Vaccination and non-pharmaceutical interventions for COVID-19: a mathematical modelling study

Abstract

Background: The dynamics of vaccination against SARS-CoV-2 are complicated by age-dependent factors, changing levels of infection, and the relaxation of non-pharmaceutical interventions (NPIs) as the perceived risk declines, necessitating the use of mathematical models. Our aims were to use epidemiological data from the UK together with estimates of vaccine efficacy to predict the possible long-term dynamics of SARS-CoV-2 under the planned vaccine rollout.

Methods: In this study, we used a mathematical model structured by age and UK region, fitted to a range of epidemiological data in the UK, which incorporated the planned rollout of a two-dose vaccination programme (doses 12 weeks apart, protection onset 14 days after vaccination). We assumed default vaccine uptake of 95% in those aged 80 years and older, 85% in those aged 50-79 years, and 75% in those aged 18-49 years, and then varied uptake optimistically and pessimistically. Vaccine efficacy against symptomatic disease was assumed to be 88% on the basis of Pfizer-BioNTech and Oxford-AstraZeneca vaccines being administered in the UK, and protection against infection was varied from 0% to 85%. We considered the combined interaction of the UK vaccination programme with multiple potential future relaxations (or removals) of NPIs, to predict the reproduction number (R) and pattern of daily deaths and hospital admissions due to COVID-19 from January, 2021, to January, 2024.

Findings: We estimate that vaccination alone is insufficient to contain the outbreak. In the absence of NPIs, even with our most optimistic assumption that the vaccine will prevent 85% of infections, we estimate R to be 1·58 (95% credible intervals [CI] 1·36-1·84) once all eligible adults have been offered both doses of the vaccine. Under the default uptake scenario, removal of all NPIs once the vaccination programme is complete is predicted to lead to 21 400 deaths (95% CI 1400-55 100) due to COVID-19 for a vaccine that prevents 85% of infections, although this number increases to 96 700 deaths (51 800-173 200) if the vaccine only prevents 60% of infections. Although vaccination substantially reduces total deaths, it only provides partial protection for the individual; we estimate that, for the default uptake scenario and 60% protection against infection, 48·3% (95% CI 48·1-48·5) and 16·0% (15·7-16·3) of deaths will be in individuals who have received one or two doses of the vaccine, respectively.

Interpretation: For all vaccination scenarios we investigated, our predictions highlight the risks associated with early or rapid relaxation of NPIs. Although novel vaccines against SARS-CoV-2 offer a potential exit strategy for the pandemic, success is highly contingent on the precise vaccine properties and population uptake, both of which need to be carefully monitored.

Funding: National Institute for Health Research, Medical Research Council, and UK Research and Innovation.

Figure 1

Scheduling and impact of vaccine uptake (A) Assumed vaccine uptake over time, showing the number of vaccines given to each age group relative to the theoretical maximum when each person receives two doses. The non-linear spacing in the total number of doses occurred due to our assumption that an 84-day separation between first and second doses would be maintained throughout the entirety of the vaccination programme. (B) Estimated R for a given number of administered vaccine doses, ignoring any additional increase in immunity from natural infection (after Jan 29, 2021) and excluding any effect on contact patterns resulting from NPIs. Other values of R₀ would introduce a relative scaling of the predictions. NPIs=non-pharmaceutical interventions. R=effective reproduction number.

Figure 2

Predicted daily deaths from COVID-19 in the UK after the start of an immunisation programme and relaxation or removal of NPIs Shading indicates the level of NPIs implemented. (A, B) The effect of relaxing current NPI measures down to those implemented in early September, 2020. The dashed line indicates the point of partial NPI relaxation—February, 2021, in panel A and April, 2021, in panel B. (C, D) The total effect (cumulative deaths) of different patterns of releasing NPIs. The central black bar represents the default uptake scenario, whereas the upper and lower edges of the box correspond to the pessimistic and optimistic uptake scenarios. Panel C follows the pattern in panels A and B, reducing NPIs to September, 2020, levels at a given date and calculating the number of deaths due to COVID-19 from Jan 1, 2021. Panel D keeps all NPIs in place until January, 2022, such that the vaccination programme is complete and then models the effect of complete removal of all controls. (E, F) Correspond to gradual reduction in NPIs from their maximum in January, 2021, until removal of all control measures. Results of all figure panels are the mean of 500 simulations that explore the inferred parameter values, and totals are calculated until Jan 1, 2024. NPIs=non-pharmaceutical interventions.

Figure 3

Characterisation of disease dynamics in terms of vaccine status as a function of the number of doses delivered so far (A) Composition of the entire population. (B) Number of daily deaths due to COVID-19. (C) Proportion of COVID-19 deaths. For all panels, we display simulations assuming: 95%, 85% and 75% uptake for those ≥80 years, aged 50–79 years, and aged 18–49, respectively; 60% protection against infection; and with a moderate reduction in NPIs at the start of February, 2021. Results are the mean of 500 simulations that explore the inferred parameter values.