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

Evidence-based controls for epidemics using spatio-temporal stochastic models in a Bayesian framework.

The control of highly infectious diseases of agricultural and plantation crops and livestock represents a key challenge in epidemiological and ecological modelling, with implemented control strategies often being controversial. Mathematical models, including the spatio-temporal stochastic models considered here, are playing an increasing role in the design of control as agencies seek to strengthen the evidence on which selected strategies are based. Here, we investigate a general approach to informing the choice of control strategies using spatio-temporal models within the Bayesian framework. We illustrate the approach for the case of strategies based on pre-emptive removal of individual hosts. For an exemplar model, using simulated data and historic data on an epidemic of Asiatic citrus canker in Florida, we assess a range of measures for prioritizing individuals for removal that take account of observations of an emerging epidemic. These measures are based on the potential infection hazard a host poses to susceptible individuals (hazard), the likelihood of infection of a host (risk) and a measure that combines both the hazard and risk (threat). We find that the threat measure typically leads to the most effective control strategies particularly for clustered epidemics when resources are scarce. The extension of the methods to a range of other settings is discussed. A key feature of the approach is the use of functional-model representations of the epidemic model to couple epidemic trajectories under different control strategies. This induces strong positive correlations between the epidemic outcomes under the respective controls, serving to reduce both the variance of the difference in outcomes and, consequently, the need for extensive simulation.Hola Adrakey was supported during the course of this research by a James Watt Postgraduate Research Scholarship from Heriot–Watt University

A mechanistic spatio-temporal framework for modelling individual-to-individual transmission—With an application to the 2014-2015 West Africa Ebola outbreak

In recent years there has been growing availability of individual-level spatio-temporal disease data, particularly due to the use of modern communicating devices with GPS tracking functionality. These detailed data have been proven useful for inferring disease transmission to a more refined level than previously. However, there remains a lack of statistically sound frameworks to model the underlying transmission dynamic in a mechanistic manner. Such a development is particularly crucial for enabling a general epidemic predictive framework at the individual level. In this paper we propose a new statistical framework for mechanistically modelling individual-to-individual disease transmission in a landscape with heterogeneous population density. Our methodology is first tested using simulated datasets, validating our inferential machinery. The methodology is subsequently applied to data that describes a regional Ebola outbreak in Western Africa (2014-2015). Our results show that the methods are able to obtain estimates of key epidemiological parameters that are broadly consistent with the literature, while revealing a significantly shorter distance of transmission. More importantly, in contrast to existing approaches, we are able to perform a more general model prediction that takes into account the susceptible population. Finally, our results show that, given reasonable scenarios, the framework can be an effective surrogate for susceptible-explicit individual models which are often computationally challenging

Spread model for PPR

<p>Concerning the spread of PPR within a country, there are several ways to model the susceptible population. Data from Tunisia provide information on infected sub-populations, suggesting that a meta-population approach where susceptibles are modelled as a network of interconnected nodes would be appropriate. Although not implemented in this study, this framework would offer the scope to capture heterogeneity across nodes, representing the species composition of individual farms. The strength of connections in this network would then be influenced by the perceived strength of the infectious challenge between nodes. A natural initial approach to this would be to represent the strength of interactions as being monotonically related to Euclidean distance.</p> <p>Anticipating the problems regarding a lack of knowledge on the susceptible population, it is also beneficial to consider frameworks where the susceptible population is represented via a continuous spatial intensity, which then moderates the occurrence of new infections. In particular, it was noted that a framework in which spatial contact distribution models (described later) for the initiation of new infections are used to formulate a marked point process model in which marks are drawn from a distribution - representing the diversity of units forming the susceptible population - may be appropriate, and may offer a way of accommodating the lack of information on the susceptible population.</p> <p>It was identified as being important that parameter uncertainty could be treated properly for any models that are fitted to data on PPR, so that these uncertainties could be propagated through to predictions. With this in mind, particular consideration was given to finding models that could be fitted using either likelihood-based methods (to extract maximum information from data) or a fully Bayesian approach, for uncertainty propagation. As previously mentioned, it was considered important that any approach to model fitting could cope with unobserved processes, or with the increased model complexity that arises from, for example, including parameters for the probability of non-reporting of infections. For methods that use data on final size, the inference of epidemic parameters is potentially relevant.</p

Bayesian inference for spatio-temporal stochastic transmission of plant disease in the presence of roguing: A case study to characterise the dispersal of Flavescence dorée

Estimating the distance at which pathogens disperse from one season to the next is crucial for designing efficient control strategies for invasive plant pathogens and a major milestone in the reduction of pesticide use in agriculture. However, we still lack such estimates for many diseases, especially for insect-vectored pathogens, such as Flavescence dorée (FD). FD is a quarantine disease threatening European vineyards. Its management is based on mandatory insecticide treatments and the removal of infected plants identified during annual surveys. This paper introduces a general statistical framework to model the epidemiological dynamics of FD in a mechanistic manner that can take into account missing hosts in surveyed fields (resulting from infected plant removals). We parameterized the model using Markov chain Monte Carlo (MCMC) and data augmentation from surveillance data gathered in Bordeaux vineyards. The data mainly consist of two snapshot maps of the infectious status of all the plants in three adjacent fields during two consecutive years. We demonstrate that heavy-tailed dispersal kernels best fit the spread of FD and that on average, 50% (resp. 80%) of new infection occurs within 10.5 m (resp. 22.2 m) of the source plant. These values are in agreement with estimates of the flying capacity of Scaphoideus titanus, the leafhopper vector of FD, reported in the literature using mark-capture techniques. Simulations of simple removal scenarios using the fitted model suggest that cryptic infection hampered FD management. Future efforts should explore whether strategies relying on reactive host removal can improve FD management

Field and Landscape Risk Factors Impacting Flavescence Dorée Infection: Insights from Spatial Bayesian Modeling in the Bordeaux Vineyards

Flavescence dorée (FD) is a quarantine disease threatening European vineyards. Its management is based on mandatory insecticide treatments and the uprooting of infected plants identified during annual surveys. Field surveys are currently not optimized because the drivers affecting FD spread in vineyard landscapes remain poorly understood. We collated a georeferenced dataset of FD detection, collected from 34,581 vineyard plots over 5 years in the South West France wine region. Spatial models fitted with integrated nested Laplace approximation were used to identify local and landscape factors affecting FD detection and infection. Our analysis highlights the importance of sampling period on FD detection and of local practices and landscape context on FD infection. At field scale, altitude and cultivar choice were the main factors affecting FD infection. In particular, the odds ratio of FD infection in fields planted with the susceptible Cabernet Sauvignon, Cabernet Franc, or Muscadelle varieties were approximately twice those in fields planted with the less susceptible Merlot. Field infection was also affected by the field’s immediate surroundings (within a circle with a radius of 150 to 200 m), corresponding to landscapes of 7 to 12 ha. In particular, the probability of FD infection increased with the proportions of forest and urban land and with the proportion of susceptible cultivars, demonstrating that the cultivar composition impacts FD epidemiology at landscape scale. The satisfactory predictive performance of the model for identifying districts with a prevalence of FD detection >10% of the fields suggests that it could be used to target areas in which future surveys would be most valuable

GPS locations of individual Ebola deaths (2014-2016) in the community identified through the use of mobile phones, collected in the neighbouring area of the capital (Freetown) in Sierra Leone.

<p>See the section <i>Ebola Outbreak Data</i> for more details.</p

Posterior predictive distributions of temporal and spatial summary statistics of epidemics forward simulated from the estimated model.

<p>(a) One-epidemic ahead in-sample model prediction. The observed epidemic is indicated by the dots and the line. 95% C.I. of the simulated epidemics at each week are indicated by the grey bands. Dashed line represents the median values of the simulated epidemics. (b) One-epidemic ahead in-sample and out-of-sample model prediction. We first estimate the model parameters using data from the first half of the epidemic duration (week 1 to week 11) and re-simulate from the estimated model from the beginning to the end of the epidemic duration (week 24). (c) Measure of global spatial autocorrelation using Moran’s I index (Refs. [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005798#pcbi.1005798.ref007" target="_blank">7</a>]) which ranges from -1 to 1 (a value close to 1 indicating strong clustering and close to -1 indicating strong dispersion), applied to epidemics before and after peak. The index corresponding to the observed epidemic is indicated by the dotted line. (d) Measure of clustering/dispersion using Ripley’s K, or its transformation Ripley’s L [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005798#pcbi.1005798.ref040" target="_blank">40</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005798#pcbi.1005798.ref041" target="_blank">41</a>]. Compared to global measures such as the Moran’s I, this function determines clustering/dispersion of point data over <i>a range</i> of distances (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005798#pcbi.1005798.s001" target="_blank">S1 Text</a> for more details), <i>without</i> requiring certain aggregation of the points, hence representing a more powerful and informative measure for our context. We consider and compute the L function using the the R package <i>spatstat</i> [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005798#pcbi.1005798.ref042" target="_blank">42</a>]. The measure corresponding to the observed epidemic is indicated by the solid line, along with the 95% C.I. of the simulated epidemics enclosed in the grey band. They indicate that the spatial clustering/dispersion of observed (point) data are captured reasonably well.</p