 0 indicate that the parameter and the output are negatively correlated, indicating that as the parameter value increases, the outcome decreases (and vice versa). Parameters with an absolute PRCC value greater than 0.5 are considered significant [[
To further investigate the uncertainty of the model parameters, we projected the hospitalizations under partial reopening using the parameters in the confidence interval. We compared the scenario with highest and lowest coverages (Figure SI4). We observe that with lowest coverages, hospitalizations are much higher than those with maximum coverages in all age groups. We can also observe that within the confidence interval, the mean value (solid lines) follows the trend of the confidence interval, hence we use the mean values to generate our projections.
We investigated the effective reproduction number (
We observe that, with high level of restrictions, the reproduction number remains below 1 if at least 50% of adults aged 20- 59 are vaccinated (see Figure SI5A). If current contacts are increased by 50% and PP behaviors are in place, the reproduction number remains below 1 if a minimum coverage of 90% is achieved in both the age groups 20–39 and 40–59 years (see SI Figure SI5B). On the other hand, if total reopening or pre-pandemic reopening occurs, at any time, the reproduction number will be above 1, with highest values for pre-pandemic reopening (see Figure SI5C-D).
The figures in the following sections represent the percentage change of the shown scenario with respect to the baseline case, defined as the minimum coverages of each sub-populations and no reopening scenario (see Figure SI3).
Figure 2 shows the percentage change of cumulative cases and deaths by the end of December 2021, with respect to the baseline in Figure SI3, when partial reopening occurs on September 15. In general, when efforts are mainly put into vaccinating the 10–19 years age group (Fig. 2A), the change in cases does not appear to be significant, unless individuals in the 20–39 years age group reach a higher coverage. For example, with a 60% coverage of the 20–39 age group, if vaccine coverage in the youngest group is increased from 20 to 40%, cases are reduced from 55.6% to 55.5%. If the youngest age group is at minimum coverage (i.e., 20%), the cumulative cases remarkably decrease as the coverage of age groups 20–39 years and 40–59 years increase (Fig. 2B). We observe that if 20–39- and 40–59-years groups are vaccinated above 80%, the increase from the baseline varies between 2.95% and -3.25%. If the 20–39 age group reaches 80% coverage, then increasing the coverage of the 40–59 age group from 70 to 80% or 90% reduces cases by 74% and 128%, respectively.
Graph: Fig. 2 Percentage change of cumulative cases and deaths with respect to the baseline no reopening in SI Figure SI3 with partial reopening in September, when age groups 60–79 and 80 + reach coverages 80%, 90% by June 14. Cases and deaths are reported comparing different coverages for age group 10–19 years, assuming 40–59 years fixed at 70% coverage and comparing different coverages for age group 40–59 years, assuming 10–19 years fixed at 20% coverage. The second dose is given at a rate of 1/112 days.−1. We observe that the highest increase occurs when the sub-populations' coverage is the minimum level considered. Moreover, keeping adults aged between 50–69 years at 70% and increase the coverages of teenagers does not provide significant reduction in cases nor deaths. On the other hand, the smallest increase is provided by the highest coverage in the two adults age groups
We note that the increase with 30% coverage among teenagers is slightly higher than the ones with 20% coverage. This result is because after June 14 the vaccination process continues until the total eligible population reaches 80%. If we increase the vaccination rate of the 10–19 age group, the total coverage is reached earlier leaving some age groups still susceptible. In particular, the age group 40–59 years will not reach sufficient coverage to prevent the increase of cases.
The results for cumulative deaths are similar to those for cumulative cases. Since the elderly population is already highly vaccinated, it is important to focus on the immunization of the age groups 20–39 and 40–59 years reach at least 80% coverage to reduce deaths after reopening.
Figure 3 shows hospitalizations under the scenario of partial reopening in September, if 60%-80% of the 20–39 age group is vaccinated and the 10–19 age group coverage is 20%-40% (A) or the 40–59 age group is 70%-90% (B). In both analyses, we observe an increasing trend of hospitalizations after the reopening, suggesting that a partial reopening strategy is not beneficial. Figure 3 also confirms what we observed in Fig. 2. It appears that the hospitalizations are not significantly reduced if teenagers are vaccinated; however, even with minimum coverage for age group 10–19 years, if age groups 20–39 years and 40–59 years are vaccinated to their maximum coverage, the hospitalization at the end of December will be about 500.
Graph: Fig. 3 Hospitalizations with partial reopening in September (A) if 10–19 is vaccinated 20%-40%, 20–39 60%, 80% and 40–59, 60–79 and 80 + reached coverages 70%, 80%, 90%; (B) if 40–59 is vaccinated 70%-90%, 20–39 60%, 80% and 10–19, 60–79 and 80 + reached coverages 20%, 80%, 90%. The second dose is given at a rate of 1/112 days.−1. Cumulative cases are reported on the figure for reference. The projections of hospitalizations show that even a partial reopening in September will result in resurgence of the infection. From (A), we observe that vaccinating more teenagers and young adults is not statistically beneficial. On the other hand, even with lowest coverage of teenagers (B) if more adults are vaccinated, the hospitalizations from roughly 4000 to 500
From Fig. 4, we immediately observe that if partial reopening occurs in August, cases increase up to 130.2% from the baseline, with a 9.4% increase in the scenario of highest vaccination coverage in the age groups 20–39 and 40–59 years. A partial late reopening is more beneficial than an early one, even with the lowest vaccine coverages (55.6% increase versus 130.2%). A similar pattern is shown with total reopening (Table SI5). On the other hand, we observe that with lifting NPIs to pre-pandemic levels (Table SI5), reopening in August is slightly more beneficial than reopening in September. This is due to the assumption of a fast-waning immunity rate for partially immunized individuals, whereas if reopening occurs later, more individuals become susceptible within the period of pre-reopening, and the infection spreads once NPI's are lifted completely.
Graph: Fig. 4 Percentage change of cumulative cases with respect to the baseline no reopening in SI Figure SI3 with partial reopening in August and September, when age groups 10–19, 60–79 and 80 + reach coverages 20%, 80%, 90%. The second dose is given at a rate of 1/112 days.−1. It is evident that reopening earlier will give a larger increase of cases, even with the highest coverage among adults
From Table SI5 and Table SI6, we also observe that a partial reopening gives the lowest increase of cases and deaths. As the transmission increases (due to higher number of contacts and/or higher probability of transmission like more transmissible variant), the percentage change escalates. This result is given if the reopening occurs in August or in September.
Projections of cumulative deaths show similar results of cumulative cases (Table SI6). However, with a pre-pandemic level reopening in September, if the coverage of 40–59 years age group is above 80%, the deaths are lower than the ones reported with reopening in August.
Hospitalizations are affected by the timing of lifting as well (Fig. 3B and Figure SI6). With minimal coverages in age groups 20–39 years and 40–59 years, the number of hospitalizations changes from 8000 to 4000 at the end of December, with partial reopening in August or in September, respectively. With maximum coverages of these age groups, reopening in September will drop the hospitalization on December 31, by roughly 50%.
With new variants circulating, the vaccine efficacy might be reduced. Figure 5 presents the percentage change of cumulative cases under different NPI lift levels, with the vaccine efficacy against the virus reduced by 10%. We observe that a lower efficacy leads to a large increase of cases, if compared to the highest efficacy analyzed. However, like the previous results, a partial reopening (orange bars) is much more beneficial than the total one (blue bars). Also, reopening to a pre-pandemic level (Table SI6) present the highest increase. However, it is important to mention that as the vaccination coverage of age group 20–39 and 40–59 years increase, cases decrease visibly (from a 84% to 5.8% increase for partial reopening, and 611% to 355% increase for total reopening).
Graph: Fig. 5 Percentage change of cumulative cases with respect to the base line no reopening in SI Figure SI3, reducing efficacy by 10%, with partial reopening when age groups 10–19, 60–79 and 80 + reach coverages 20%, 80%, 90%. A total reopening presents the highest increase compared to the partial reopening (both with lower efficacy and with the base line value). In general, if the vaccine is less efficient, the increase in cases is higher
A reduction of 10% in vaccine efficacy will result in an increase of hospitalizations from roughly 4000 to roughly 5500, with low coverage of vaccination of adults, and from roughly 500 to 1000, with highest coverage of these two groups (Figure SI7).
The percentage change of cumulative deaths is reported in Table SI7. Similar to the cases, a lower vaccine efficacy results in higher reported deaths.
Until the end of May 2021, in Ontario the second dose of vaccine was given after 16 weeks from the first one. Thereafter, this timeframe was shortened to 12 weeks [[
Graph: Fig. 6 Percentage change of cumulative cases with respect to the base line no reopening in SI Figure SI3 with partial reopening in September and second dose given after 21, 50 or 112 days. Age groups 10–19, 60–79 and 80 + are assumed to reach coverages 20%, 80%, 90% by mid June 2021. We observe that reducing the time between the two doses is always beneficial. Also, with 21 days between doses, a decrease of cases is shown even if the age group 20–39 years reaches 60% of coverage, as long as the 40–59 years age group reaches 80%
We observe that a faster rollout of second dose is always beneficial. With minimal coverage of age groups 40–59 years and 20–39 years, if the full immunization is reached after 21 days rather than 50 or 112, the percentage change of cases compared to the baseline drops from 55.6% to 19% to 1.7%. For the highest vaccination coverage, the increase is smaller than the one projected under the no reopening scenario, however a three-week gap between doses is still more beneficial. Also, a better control of the infection is possible even if the coverage of 20–39 years age group is 60% as long as the coverage of age group 40–59 years is 80%. Even with other reopening levels, the reduced time between doses appears to be more beneficial (Table SI8).
Minimizing the time between doses is also advantageous to reduce the number of deaths and hospitalizations (see Table SI9 and Figure SI8). With a partial reopening and minimum vaccine coverages among adults between 20 and 59 years, hospitalizations are decreased by roughly 60% and 85% if the second dose is given after 50 or 21 days respectively instead of 112 days. If the vaccination coverage is the highest, hospitalization at the end of December 2021 will be roughly 0 or 100, if the second dose is given after 21 or 50 days respectively.
Sensitivity analysis conducted on the daily doses and rate at which the second dose is given shows that the model parameters having the highest impact on the cumulative cases, deaths, and hospitalizations 50 days after reopening are the vaccination rates of age groups 20–39 and 40–59 years and the time between doses (Table SI11). In particular, the PRCC values show negative correlation between these parameters and the model outcomes. This result suggests that not only adults need to be targeted to reduce cases, deaths, and hospitalizations, but also reducing the time between doses is beneficial. We also conducted sensitivity analysis of the infection-related parameters, such as number of contacts and age-dependent susceptibility on cumulative cases and deaths (Table SI12). The PRCC values show that contacts and susceptibility in ages 20–39 and 40–59 years have a significantly positive effect on the model outcomes.
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 [[
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 [[
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 [[
We would like to acknowledge Toronto Public Health for the use of case and vaccination data in this study.
Research design: H.Z., E.A., P.Y., Y.T., E.G., S.C; Literature search: E.A., P.Y., Y.T.; Data collection: E.A., P.Y., Y.T; Modeling: H.Z. and all; Model analysis: E.A., P.Y., Y.T.; Simulations: E.A., P.Y., Y.T; Draft preparation: E.A., P.Y., Y.T, H.Z.; Writing reviewing-editing: H.Z., E.A., P.Y, Y.T., E.G., I.M., J.B., J.W., S.C., J.A., Supervision: H.Z. The author(s) read and approved the final manuscript.
This research was supported by the One Health Modelling Network for Emerging Infections (OMNI), a Canadian NSERC and PHAC Emerging Infectious Diseases Modelling Initiative (HZ, EA, PY, YT, IM, JA, JB, JW). This research was also supported by the Canadian Institutes of Health Research (CIHR), Canadian COVID-19 Math Modelling Task Force (JA, JB, JW, HZ), the Natural Sciences and Engineering Research Council of Canada (JA, JB, JW, IM, HZ) and York University Research Chair program (HZ).
The datasets generated and/or analysed during the current study are available in the Covid_vaccine_NPIs_paper repository, https://github.com/EAruffo/Covid%5fvaccine%5fNPIs%5fpaper.git Parameters used to generate analyses are provided in Supplementary Information.
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The authors declare that they have no competing interests.
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By Elena Aruffo; Pei Yuan; Yi Tan; Evgenia Gatov; Iain Moyles; Jacques Bélair; James Watmough; Sarah Collier; Julien Arino and Huaiping Zhu
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