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: Short-term forecasts for the UK, Contact tracing to control the early outbreak, Potential exit strategies, School reopening, Social Bubbles, Forecasts for Kenya, and Global predictions of transmission potential.
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.
|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, ISARIC4C Investigators, Tildesley, M. J. and Hill, E.M. (2020) “Fitting models to the COVID-19 outbreak and estimating R” medRxiv https://doi.org/10.1101/2020.08.04.20163782
Contact tracing together with testing is viewed as a necessary tool in the relaxation of lockdown methods. Work by SBIDER, in collaboration with Oxford and Lancaster Universities, considered the use of contact tracing in the early stages of the outbreak as a means of controlling or containing the pandemic in the UK.
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)" medRxiv. https://doi.org/10.1101/2020.02.14.20023036
(to appear in 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" medRxiv
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. (2020). "The impact of school reopening on the spread of COVID-19 in England" medRxiv
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-Covid0-19 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" medRxiv.
Matt Keeling (Professor, Maths & SLS)
Louise Dyson (Assistant Professor, Maths & SLS)
Ed Hill (PDRA, Maths & SLS)
Mike Tildesley (Associate Professor, 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)
Hector McKimm (OxWaSP PhD student)
Massimiliano Tamborrino (Assistant Professor, Statistics)
Emma Southall (MathSys PhD student)
Andrea Parisi (PDRA, Life Sciences)
Ben Atkins (PDRA, Maths)