COVID-19: Bayesian inference for high resolution stochastic modelling for the UK

Lead Research Organisation: Lancaster University
Department Name: Medicine


We will develop an efficient and robust MCMC-based framework for fully Bayesian inference methodology for spatially explicit, stochastic, and partially observed meta-population epidemic models within human populations. This will be applied to the current UK Covid-19 epidemic. We particularly focus on the challenge of providing continuously updated parameter estimation and risk assessment in the face of censored data observations and hence detailed age- and space-specific predictions of Covid-19 prevalence and incidence in the UK. Our predictions will be targeted at disease management, providing early warning of spatial "hotspots" of epidemic resurgence as Behavioural and Social Intervention (lockdown) measures are lifted, as well as informing targeted disease surveillance to space- and age-related sub-populations.

We respond to the observation that existing differential equation based models informing SAGE cannot operate at high population resolution, since as meta-populations get smaller, stochastic fluctuations intrinsic to the epidemic process begin to dominate case observation noise. Whilst stochastic models of Covid-19 spread (based on pre-existing influenza models) do exist, methods to fit them at scale in the face of changing data availability require development. To address this, we will extend our existing Bayesian approach to real-time risk prediction for individual level models, developing a data-augmentation MCMC approach to state-transition models defined on high-dimensional meta-population structures. Inference and forward simulation algorithms will be built using Google's TensorFlow library, providing appropriate balance between rapid algorithm development and fast GPU-accelerated computations to ensure that our results are timely, and appropriate for Covid-19 decision support across the UK.


10 25 50
Description So far this this award, we have constructed a novel fitting algorithm capable of estimating the parameters of a discrete-time spatial epidemic model for SARS-CoV-2 at the level of the 380 Local Authorities in the UK. This algorithm allows us to account for for unobserved epidemiological events such as individuals' infection events (you never know you've been infected until you start coughing) and the onset of infectivity prior to the occurrence of clinical signs of disease. The algorithm itself is based on Markov chain Monte Carlo (MCMC) data augmentation, with novel developments to improve algorithm efficiency by reflecting temporal constraints on the ordering of epidemic events for any given dataset. These methods are currently in preparation for publication, with software modules available via the `gemlib` library ( We believe ours is the only method in existence that is capable of fitting a fine-detail stochastic epidemic model, and to this end we have been able to provide daily nowcasts and short-range forecasts of the spatial pattern of SARS-CoV-2 spread to the UK Cabinet Office (via the SPI-M-O SAGE subcommittee), Scottish Government, and local Lancashire County Council.

During this project, we are extremely grateful to have established a working relationship with software engineers at Google Research, who have helped us to implement our statistical ideas in efficient software. Our model code is publicly available for others to use and scrutinise (;, and our automated pipeline results are on a publicly available dashboard available at

For the remaining 9 months of our project, we are working on improved MCMC samplers to allow us to incorporate multiple sources of data in a more complex model (the SEIOHR model posited in our proposal). We will need to modify our model to take account of the expected reduction in apparent SARS-CoV-2 incidence expected as a result of reduced community-based testing, though we are confident that our ongoing methodological developments will accommodate this requirement.
Exploitation Route The SARS-CoV-2 pandemic has exposed a deep capability gap in statistics, and in particular our ability to fit the complex, stochastic epidemic models that are required to provide answers to pressing questions. Many of these questions, such as how deprivation and population age structure interact with space during a pandemic, remain unanswered through lack of suitable statistical tools to calibrate such models. We envisage that the outcomes of this funding will:

1. Encourage others to use our software models to apply to a wide range of different dynamical disease models looking at different aspects of the recent SARS-CoV-2 epidemic, thus answering extant questions on pandemic spread and control;
2. Lead to renewed interest in the use of spatial epidemic models for human populations to provide policy-makers with badly-needed detailed information during outbreaks;
3. We look forward to providing our outcomes as a flexible discipline-norm software environment -- enjoyed by many applied research subjects but not thus far epidemic research. We see this as a vital step for epidemics researchers to become more agile and responsive to future emergency outbreaks, as well as providing a point of reference for model comparison and choice in any given application area;
4. Beyond epidemic modelling, our outcomes are useful to subjects in which discrete-time state transition models are routinely used. Examples beyond epidemiological research are in engineering, ecology, and process modelling in industry.
Sectors Agriculture, Food and Drink,Communities and Social Services/Policy,Environment,Healthcare,Manufacturing, including Industrial Biotechology,Retail

Description Our daily and weekly SARS-CoV-2 outputs have been provided to the SPI-M-O modelling subcommittee of SAGE. Maps detailing spatial measures of reproduction number, spatial anomalies in case incidence ("hotspots"), and short-range predictions are included in the weekly SPI-M-O "slide pack" which is sent to SAGE for summarisation into advice for Cabinet Office. In addition, we provide weekly short-term predictions for Scottish Government, as well as for local Lancashire County Council resource planning. Our activities have therefore informed national SARS-CoV-2 tactics and strategy, and we are delighted to have submitted a successful REF2021 Impact Case Study based on this.
First Year Of Impact 2021
Sector Communities and Social Services/Policy,Healthcare
Impact Types Societal,Policy & public services

Description SPI-M-O reporting
Geographic Reach National 
Policy Influence Type Implementation circular/rapid advice/letter to e.g. Ministry of Health
Impact Our weekly reports have fed into spatial resource allocation for the SARS-CoV-2 outbreak, informing decisions on where to send medical supplies, test kits, and focus field investigations of super-spreading events.
Description UKHSA Operational Surveillance Team 
Organisation Department of Health (DH)
Country United Kingdom 
Sector Public 
PI Contribution UKHSA Operational Surveillance Team (OST), lead by Dr Richard Elson, identified us as being able to provide a unique insight into the spatial nature of SARS-CoV-2 Omicron strain in November 2021. Our collaboration has been formalised through partial secondment of PI Jewell to the OST to facilitate access to privileged data in return for nowcasts and predictions of spread. These results contributed evidence to support the decision not to upgrade Omicron from Variant under Investigation to Variant of Concern.
Collaborator Contribution UKHSA OST have provided detailed data on SARS-CoV-2 omicron spread, which is not otherwise publicly available. They have contributed 0.1FTE of Jewell's remaining time, and we are grateful for this added resource to the existing EPSRC funded project.
Impact Outputs are currently under preparation for publication.
Start Year 2021
Title gemlib 
Description gemlib provides software building blocks for constructing discrete-time epidemic models, together with simulation and inference algorithms. In particular, we include MCMC samplers capable of efficient handling of censored epidemic event times, which is necessary for unbiased parameter estimation. 
Type Of Technology New/Improved Technique/Technology 
Year Produced 2021 
Open Source License? Yes  
Impact Production of weekly Local Authority-level spatial epidemic model-based nowcasts and short-term predictions on SARS-CoV-2 for SPI-M-O subcommittee of SAGE.