Skip to main content Skip to navigation


VaccineVaccination has had a huge impact on the pandemic in the UK. The initial roll-out of vaccine began in December of 2020 and has dramatically reduced the number of cases while having an even larger effect on hospital admissions and deaths. Modelling and analysis from the Zeeman Institute has been key in underpinning JCVI decisions on vaccination, from early priority ordering to the deployment of booster doses, and in understanding how vaccines and non-pharmaceutical interventions interact.

Our publications and pre-prints on vaccination against COVID are:

Sam Moore, Edward M. Hill, Louise Dyson, Michael J. Tildesley, Matt J. Keeling (2021) The impacts of increased global vaccine sharing on the COVID-19 pandemic; a retrospective modelling study medRxiv  DOI: 10.1101/2022.01.26.22269877

We use an age-structured model of SARS-CoV-2 dynamics, matched to national data from 152 countries, to investigate the global impact of different vaccine sharing protocols during 2021. We assume a direct relationship between the emergence of variants with increased transmissibility and the cumulative amount of global infection, such that lower global prevalence leads to a lower reproductive number within each country. We compare five vaccine sharing scenarios, from the current situation, through sharing once a particular within-country threshold is reached (e.g. all over 40s have received 2 doses), to full sharing where all countries achieve equal age-dependent vaccine deployment.

Compared to the observed distribution of vaccine uptake, we estimate full vaccine sharing would have generated a 1.5% (PI -0.1 - 4.5%) reduction in infections and a 11.3% (PI 0.6 - 23.2%) reduction in mortality globally by January 2022. The greatest benefit of vaccine sharing would have been experienced by low and middle income countries, who see an average 5.2% (PI 2.5% - 10.4%) infection reduction and 26.8% (PI 24.1% - 31.3%) mortality reduction. Many high income countries, that have had high vaccine uptake (most notably Canada, Chile, UK and USA), suffer increased infections and mortality under most of the sharing protocols investigated, assuming no other counter measures had been taken. However, if reductions in vaccine supply in these countries had been offset by prolonged use of non-pharmaceutical intervention measures, we predict far greater reductions in global infection and mortality of 64.5% (PI 62.6% - 65.4%) and 62.8% (PI 44.0% - 76.3%), respectively.



Keeling, M.J., Moore, S. (2022) "An assessment of the vaccination of school-aged children in England" BMC Medicine 20 196.

Vaccinating 12-17 year oldsVaccination, initially targeting the elderly and vulnerable but later expanded to the entire adult population, has been transformative in the control of SARS-CoV-2 in England. However, early concerns over adverse events and the lower risk associated with infection in younger individuals means that the expansion of the vaccine programme to those under 18 year of age needs to be rigorously and quantitatively assessed. In this paper we use a bespoke mathematical model matched to case and hospital data for England to calculate the potential impact of vaccinating 12-17 and 5-11 year olds. Projections generated in June 2021 suggested that an expansion of the vaccine programme to those 12-17 years old could generate substantial reductions in infection, hospital admission and deaths in the entire population, depending on population behaviour following the relaxation of control measures. The benefits within the 12-17 year old cohort were less marked, saving between 656 and 1077 (95% prediction interval 281-2260) hospital admissions and between 22 and 38 (95% PI 9-91) deaths depending on assumed population behaviour. For the more recent model formulation (November 2021), the benefits within this age group are reduced, saving on average 631 (95% PI 304-1286) hospital admissions and 11 (95% PI 5-28) deaths for 80% vaccine uptake, while the benefits to the wider population represent a reduction of 8-10% in hospital admissions and deaths. The vaccination of 5-11 year olds is projected to have a far smaller impact, in part due to the later roll-out of vaccines to this age-group.


Keeling, M.J., Thomas, A., Hill, E.M., Thompson, R.N., Dyson, L., Tildesley, M.J., Moore, S. (2021) "Waning, Boosting and a Path to Endemicity for SARS-CoV-2" medRxiv.

Waning and BoostersIn many countries, an extensive vaccination programme has substantially reduced the public-health impact of SARS-CoV-2, limiting the number of hospital admissions and deaths compared to an unmitigated epidemic. The observed waning of vaccine efficacy over time suggests that booster doses may be required to maintain population immunity especially in the most vulnerable groups. Here, using data and models for England, we consider the dynamics of COVID-19 over a two-year time-frame, and the role that booster vaccinations can play in mitigating the worst effects. Although formulated for the Delta variant, this paper has key implications for Omicron.


Hill, E.M., Keeling, M.J. (2021) "Comparison between one and two dose SARS-CoV-2 vaccine prioritization for a fixed number of vaccine doses" Interface. 18(182): 20210214.

Focusing on data from England, we investigated prioritisation of a one dose or two dose SARS-CoV-2 vaccination schedule given a fixed number of vaccine doses and with respect to a measure of maximising averted deaths. This work highlighted the advantage of a longer separation between first and second, as it enables more vulnerable people to be protected early in the epidemic, and therefore reduces hospital admissions and deaths from the pandemic.

Gog JR, Hill EM, Danon L, Thompson RN. (2021) Vaccine escape in a heterogeneous population: insights for SARS-CoV-2 from a simple model Roy. Soc. Open Sci., 8:210530. DOI: 10.1098/rsos.210530

By developing and analysing a mathematical model of two population groupings with differing vulnerability and contact rates, this paper explores the impact of the deployment of vaccines among the population on the reproduction ratio, cases, disease abundance and vaccine escape pressure. The results from this model illustrate two insights: (i) vaccination aimed at reducing prevalence could be more effective at reducing disease than directly vaccinating the vulnerable; (ii) the highest risk for vaccine escape can occur at intermediate levels of vaccination. This work demonstrates a key principle: the careful targeting of vaccines towards particular population groups could reduce disease as much as possible while limiting the risk of vaccine escape.

Moore, S., Hill, E.M., Tildesley, M., Dyson, L., Keeling, M.J. (2021) "Vaccination and non-pharmaceutical interventions for COVID-19: a mathematical modelling study " Lancet Infectious Diseases. 21(6): 793-802.

By combining models of vaccination with the methods of forwards projection, we considered the interaction between the relaxation of non-pharamaceutical interventions (NPIs) and the protection offered by the vaccine.

This paper set the tone for unlocking the UK in 2021: Our modelled scenarios highlighted the risks associated with early or rapid relaxation of NPIs, stressing the need for slow release of control measures if large-scale waves of infection are to be avoided.

We conclude that while the 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.


Moore, S., Hill, E.M., Dyson, L., Tildesley, M., Keeling, M.J. (2021) "Modelling optimal vaccination strategy for SARS-CoV-2 in the UKLink opens in a new window" PLoS Comp. Biol. 17(5): e1008849.

In an early extension to the Warwick COVID model, we introduced a vaccinated class and a population with health conditions that are believed to have a significant impact on COVID-19 outcomes. At the time a number of different vaccine candidates were in development and the results from clinical trials were not fully available, leading to a large degree of uncertainty regarding the performance of these products. We therefore tested a range of efficacies (including reduced efficacy in the elderly) and three different types of vaccine each delivering a different level of protection.

This paper highlighted the importance of prioritising vaccination towards the oldest and most vulnerable in the population, as this generates the maximum reduction in deaths and other severe outcomes.

Figure: Impact of vaccination targeted at different age-groups. Orange: targeting by age, the optimal is to vaccinate the oldest age groups first. Purple: including co-morbidities, these are optimally ordered between 60 and 80 year olds. Blue: random vaccination.

See our introductory articles on "Who should be vaccinated first?" and "Vaccination: Where do we stand and where are we going?" courtesy of our friends at +plus magazine.