Members of the Zeeman Institute are contributing to the COVID-19 modelling response, both in the UK and abroad. This page details the research undertaken by the Zeeman Institute.
Our work includes:
Our group supports the UK response to COVID-19 through membership of the Scientific Pandemic Influenza Group on Modelling (SPI-M), an expert group advising the Scientific Advisory Group for Emergencies (SAGE). Scientific evidence supporting the UK government response to COVID-19 can be found on the SAGE website, including modelling inputs and reports from SPI-M to SAGE.
Of particular note are the series of documents from February to July that have provided the scientific projections that are part of the roadmap to relaxation. These can be found on the government's SAGE web page: February Roadmap; March Roadmap; May Roadmap; June Roadmap; July Roadmap.
|Figure right shows how the short-term predictions from the Warwick model have changed over time for deaths in the Midlands. While it is clear that early forecasts were extremely pessimistic (as the impact of the lockdown was unknown), later forecasts are in far better agreement with the data and give us considerable certainty on the likely course of the epidemic over the next 2-3 weeks.|
|Keeling, M.J., Dyson, L., Guyver-Fletcher, G., Holmes, A., Semple, M.G., ISASIC4C Investigators, Tildesley, M.J. & Hill, E.M. (2020) Fitting to the UK COVID-19 outbreak, short-term forecasts and estimating the reproductive number medRxiv https://doi.org/10.1101/2020.08.04.20163782|
Contact tracing before the implementation of social distancing and lockdown measures.
The top figure shows a cartoon of contact tracing around a central infected figure (blue); some individuals are known to the index case and match the tracing criteria (green), others are known but contact time is considered too short (grey), but some contacts are unknown and hence untraceable (orange).
Before lockdown, each person had many contacts that were made over a 7-day period (mean contacts 216, mean contacts to trace 36), so contact tracing logistics could soon be overwhelmed with just a few infectious cases.
If we are able to trace all the contacts meeting the close contact definition, then our results show that an outbreak could be contained, although the "untraceable" contacts could still give rise to a low number of secondary cases.
| Keeling, M.J., Hollingsworth, T.D. & Read, J.M. (2020) "The Efficacy of Contact Tracing for the Containment of the 2019 Novel Coronavirus (COVID-19)" J. Epidemiology & Community Health http://dx.doi.org/10.1136/jech
The Warwick model for COVID-19 is a deterministic, age-structured, compartmental model in which the population is stratified into susceptibles (uninfected), exposed (infected, but not yet infectious), infectious and recovered. Infectious individuals may be either symptomatic (detectable) or asymptomatic (undetectable), and asymptomatic infections are assumed to transmit at a reduced rate. Further details regarding the model may be found in Keeling et al. (2020, medRxiv).
Figure above. The flow through the multiple sections of the compartmental model, from susceptible to exposed, to either symptomatic or asymptomatic, to ultimately recovered.
Figure right. Examples of epidemic trajectories following different relaxations of lockdown for 2020 and lockdown in 2021. Very rapid relaxation leads to a pronounced early peak, whereas tight controls leads to a later peak in when controls are lifted in 2021.
In this paper we also focus on potential exit strategies, such as different changes to the early lock-down restrictions, age-based easing of the lockdown and basing the lockdown on local ICU capacity. We conclude that any route out of lockdown that does not involve pharmaceutical interventions (such as vaccination) has be be very slow and measured.
|Keeling, M. J., Hill, E., Gorsich, E., Penman, B., Guyver-Fletcher, G., Holmes, A., McKimm, H., Tamborrino, M, Dyson, L., and Tildesley, M. (2020). "Predictions of COVID-19 dynamics in the UK: short-term forecasting and analysis of potential exit strategies" PLoS Comput Biol 17(1): e1008619. https://doi.org/10.1371/journal.pcbi.1008619|
We have used the Warwick COVID model for the UK to investigate potential scenarios for reopening schools in England. We consider different combinations of years returning to school, including the potential for teaching students in smaller classes which reduces infection risk. We find that, on its own, returning children to school is unlikely to lead to a second wave of infection, however there remains uncertainty if other measures are relaxed simultaneously.
Even if R remains below one, any return of children to school will inevitably lead to some increase in transmission and therefore to an increase in cases, ICU admissions and, regrettably, deaths. We find that secondary school students returning leads to higher increases than if only primary schools reopen, though in all scenarios the magnitude of changes depends upon the wider context when the reopening of schools occurs. This can be seen in the figure above: if transmission in the general community increases, this alone increases cases (faded colours) and exacerbates the increases seen in by school reopening (solid colours). However the size of the increase due to schools returning is much smaller than the increase due directly to the increase in community transmission. More detail may be found in our preprint below. Please note that this work has not yet been peer reviewed.
|Keeling, M. J., Tildesley, M. J., Atkins, B. D., Penman, B., Southall, E., Guyver-Fletcher, G., Holmes, A., McKimm, H., Gorsich, E., Hill, E. M., and Dyson, L. (2021). "The impact of school reopening on the spread of COVID-19 in England"Philosophical Transactions of the Royal Society B. 376(1829): 20200261.|
Follow-up work has analysed data on pupil and staff absences due to confirmed COVID-19 infection during September-December 2020.
There has also been the development of an individual-based model formed of exclusive year group bubbles to simulate infections over the course of a seven-week half-term, which was used to compare impact of differing isolation and rapid test strategies on transmission, absences, and testing volume. We then subsequently fit the individual-based model of secondary schools to community swab testing data and secondary school absences data, simulating outbreaks from 31st Aug 2020 - 21st May 2021 to quantify SARS-CoV-2 transmission in secondary schools in England. With this fitted model, we explored the impact of twice weekly lateral flow testing (LFT) of pupils on transmission, alternative strategies to isolation of close contacts that could reduce absences and the benefit of higher LFT uptake in pupils
In an extension to the Warwick COVID model, we introduce a vaccinated class and a population with health conditions that are believed to have a significant impact on COVID-19 outcomes.
A number of different vaccine candidates are in development, resulting in a large degree of uncertainty regarding the performance of these products. We therefore tested a range of efficacies (including reduced efficacy in the elderly) for three different types of vaccine each delivering a different level of protection:
- Type 1: generates reduced susceptibility, preventing infection and onward transmission;
- Type 2: generates reduced probability of becoming symptomatic, and hence partially reduces onward transmission;
- Type 3: generates a reduced probability in experiencing severe symptoms, but has no impact on epidemiological spread.
|Figure Left: impact of vaccination on 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.
|Moore, S., Hill, E.M., Dyson, L., Tildesley, M., Keeling, M.J. (2021) "Modelling optimal vaccination strategy for SARS-CoV-2 in the UK" PLOS Computational Biology 17(5): e1008849.|
Follow-up work has considered the interaction between the UK two-dose vaccination programme and future relaxation (or removal) of NPIs. Our predictions highlight the population-level risks of early relaxation leading to a pronounced wave of infections, and the individual-level risk relative to vaccine status.
|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. https://doi.org/10.1016/S1473-3099(21)00143-2|
Focusing on data from England, we also 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.
|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"|
The higher education system in the United Kingdom comprises a large student population. Therefore, in the setting of the COVID-19 pandemic bringing together these student communities presents questions regarding the strength of interventions required to control transmission. We constructed a network-based model to capture the interactions of a student population in different settings within a university environment (housing, social and study) and ran an SEIR type epidemic process.
Infection and isolation epidemiological measures over the autumn term under differing levels of adherence to nonpharmaceutical interventions.
Top figure: Proportion infected
Bottom figure: Proportion of time adhering students spend in isolation.
Distributions relative to students resident on-campus only (green violin plots), students resident off-campus only (orange violin plots) and to the overall student population (purple violin plots).
The white markers denote medians and solid black lines span the 25th to 75th percentiles.
Our work shows high adherence to isolation guidance and effective contact tracing both curbed transmission and reduced the expected time an adhering student would spend in isolation. Irrespective of the adherence to isolation measures, on average a higher proportion of students resident on-campus became infected compared with students resident off-campus. Room isolation as an additional intervention generated minimal benefits. Finally, a one-off mass-testing instance would not drastically reduce the term-long case load or end-of-term prevalence, but regular weekly or fortnightly testing could reduce both measures by more than 50% (compared to having no mass testing).
Hill, E.M., Atkins, B.D., Keeling, M.J., Tildesley, M., Dyson, L. (2021) "Modelling SARS-CoV-2 transmission in a UK university setting" Epidemics 36: 100476.
As part of a concerted pandemic response to protect public health, businesses can enact non-pharmaceutical controls to minimise exposure to pathogens in workplaces and premises open to the public. Amendments to working practices can lead to the amount, duration and/or proximity of interactions being changed, ultimately altering the dynamics of disease spread. We used an individual-based network model to analyse transmission of SARS-CoV-2 amongst a working population that was stratified into work sectors.
Infectious case prevalence, isolation and effective reproduction number temporal profiles under alternative worker practices and scheduling. Lighter intensities correspond to: a higher fraction of workers working from home (ranging from 0 to 1; left column); a greater number of days per week being spent working from home rather than spent at the workplace (ranging from 0 days to 5 days; central and right column).
Our study found the progress of an outbreak to be significantly hindered by instructing a significant proportion of the workforce to work from home. Furthermore, asynchronous work patterns may help to reduce infections when compared with scenarios where all workers work on the same days, particularly for longer working weeks. Finally, smaller work teams and a greater reduction in transmission risk led to a flatter temporal profile for both infections and the number of people isolating, and reduced the probability of large, long outbreaks.
Hill, E.M., Atkins, B.D., Keeling, M.J., Dyson, L., Tildesley, M. (2021) "A network modelling approach to assess non-pharmaceutical disease controls in a worker population: An application to SARS-CoV-2" PLoS Comput Biol 17(6): e1009058.
Social bubbles have been proposed as a means of allowing extended contacts beyond the household while minimising the associated transmission risks. The concept is that members of one household are allowed to meet exclusively with members of one other household - while this increases the risk of transmission the premise is that the bubble remains relatively isolated.
Left: examples of how households and social bubbles can be captured by a next generation matrix.
Above: relative increase in fatalities and the reproductive number, R, due to different types of social bubble (Scenarios 1-6) and other forms of increased social interaction (C2 & C3).
Our modelling work shows that social bubbles reduced cases and fatalities by 17% compared to an unclustered increase of contacts. Social bubbles may be extremely effective if targeted towards those small isolated households with the greatest need for additional social interactions and support.
Leng, T., White, C., Hilton, J., Kucharski, A., Pellis, L., Stage, H., Davies, N., CMMID-Covid-19 WG, Keeling, M.J., Flasche, S. (2020) The effectiveness of social bubbles as part of a Covid-19 lockdown exit strategy, a modelling study
To investigate COVID-19 in Kenya, we developed KenyaCoV, a spatial- and age-structure stochastic model of SARS-CoV-2 transmission in Kenya. Epidemiological characteristics of SARS-CoV-2 were drawn from the literature, while the rate of contact between individuals currently in the same region was drawn from an estimated age-mixing contact matrix from Prem et al., 2017. Other modelling information may be found in Brand et al., 2020, and code and open source data may be found at https://github.com/SamuelBrand1/KenyaCoV.
We find that, if within-Kenya transmission becomes established, it is crucial to identify the role of asymptomatically infected individuals. If asymptomatically infected individuals transmit significantly we predict that the subsequent epidemic cannot be contained by case isolation alone, with the potential for a large proportion of the population becoming infected. Conversely, in a scenario in which undetected infections are not infectious, self-isolation may be sufficient to contain the epidemic. Unfortunately in all simulations including some asymptomatic transmission, case isolation was found to be insufficient to prevent a major outbreak or to substantially delay the peak or reduce total cases.
Brand, S. P., Aziza, R., Kombe, I. K., Agoti, C. N., Hilton, J., Rock, K. S., Parisi, A., Nokes, D.J., Keeling, M., and Barasa, E. (2020). "Forecasting the scale of the COVID-19 epidemic in Kenya". medRxiv.
The value of the basic reproductive ratio, R0, changes both according to the epidemiological characteristics of the virus, but also the context in which it spreads. Since susceptibility and transmission of COVID-19 changes with the age of the individual, the age-structure of the population can have a big effect on the value of R0. This work examines the risk posed by COVID-19 in different areas of the world. For some parameter choices (see below), the large proportion of children in Africa effectively buffer transmission leading to a much lower R0; notably under these parameters Italy is an obvious hot-spot while Germany has the lowest transmission in Europe.
Hilton, J., and Keeling, M. J. (2020). " Estimation of country-level basic reproductive ratios for novel Coronavirus (COVID-19) using synthetic contact matrices"
When cases of COVID-19 are rising exponentially, we consider the impact of a short 2-week period of intense control. Using two different modelling approaches we show that a short, sharp 2-week break leads to a decline in cases, with similar declines in hospitalisation and mortality over a short period - this could potentially reduce the acute load on the NHS enabling it to continue non-COVID care into the winter months.
A two-week precautionary break during half time reduces infection (left) and introduces a temporal reset (right). We consider a range of control strengths during the break (lines from red to blue), and a range of growth rates outside of the precautionary break (x-axis).
A precautionary break is not a lasting control measure, but effectively buys more time to put other controls in place; it takes us ‘back to a time when cases were lower’. To save lives over longer time scales requires driving R below one.
The reduction in cases also allows measures which are resource limited (such as test-trace-and-isolate) to potentially have a greater impact.
Keeling, M.J., Guyver-Fletcher, G, Holmes, A., Dyson, L., Tildesley, M.J., Hill, E.M. and Medley, G.F. (2020) medRxiv. Precautionary breaks: planned, limited duration circuit breaks to control the prevalence of COVID-19.
Here, we analyse 208 publicly available SARS-CoV-2 genome sequences collected during the early outbreak phase. We combine phylogenetic analysis with Bayesian inference under an epidemiological model to trace person-to-person transmission. The dispersion parameter of the offspring distribution in the inferred transmission chain was estimated to be 0.23 (95% CI: 0.13–0.38), indicating there are individuals who directly infected a disproportionately large number of people. Our results showed that super-spreading events played an important role in the early stage of the COVID-19 outbreak.
Wang, L., Didelot, X., Yang, J., Wong, G., Shi, Y., Liu, W., Gao, G.F. and Bi, Y. (2020) "Inference of person-to-person transmission of COVID-19 reveals hidden super-spreading events during the early outbreak phase" Nature Communications 11 5006.
Fountain-Jones, N.M., Appaw, R.C., Carver, S., Didelot, X., Volz, E. and Charleston M. (2020) Emerging phylogenetic structure of the SARS-CoV-2 pandemic. Virus Evolution 6 veaa082 https://doi.org/10.1093/ve/veaa082
As the COVID-19 pandemic continues there is an ever-present risk of more variants of concern (VOCs) arising. These VOCs may have beneficial mutations aiding their spread. Quickly assessing a substantial change in the risk of infection, morbidity and mortality posed by a new SARS-CoV-2 variant is challenging, with no simple relationship to describe the interactions between any novel variant, disease control policy, adherence to interventions and the historic patterns of infection and vaccination.
Nevertheless, countering the emergence and establishment of a problematic VOC requires rapid early detection and a swift public health response to extinguish infection clusters. Close monitoring of the evolution of SARS-CoV-2 across a range of geographical scales is needed to enhance local situational awareness and quantify risk from VOCs. In conjunction, mathematical models, matched to epidemic data, remain a contributory public health tool for both assessing new threats and for scoping potential dangers.
We used three mathematical models to examine the potential drivers of SARS-CoV-2 VOC epidemics in England. We found epidemiological trajectories for putative VOCs are wide-ranging and dependent on their transmissibility, immune escape capability, and the introduction timing of a postulated VOC-targeted vaccine. In particular, a variant that is less transmissible, but shows partial immune-escape, could provoke a wave of infection that would not be revealed until control measures are further relaxed.
Louise Dyson, Edward M Hill , Sam Moore, Jacob Curran-Sebastian, Michael J Tildesley, Katrina A Lythgoe, Thomas House, Lorenzo Pellis, Matt J Keeling. (2021) "Possible future waves of SARS-CoV-2 infection generated by variants of concern with a range of characteristics" Nature Communications 12: 5370.
Infection burden for illustrative variant of concern (VOC) scenarios, produced using a non-age structured, two-strain SEIR-type SARS-CoV-2 transmission model. In panels a and c, we considered three putative VOCs with differing transmissibility and immune-escape characteristics: more transmissible (VOC MT, blue line with square markers), equal transmissibility with immune escape (VOC E, orange line with plus sign markers), less transmissible with immune escape (VOC LT+E, yellow line with circle markers). We also present temporal dynamics for resident variants in the absence of any VOC being introduced (black line with no markers). a VOC infectious prevalence over time. In each scenario, alongside resident variants, we introduced one of the VOCs on 17th May 2021 with 2000 initial infecteds. c Instantaneous R of a VOC accounting for population-level immunity (y axis) calculated at the time of its introduction (x axis). In panels b and d, we explored the sensitivity of two epidemiological outcomes to the relative transmissibility of the VOC compared with resident variants and the proportional efficacy (vaccine and natural immunity) against the VOC: b outbreak final size; d peak in VOC-infection cases.
Matt Keeling (Professor, Maths & SLS)
Louise Dyson (Associate Professor, Maths & SLS)
Ed Hill (PDRA, Maths & SLS)
Mike Tildesley (Reader, Maths & SLS)
Erin Gorsich (Assistant Professor, Life Sciences)
Bridget Penman (Assistant Professor, Life Sciences)
Sam Brand (PDRA, Life Sciences)
Rabia Aziza (PDRA, Life Sciences)
Joe Hilton (PDRA, Maths & SLS)
James Nokes (Professor, Life Sciences)
Glen Guyver-Fletcher (PhD student, MIBTP)
Alex Holmes (MathSys PhD student)
Trystan Leng (MathSys PhD student)
Massimiliano Tamborrino (Assistant Professor, Statistics)
Emma Southall (MathSys PhD student)
Ben Atkins (PDRA, Maths)
Sam Moore (PDRA, Maths)
Hector McKimm (OxWaSP PhD student)
Andrea Parisi (PDRA, Life Sciences)