Bayesian epidemic models for spatially aggregated count data

Epidemic data often possess certain characteristics, such as the presence of many zeros, the spatial nature of the disease spread mechanism, environmental noise, serial correlation and dependence on time‐varying factors. This paper addresses these issues via suitable Bayesian modelling. In doing so, we utilize a general class of stochastic regression models appropriate for spatio‐temporal count data with an excess number of zeros. The developed regression framework does incorporate serial correlation and time‐varying covariates through an Ornstein–Uhlenbeck process formulation. In addition, we explore the effect of different priors, including default options and variations of mixtures of g‐priors. The effect of different distance kernels for the epidemic model component is investigated. We proceed by developing branching process‐based methods for testing scenarios for disease control, thus linking traditional epidemiological models with stochastic epidemic processes, useful in policy‐focused decision making. The approach is illustrated with an application to a sheep pox dataset from the Evros region, Greece

Stochastic modelling of the spatial spread of influenza in Germany

In geographical epidemiology, disease counts are typically available in discrete spatial units and at discrete time-points. For example, surveillance data on infectious diseases usually consists of weekly counts of new infections in pre-defined geographical areas. Similarly, but on a different time-scale, cancer registries typically report yearly incidence or mortality counts in administrative regions. A major methodological challenge lies in building realistic models for space-time interactions on discrete irregular spatial graphs. In this paper, we will discuss an observation-driven approach, where past observed counts in neighbouring areas enter directly as explanatory variables, in contrast to the parameter-driven approach through latent Gaussian Markov random fields (Rue and Held, 2005) with spatio-temporal structure. The main focus will lie on the demonstration of the spread of influenza in Germany, obtained through the design and simulation of a spatial extension of the classical SIR model (Hufnagel et al., 2004)

Control and surveillance of partially observed stochastic epidemics in a Bayesian framework

This thesis comprises a number of inter-related parts. For most of the thesis we are concerned with developing a new statistical technique that can enable the identi cation of the optimal control by comparing competing control strategies for stochastic epidemic models in real time. In the second part, we develop a novel approach for modelling the spread of Peste des Petits Ruminants (PPR) virus within a given country and the risk of introduction to other countries. The control of highly infectious diseases of agriculture crops, animal and human diseases is considered as one of the key challenges in epidemiological and ecological modelling. Previous methods for analysis of epidemics, in which different controls are compared, do not make full use of the trajectory of the epidemic. Most methods use the information provided by the model parameters which may consider partial information on the epidemic trajectory, so for example the same control strategy may lead to different outcomes when the experiment is repeated. Also, by using partial information it is observed that it might need more simulated realisations when comparing two different controls. We introduce a statistical technique that makes full use of the available information in estimating the effect of competing control strategies on real-time epidemic outbreaks. The key to this approach lies in identifying a suitable mechanism to couple epidemics, which could be unaffected by controls. To that end, we use the Sellke construction as a latent process to link epidemics with different control strategies. The method is initially applied on non-spatial processes including SIR and SIS models assuming that there are no observation data available before moving on to more complex models that explicitly represent the spatial nature of the epidemic spread. In the latter case, the analysis is conditioned on some observed data and inference on the model parameters is performed in Bayesian framework using the Markov Chain Monte Carlo (MCMC) techniques coupled with the data augmentation methods. The methodology is applied on various simulated data sets and to citrus canker data from Florida. Results suggest that the approach leads to highly positively correlated outcomes of different controls, thus reducing the variability between the effect of different control strategies, hence providing a more efficient estimator of their expected differences. Therefore, a reduction of the number of realisations required to compare competing strategies in term of their expected outcomes is obtained. The main purpose of the final part of this thesis is to develop a novel approach to modelling the speed of Pest des Petits Ruminants (PPR) within a given country and to understand the risk of subsequent spread to other countries. We are interested in constructing models that can be fitted using information on the occurrence of outbreaks as the information on the susceptible population is not available, and use these models to estimate the speed of spatial spread of the virus. However, there was little prior modelling on which the models developed here could be built. We start by first establishing a spatio-temporal stochastic formulation for the spread of PPR. This modelling is then used to estimate spatial transmission and speed of spread. To account for uncertainty on the lack of information on the susceptible population, we apply ideas from Bayesian modelling and data augmentation by treating the transmission network as a missing quantity. Lastly, we establish a network model to address questions regarding the risk of spread in the large-scale network of countries and introduce the notion of ` first-passage time' using techniques from graph theory and operational research such as the Bellman-Ford algorithm. The methodology is first applied to PPR data from Tunisia and on simulated data. We also use simulated models to investigate the dynamics of spread through a network of countries

Dynamic modelling of hepatitis C virus transmission among people who inject drugs: a methodological review

Equipment sharing among people who inject drugs (PWID) is a key risk factor in infection by hepatitis C virus (HCV). Both the effectiveness and cost-effectiveness of interventions aimed at reducing HCV transmission in this population (such as opioid substitution therapy, needle exchange programs or improved treatment) are difficult to evaluate using field surveys. Ethical issues and complicated access to the PWID population make it difficult to gather epidemiological data. In this context, mathematical modelling of HCV transmission is a useful alternative for comparing the cost and effectiveness of various interventions. Several models have been developed in the past few years. They are often based on strong hypotheses concerning the population structure. This review presents compartmental and individual-based models in order to underline their strengths and limits in the context of HCV infection among PWID. The final section discusses the main results of the papers

Optimal treatment allocations in space and time for on-line control of an emerging infectious disease

A key component in controlling the spread of an epidemic is deciding where, whenand to whom to apply an intervention.We develop a framework for using data to informthese decisionsin realtime.We formalize a treatment allocation strategy as a sequence of functions, oneper treatment period, that map up-to-date information on the spread of an infectious diseaseto a subset of locations where treatment should be allocated. An optimal allocation strategyoptimizes some cumulative outcome, e.g. the number of uninfected locations, the geographicfootprint of the disease or the cost of the epidemic. Estimation of an optimal allocation strategyfor an emerging infectious disease is challenging because spatial proximity induces interferencebetween locations, the number of possible allocations is exponential in the number oflocations, and because disease dynamics and intervention effectiveness are unknown at outbreak.We derive a Bayesian on-line estimator of the optimal allocation strategy that combinessimulation–optimization with Thompson sampling.The estimator proposed performs favourablyin simulation experiments. This work is motivated by and illustrated using data on the spread ofwhite nose syndrome, which is a highly fatal infectious disease devastating bat populations inNorth America

Adequacy of SEIR models when epidemics have spatial structure: Ebola in Sierra Leone.

Dynamic SEIR (Susceptible, Exposed, Infectious, Removed) compartmental models provide a tool for predicting the size and duration of both unfettered and managed outbreaks-the latter in the context of interventions such as case detection, patient isolation, vaccination and treatment. The reliability of this tool depends on the validity of key assumptions that include homogeneity of individuals and spatio-temporal homogeneity. Although the SEIR compartmental framework can easily be extended to include demographic (e.g. age) and additional disease (e.g. healthcare workers) classes, dependence of transmission rates on time, and metapopulation structure, fitting such extended models is hampered by both a proliferation of free parameters and insufficient or inappropriate data. This raises the question of how effective a tool the basic SEIR framework may actually be. We go some way here to answering this question in the context of the 2014-2015 outbreak of Ebola in West Africa by comparing fits of an SEIR time-dependent transmission model to both country- and district-level weekly incidence data. Our novel approach in estimating the effective-size-of-the-populations-at-risk ( Neff) and initial number of exposed individuals ( E0) at both district and country levels, as well as the transmission function parameters, including a time-to-halving-the-force-of-infection ( tf/2) parameter, provides new insights into this Ebola outbreak. It reveals that the estimate R0 ≈ 1.7 from country-level data appears to seriously underestimate R0 ≈ 3.3 - 4.3 obtained from more spatially homogeneous district-level data. Country-level data also overestimate tf/2 ≈ 22 weeks, compared with 8-10 weeks from district-level data. Additionally, estimates for the duration of individual infectiousness is around two weeks from spatially inhomogeneous country-level data compared with 2.4-4.5 weeks from spatially more homogeneous district-level data, which estimates are rather high compared with most values reported in the literature. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'. This issue is linked with the subsequent theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'

A motif-based approach to network epidemics

Networks have become an indispensable tool in modelling infectious diseases, with the structure of epidemiologically relevant contacts known to affect both the dynamics of the infection process and the efficacy of intervention strategies. One of the key reasons for this is the presence of clustering in contact networks, which is typically analysed in terms of prevalence of triangles in the network. We present a more general approach, based on the prevalence of different four-motifs, in the context of ODE approximations to network dynamics. This is shown to outperform existing models for a range of small world networks