Infectious diseases on farms pose both public and animal health risks, so understanding how they spread between farms is crucial for developing disease control strategies to prevent future outbreaks. We develop novel Bayesian nonparametric methodology to fit spatial stochastic transmission models in which the infection rate between any two farms is a function that depends on the distance between them, but without assuming a specified parametric form.Making nonparametric inference in this context is challenging since the likelihood function of the observed data is intractable because the underlying transmission process is unobserved. We adopt a fully Bayesian approach by assigning a transformed Gaussian process prior distribution to the infection rate function, and then develop an efficient data augmentation Markov Chain Monte Carlo algorithm to perform Bayesian inference. We use the posterior predictive distribution to simulate the effect of different disease control methods and their economic impact. We analyse a large outbreak of avian influenza in the Netherlands and infer the between-farm infection rate, as well as the unknown infection status of farms which were pre-emptively culled. We use our results to analyse ring-culling strategies,This is an open access article under the terms of the Creat ive Commo ns Attri bution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Significance Mathematical models of infectious disease transmission continue to play a vital role in understanding, mitigating, and preventing outbreaks. The vast majority of epidemic models in the literature are parametric, meaning that they contain inherent assumptions about how transmission occurs in a population. However, such assumptions can be lacking in appropriate biological or epidemiological justification and in consequence lead to erroneous scientific conclusions and misleading predictions. We propose a flexible Bayesian nonparametric framework that avoids the need to make strict model assumptions about the infection process and enables a far more data-driven modeling approach for inferring the mechanisms governing transmission. We use our methods to enhance our understanding of the transmission mechanisms of the 2001 UK foot and mouth disease outbreak.

Finding the deprived areas in any country or city can allow policy makers to design interventions which support citizens in these areas. Locating these areas is often challenging in developing countries where official statistics may not be collected or are unreliable. Comparative judgement models, such as the Bradley-Terry model, offer a solution leveraging local knowledge by comparing different areas based on affluence. Existing comparative judgement methods require a large amount of data to be collected, which can be expensive and time consuming, particularly in developing countries. In this article we develop the Bayesian Spatial Bradley-Terry model, which substantially decreases the amount of data that needs to be collected. We do this by constructing a network representation of the city and incorporating an assumption of spatial smoothness, meaning we can learn about the level of deprivation in one area from neighbouring areas. We demonstrate our method on a novel comparative judgement data set collected in Dar es Salaam, Tanzania, where we are able to identify several slums and the level of deprivation of each slum.

Identifying the most deprived regions of any country or city is key if policy makers are to design successful interventions. However, locating areas with the greatest need is often surprisingly challenging in developing countries. Due to the logistical challenges of traditional household surveying, official statistics can be slow to be updated; estimates that exist can be coarse, a consequence of prohibitive costs and poor infrastructures; and mass urbanization can render manually surveyed figures rapidly out-of-date. Comparative judgement models, such as the Bradley-Terry model, offer a promising solution. Leveraging local knowledge, elicited via comparisons of different areas' affluence, such models can both simplify logistics and circumvent biases inherent to household surveys. Yet widespread adoption remains limited, due to the large amount of data existing approaches still require. We address this via development of a novel Bayesian Spatial Bradley-Terry model, which substantially decreases the number of comparisons required for effective inference. This model integrates a network representation of the city or country, along with assumptions of spatial smoothness that allow deprivation in one area to be informedThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.