Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Research Postgraduate







Huxley BuildingSouth Kensington Campus





Publication Type

7 results found

Unwin H, Mishra S, Bradley V, Gandy A, Mellan T, Coupland H, Ish-Horowicz J, Vollmer M, Whittaker C, Filippi S, Xi X, Monod M, Ratmann O, Hutchinson M, Valka F, Zhu H, Hawryluk I, Milton P, Ainslie K, Baguelin M, Boonyasiri A, Brazeau N, Cattarino L, Cucunuba Z, Cuomo-Dannenburg G, Dorigatti I, Eales O, Eaton J, van Elsland S, Fitzjohn R, Gaythorpe K, Green W, Hinsley W, Jeffrey B, Knock E, Laydon D, Lees J, Nedjati-Gilani G, Nouvellet P, Okell L, Parag K, Siveroni I, Thompson H, Walker P, Walters C, Watson O, Whittles L, Ghani A, Ferguson N, Riley S, Donnelly C, Bhatt S, Flaxman Set al., 2020, State-level tracking of COVID-19 in the United States, Nature Communications, Vol: 11, Pages: 1-9, ISSN: 2041-1723

As of 1st June 2020, the US Centers for Disease Control and Prevention reported 104,232 confirmed or probable COVID-19-related deaths in the US. This was more than twice the number of deaths reported in the next most severely impacted country. We jointly model the US epidemic at the state-level, using publicly available deathdata within a Bayesian hierarchical semi-mechanistic framework. For each state, we estimate the number of individuals that have been infected, the number of individuals that are currently infectious and the time-varying reproduction number (the average number of secondary infections caused by an infected person). We use changes in mobility to capture the impact that non-pharmaceutical interventions and other behaviour changes have on therate of transmission of SARS-CoV-2. We estimate thatRtwas only below one in 23 states on 1st June. We also estimate that 3.7% [3.4%-4.0%] of the total population of the US had been infected, with wide variation between states, and approximately 0.01% of the population was infectious. We demonstrate good 3 week model forecasts of deaths with low error and good coverage of our credible intervals.

Journal article

Monod M, Blenkinsop A, Xi X, Herbert D, Bershan S, Tietze S, Bradley V, Chen Y, Coupland H, Filippi S, Ish-Horowicz J, McManus M, Mellan T, Gandy A, Hutchinson M, Unwin H, Vollmer M, Weber S, Zhu H, Bezancon A, Ferguson N, Mishra S, Flaxman S, Bhatt S, Ratmann O, Ainslie K, Baguelin M, Boonyasiri A, Boyd O, Cattarino L, Cooper L, Cucunuba Perez Z, Cuomo-Dannenburg G, Djaafara A, Dorigatti I, van Elsland S, Fitzjohn R, Gaythorpe K, Geidelberg L, Green W, Hamlet A, Jeffrey B, Knock E, Laydon D, Nedjati Gilani G, Nouvellet P, Parag K, Siveroni I, Thompson H, Verity R, Walters C, Donnelly C, Okell L, Bhatia S, Brazeau N, Eales O, Haw D, Imai N, Jauneikaite E, Lees J, Mousa A, Olivera Mesa D, Skarp J, Whittles Let al., 2020, Report 32: Targeting interventions to age groups that sustain COVID-19 transmission in the United States, Pages: 1-32

Following ini􀀂al declines, in mid 2020, a resurgence in transmission of novel coronavirus disease (COVID-19) has occurred in the United States and parts of Europe. Despite the wide implementa􀀂on of non-pharmaceu􀀂cal inter-ven􀀂ons, it is s􀀂ll not known how they are impacted by changing contact pa􀀁erns, age and other demographics. As COVID-19 disease control becomes more localised, understanding the age demographics driving transmission and how these impact the loosening of interven􀀂ons such as school reopening is crucial. Considering dynamics for the United States, we analyse aggregated, age-specific mobility trends from more than 10 million individuals and link these mechanis􀀂cally to age-specific COVID-19 mortality data. In contrast to previous approaches, we link mobility to mortality via age specific contact pa􀀁erns and use this rich rela􀀂onship to reconstruct accurate trans-mission dynamics. Contrary to anecdotal evidence, we find li􀀁le support for age-shi􀀃s in contact and transmission dynamics over 􀀂me. We es􀀂mate that, un􀀂l August, 63.4% [60.9%-65.5%] of SARS-CoV-2 infec􀀂ons in the United States originated from adults aged 20-49, while 1.2% [0.8%-1.8%] originated from children aged 0-9. In areas with con􀀂nued, community-wide transmission, our transmission model predicts that re-opening kindergartens and el-ementary schools could facilitate spread and lead to considerable excess COVID-19 a􀀁ributable deaths over a 90-day period. These findings indicate that targe􀀂ng interven􀀂ons to adults aged 20-49 are an important con-sidera􀀂on in hal􀀂ng resurgent epidemics, and preven􀀂ng COVID-19-a􀀁ributable deaths when kindergartens and elementary schools reopen.

Journal article

Flaxman S, Mishra S, Gandy A, Unwin HJT, Mellan TA, Coupland H, Whittaker C, Zhu H, Berah T, Eaton JW, Monod M, Perez Guzman PN, Schmit N, Cilloni L, Ainslie K, Baguelin M, Boonyasiri A, Boyd O, Cattarino L, Cucunuba Perez Z, Cuomo-Dannenburg G, Dighe A, Djaafara A, Dorigatti I, van Elsland S, Fitzjohn R, Gaythorpe K, Geidelberg L, Grassly N, Green W, Hallett T, Hamlet A, Hinsley W, Jeffrey B, Knock E, Laydon D, Nedjati Gilani G, Nouvellet P, Parag K, Siveroni I, Thompson H, Verity R, Volz E, Walters C, Wang H, Watson O, Winskill P, Xi X, Walker P, Ghani AC, Donnelly CA, Riley SM, Vollmer MAC, Ferguson NM, Okell LC, Bhatt Set al., 2020, Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe, Nature, Vol: 584, Pages: 257-261, ISSN: 0028-0836

Following the emergence of a novel coronavirus1 (SARS-CoV-2) and its spread outside of China, Europe has experienced large epidemics. In response, many European countries have implemented unprecedented non-pharmaceutical interventions such as closure of schools and national lockdowns. We study the impact of major interventions across 11 European countries for the period from the start of COVID-19 until the 4th of May 2020 when lockdowns started to be lifted. Our model calculates backwards from observed deaths to estimate transmission that occurred several weeks prior, allowing for the time lag between infection and death. We use partial pooling of information between countries with both individual and shared effects on the reproduction number. Pooling allows more information to be used, helps overcome data idiosyncrasies, and enables more timely estimates. Our model relies on fixed estimates of some epidemiological parameters such as the infection fatality rate, does not include importation or subnational variation and assumes that changes in the reproduction number are an immediate response to interventions rather than gradual changes in behavior. Amidst the ongoing pandemic, we rely on death data that is incomplete, with systematic biases in reporting, and subject to future consolidation. We estimate that, for all the countries we consider, current interventions have been sufficient to drive the reproduction number Rt below 1 (probability Rt< 1.0 is 99.9%) and achieve epidemic control. We estimate that, across all 11 countries, between 12 and 15 million individuals have been infected with SARS-CoV-2 up to 4th May, representing between 3.2% and 4.0% of the population. Our results show that major non-pharmaceutical interventions and lockdown in particular have had a large effect on reducing transmission. Continued intervention should be considered to keep transmission of SARS-CoV-2 under control.

Journal article

Mellan T, Hoeltgebaum H, Mishra S, Whittaker C, Schnekenberg R, Gandy A, Unwin H, Vollmer M, Coupland H, Hawryluk I, Rodrigues Faria N, Vesga J, Zhu H, Hutchinson M, Ratmann O, Monod M, Ainslie K, Baguelin M, Bhatia S, Boonyasiri A, Brazeau N, Charles G, Cooper L, Cucunuba Perez Z, Cuomo-Dannenburg G, Dighe A, Djaafara A, Eaton J, van Elsland S, Fitzjohn R, Fraser K, Gaythorpe K, Green W, Hayes S, Imai N, Jeffrey B, Knock E, Laydon D, Lees J, Mangal T, Mousa A, Nedjati Gilani G, Nouvellet P, Olivera Mesa D, Parag K, Pickles M, Thompson H, Verity R, Walters C, Wang H, Wang Y, Watson O, Whittles L, Xi X, Okell L, Dorigatti I, Walker P, Ghani A, Riley S, Ferguson N, Donnelly C, Flaxman S, Bhatt Set al., 2020, Report 21: Estimating COVID-19 cases and reproduction number in Brazil

Brazil is an epicentre for COVID-19 in Latin America. In this report we describe the Brazilian epidemicusing three epidemiological measures: the number of infections, the number of deaths and the reproduction number. Our modelling framework requires sufficient death data to estimate trends, and wetherefore limit our analysis to 16 states that have experienced a total of more than fifty deaths. Thedistribution of deaths among states is highly heterogeneous, with 5 states—São Paulo, Rio de Janeiro,Ceará, Pernambuco and Amazonas—accounting for 81% of deaths reported to date. In these states, weestimate that the percentage of people that have been infected with SARS-CoV-2 ranges from 3.3% (95%CI: 2.8%-3.7%) in São Paulo to 10.6% (95% CI: 8.8%-12.1%) in Amazonas. The reproduction number (ameasure of transmission intensity) at the start of the epidemic meant that an infected individual wouldinfect three or four others on average. Following non-pharmaceutical interventions such as school closures and decreases in population mobility, we show that the reproduction number has dropped substantially in each state. However, for all 16 states we study, we estimate with high confidence that thereproduction number remains above 1. A reproduction number above 1 means that the epidemic isnot yet controlled and will continue to grow. These trends are in stark contrast to other major COVID19 epidemics in Europe and Asia where enforced lockdowns have successfully driven the reproductionnumber below 1. While the Brazilian epidemic is still relatively nascent on a national scale, our resultssuggest that further action is needed to limit spread and prevent health system overload.


Zhu H, Liu X, Kang R, Shen Z, Flaxman S, Briol F-Xet al., Bayesian Probabilistic Numerical Integration with Tree-Based Models

Bayesian quadrature (BQ) is a method for solving numerical integrationproblems in a Bayesian manner, which allows users to quantify their uncertaintyabout the solution. The standard approach to BQ is based on a Gaussian process(GP) approximation of the integrand. As a result, BQ is inherently limited tocases where GP approximations can be done in an efficient manner, thus oftenprohibiting very high-dimensional or non-smooth target functions. This paperproposes to tackle this issue with a new Bayesian numerical integrationalgorithm based on Bayesian Additive Regression Trees (BART) priors, which wecall BART-Int. BART priors are easy to tune and well-suited for discontinuousfunctions. We demonstrate that they also lend themselves naturally to asequential design setting and that explicit convergence rates can be obtainedin a variety of settings. The advantages and disadvantages of this newmethodology are highlighted on a set of benchmark tests including the Genzfunctions, and on a Bayesian survey design problem.

Journal article

Liu X, Zhu H, Ton J-F, Wynne G, Duncan Aet al., Grassmann Stein Variational Gradient Descent

Stein variational gradient descent (SVGD) is a deterministic particleinference algorithm that provides an efficient alternative to Markov chainMonte Carlo. However, SVGD has been found to suffer from varianceunderestimation when the dimensionality of the target distribution is high.Recent developments have advocated projecting both the score function and thedata onto real lines to sidestep this issue, although this can severelyoverestimate the epistemic (model) uncertainty. In this work, we proposeGrassmann Stein variational gradient descent (GSVGD) as an alternativeapproach, which permits projections onto arbitrary dimensional subspaces.Compared with other variants of SVGD that rely on dimensionality reduction,GSVGD updates the projectors simultaneously for the score function and thedata, and the optimal projectors are determined through a coupledGrassmann-valued diffusion process which explores favourable subspaces. Bothour theoretical and experimental results suggest that GSVGD enjoys efficientstate-space exploration in high-dimensional problems that have an intrinsiclow-dimensional structure.

Journal article

Zhu H, Howes A, Eer OV, Rischard M, Li Y, Sejdinovic D, Flaxman Set al., Aggregated Gaussian Processes with Multiresolution Earth Observation Covariates

For many survey-based spatial modelling problems, responses are observed asspatially aggregated over survey regions due to limited resources. Covariates,from weather models and satellite imageries, can be observed at many differentspatial resolutions, making the pre-processing of covariates a key challengefor any spatial modelling task. We propose a Gaussian process regression modelto flexibly handle multiresolution covariates by employing an additive kernelthat can efficiently aggregate features across resolutions. Compared toexisting approaches that rely on resolution matching, our approach bettermaintains distributional information across resolutions, leading to betterperformance and interpretability. Our model yields stronger predictiveperformance and interpretability on both simulated and crop yield datasets.

Journal article

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