InFER: Likelihood-based Inference for Epidemic Risk

Lead Research Organisation: University of Warwick
Department Name: Statistics


The work is motivated by the need to assess the risk due to spread of infectious diseases within the UK farming sector. We focus on two distinctly different contexts: the epidemic context, where disease response is required to be extremely rapid, and the endemic situation in which more long term control strategies are required for optimal disease control. In the epidemic context, risk assessment needs to be sufficiently rapid in order to effectively inform control strategies. A particular interest lies in foot and mouth disease and in Avian Influenza within the poultry industry. However the methodology developed will not be restricted to these contexts, and the project will construct software which can be rapidly adapted to other situations by expert users. Within the endemic context, the main problem will be the partiality of data rendering formal statistical methods based upon transition models difficult to carry out without highly optimised and application specific algorithms. We will have a particular focus on bovine TB, Leptospira hardjo and Neospora caninum, though again we anticipate that our approach will be sufficiently generic to permit the transportation of methodology developed to different disease contexts. The project will build realistic mathematical models for the random evolution of epidemics of infectious diseases. In particular, methodology will be developed for inferring progressively about the parameters within the model as the epidemic progresses with a view to assessing the risk of future disease propagation. Our approach will be explicitly population-based. In the applications above, the population consists of farms whose status is modelled explicitly through time (typically as susceptible, infectious with or without detection, removed, or occasionally other states). The effect of control strategies can be easily investigated within this population-level approach. Models will also be spatially explicit, allowing for the spread of the disease through local mechanisms such as direct local contact and wind-borne spread. However the spread of the disease through other contacts (perhaps through commercial links) will also also be modelled through network structures where appropriate. In many cases, information about network structure will be partial and the project will develop statistical methods for dealing with this. Particularly in the early stages of an epidemic, governmental authorities (such as Defra) acquire information from infected farms on their recent movements and contacts (so-called dangerous contacts). An important task in our project will be to develop a statistical methodology for assessing the importance of this information and using it to refine risk assessment and control. We place great emphasis on the dissemination of our work and its results to as general audience as possible. To this end, we shall develop a visualisation package to be used in conjunction with the output from our statistical analysis. This will permit the implications of our findings, in terms of risk prediction, economic impact and the implications of control strategies to be easily observed. Our statistical approach will be fully Bayesian, and will be carried out through powerful Markov chain Monte Carlo (and related) techniques. Computational efficiency and speed will be a crucial part of making the methodology practically useful, and the project will investigate new algorithmic and computational advances in order to ensure that the approach can be used in real-time within populations of medium size (for instance around 100 000 in the case of foot and mouth disease).

Technical Summary

The project will develop a fully Bayesian methodology for the assessment of risk in infectious disease epidemics. The project will consider both epidemic and endemic contexts. It will consider well-characterised populations and application areas within UK agriculture will include foot and mouth disease, Avian Influenza, bovine TB, Leptospira hardjo and Neospora caninum. Detailed stochastic population-based models will be considered in each case through a common inferential paradigm adopted across all applications. Within this framework, study of control strategies is readily facilitated. The approach will take into account uncertainty in model parameters (whose distribution will evolve as information accrues according to Bayesian learning), current infectious status of individual farms and stochasticity in the future epidemic dynamics. The project will use state-of-the-art Markov chain Monte Carlo (and related) methodology, allowing missing data to be imputed iteratively using data-augmentation techniques. All models will be explicitly spatial and heterogeneity will be modelled through spatial distance and through network connectivity. The project will develop methods which can incorporate imperfect information on network structure, and will also consider the problem of incorporation of dangerous contact information from local searches in the vicinity of infections, into models constructed from stationary infection rates. Model diagnostics and model choice methodology for this framework will also be developed and software will be developed for use by other researchers working in different epidemic contexts.

Planned Impact

Dissemination and links with user communities will be achieved through the following means. 1. We will maintain close links with Defra within the project. Discussions have already taken place with Defra about the possibility of inviting a delegation to Warwick to learn more about the group's extensive activities. 2. The breadth of the group will ensure that the work is easily disseminated to other user areas. For instance, CI2 has extensive veterinary connections and will ensure that the work is publicised within that community through publications and presentations, Nigel French's position in Massey New Zealand involves strong connectivity with government policy makers, and both the PDRA and the PI will visit New Zealand to reinforce this connection. 3. Presenting findings at international conferences will be a priority for rapid dissemination of the work (eg SVEPM, ISVEE, GISVet, ISBA, IMS conferences). The project conference will also be an ideal forum for disseminating our findings. 4. According to excellent practice, an emphasis will be placed on publication in top quality academic journals in Statistics and Veterinary Science, as well as high profile general journals such as Nature and Science. 5. A project website will be produced to present the main aspects of our findings, and to provide the software that we have written in conjunction with the research (as per the Data-Sharing Policy). The PI will manage all aspects of the project, and will take an active role in research in many parts of it (particularly modelling, construction of MCMC methods, writing etc). With his unique blend of expertise in Statistics, Veterinary Medicine and Computation, the PDRA will be actively involved in all aspects of the work and will be responsible for the core task of developing and performing the data analyses. He will oversee the work on software and visualisation (largely carried out by the PTPDRA). The PDRA will also maintain the project website. CI1 will be particularly involved in the tasks (A1) and (A2) while CI2 will take a leading role in the direction of work from a veterinary perspective, and will form an important link between the research team and the veterinary and agricultural sectors. Nigel French will carry out the day to day management of the PDRA during his extended visit to New Zealand. Immediate exploitation of our work is likely to be by Defra and/or similar governmental organisations in other countries. Our work would be used to 1. inform tactical policy on disease control in the event of a notifiable disease outbreak, such as Avian Influenza or foot and mouth disease; 2. to construct long term disease surveillance and control strategies for endemic diseases, such as bovine TB, Leptospira hardjo, Neospora caninum, bovine viral diarrhoea, bovine herpes virus. Potential commercial uses of our work involve the use of our explicit quantification of epidemic risk, for instance in insurance policies for livestock. Our work is also highly transportable, and we anticipate that our work will influence others to adopt our Bayesian computational inference paradigm to other (perhaps quite different) epidemic contexts. The research team assembled to carry out this project is extremely broad. Each of the PI, CI1, CI2, and Nigel French are acknowledged world experts in areas which are all distinct but crucial to the success of this multi-disciplinary project. Furthermore the PDRA has a unique set of multi-disciplinary skills in Statistics, Biology, Veterinary Science and Computation while the PTPDRA has particular skills and considerable experience in software development. As a result of this, all of the team will be involved in communication and dissemination activities as overseen by the PI. For public and media engagements related to the project, the team will draw on the locally available resources within the University Communication Office.


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Description The research worked non principled statistical inference (Bayesian) for carrying out real-time inference and prediction for partially observed epidemics. The work should have generic applicability to different epidemics although its main focus was on farm-based diseases such as Foot and Mouth disease. Software was developed for visualising the emerging risks for particular farms and to inform control strategies in a user-friendly interface. Significant advances in the development of effective Markov chain Monte Carlo algorithms for carrying out this inference were made.
Exploitation Route The work needs to be developed to apply to other specific epidemic contexts, including human diseases such as influenza and corona virus.
Sectors Agriculture, Food and Drink

Title BERP, Bayesian Epidemic Risk Prediction, available at 
Description A software package for carrying out Bayesian Risk Prediction using R. 
Type Of Technology software 
Year Produced 2012 
Impact No actual Impacts realised to date