A Mathematical Framework for Designing and Evaluating Control Strategies for Water- & Food-Borne Pathogens : A Norovirus Case Study

Norovirus (NoV) is a significant cause of gastroenteritis globally, and the consumption of oysters is frequently linked to outbreaks. Depuration is the principle means employed to reduce levels of potentially harmful agents or toxins in shellfish. The aim of this thesis is to construct mathematical models which can describe the depuration dynamics of water-borne pathogens, and specifically examine the dynamics of NoV during depuration for a population shellfish. Legislation is currently under consideration within the EU by the Directorate-General for Health and Consumers (DG SANCO) to limit the maximum level of NoV that consumers are exposed to via this route. Therefore it is important to the utility of the thesis that any models constructed should incorporate control measures which could be used to implement minimum NoV levels. Doing so allowed calculation of minimum depuration times that would be required to adhere to the control measures incorporated into the models. In addition to modelling the impact on pathogens during the depuration, we wished to gain some insight into how the variability, and not just the mean levels, of water-borne pathogens can be as important with respect to the length of depuration required to minimise any food safety risks to the consumer. This proved difficult in the absence of any data sets that can be used to calculate variability measures, as little data is currently available to inform these values for NoV. However, our modelling techniques were able to calculate an upper limit on the variability of water-borne pathogens that can be well approximated by lognormal distributions. Finally we construct a model which provided linkage between the depuration process and the accretion of pathogens by shellfish while still within farming waters. This model proposed that the pulses of untreated waste waters released by sewage treatment works due to high levels of rainfall would be transmitted into shellfish whilst filter-feeding

One model to rule them all? Modelling approaches across OneHealth for human, animal and plant epidemics

One hundred years after the 1918 influenza outbreak, are we ready for the next pandemic? This paper addresses the need to identify and develop collaborative, interdisciplinary and cross-sectoral approaches to modelling of infectious diseases including the fields of not only human and veterinary medicine, but also plant epidemiology. Firstly, the paper explains the concepts on which the most common epidemiological modelling approaches are based, namely the division of a host population into susceptible, infected and removed (SIR) classes and the proportionality of the infection rate to the size of the susceptible and infected populations. It then demonstrates how these simple concepts have been developed into a vast and successful modelling framework that has been used in predicting and controlling disease outbreaks for over 100 years. Secondly, it considers the compartmental models based on the SIR paradigm within the broader concept of a ‘disease tetrahedron’ (comprising host, pathogen, environment and man) and uses it to review the similarities and differences among the fields comprising the ‘OneHealth’ approach. Finally, the paper advocates interactions between all fields and explores the future challenges facing modellers

How Perturbation Strength Shapes the Global Structure of TSP Fitness Landscapes

Local optima networks are a valuable tool used to analyse and visualise the global structure of combinatorial search spaces; in particular, the existence and distribution of multiple funnels in the landscape. We extract and analyse the networks induced by Chained-LK, a powerful iterated local search for the TSP, on a large set of randomly generated (Uniform and Clustered) instances. Results indicate that increasing the perturbation strength employed by Chained-LK modifies the landscape's global structure, with the effect being markedly different for the two classes of instances. Our quantitative analysis shows that several funnel metrics have stronger correlations with Chained-LK success rate than the number of local optima, indicating that global structure clearly impacts search performance

Rigorous Performance Analysis of State-of-the-Art TSP Heuristic Solvers

Understanding why some problems are better solved by one algorithm rather than another is still an open problem, and the symmetric Travelling Salesperson Problem (TSP) is no exception. We apply three state-of-the-art heuristic solvers to a large set of TSP instances of varying structure and size, identifying which heuristics solve specific instances to optimality faster than others. The first two solvers considered are variants of the multi-trial Helsgaun's Lin-Kernighan Heuristic (a form of iterated local search), with each utilising a different form of Partition Crossover; the third solver is a genetic algorithm (GA) using Edge Assembly Crossover. Our results show that the GA with Edge Assembly Crossover is the best solver, shown to significantly outperform the other algorithms in 73% of the instances analysed. A comprehensive set of features for all instances is also extracted, and decision trees are used to identify main features which could best inform algorithm selection. The most prominent features identified a high proportion of instances where the GA with Edge Assembly Crossover performed significantly better when solving to optimality

On the Fractal Nature of Local Optima Networks

A Local Optima Network represents fitness landscape connectivity within the space of local optima as a mathematical graph. In certain other complex networks or graphs there have been recent observations made about inherent self-similarity. An object is said to be self-similar if it shows the same patterns when measured at different scales; another word used to convey self-similarity is fractal. The fractal dimension of an object captures how the detail observed changes with the scale at which it is measured, with a high fractal dimension being associated with complexity. We conduct a detailed study on the fractal nature of the local optima networks of a benchmark combinatorial optimisation problem (NK Landscapes). The results draw connections between fractal characteristics and performance by three prominent metaheuristics: Iterated Local Search, Simulated Annealing, and Tabu Search

A model for estimating pathogen variability in shellfish and predicting minimum depuration times

Norovirus is a major cause of viral gastroenteritis, with shellfish consumption being identified as one potential norovirus entry point into the human population. Minimising shellfish norovirus levels is therefore important for both the consumer’s protection and the shellfish industry’s reputation. One method used to reduce microbiological risks in shellfish is depuration; however, this process also presents additional costs to industry. Providing a mechanism to estimate norovirus levels during depuration would therefore be useful to stakeholders. This paper presents a mathematical model of the depuration process and its impact on norovirus levels found in shellfish. Two fundamental stages of norovirus depuration are considered: (i) the initial distribution of norovirus loads within a shellfish population and (ii) the way in which the initial norovirus loads evolve during depuration. Realistic assumptions are made about the dynamics of norovirus during depuration, and mathematical descriptions of both stages are derived and combined into a single model. Parameters to describe the depuration effect and norovirus load values are derived from existing norovirus data obtained from U.K. harvest sites. However, obtaining population estimates of norovirus variability is time-consuming and expensive; this model addresses the issue by assuming a ‘worst case scenario’ for variability of pathogens, which is independent of mean pathogen levels. The model is then used to predict minimum depuration times required to achieve norovirus levels which fall within possible risk management levels, as well as predictions of minimum depuration times for other water-borne pathogens found in shellfish. Times for Escherichia coli predicted by the model all fall within the minimum 42 hours required for class B harvest sites, whereas minimum depuration times for norovirus and FRNA+ bacteriophage are substantially longer. Thus this study provides relevant information and tools to assist norovirus risk managers with future control strategies

Clarifying the Difference in Local Optima Network Sampling Algorithms

We conduct the first ever statistical comparison between two Local Optima Network (LON) sampling algorithms. These methodologies attempt to capture the connectivity in the local optima space of a fitness landscape. One sampling algorithm is based on a random-walk snowballing procedure, while the other is centred around multiple traced runs of an Iterated Local Search. Both of these are proposed for the Quadratic Assignment Problem (QAP), making this the focus of our study. It is important to note the sampling algorithm frameworks could easily be modified for other domains. In our study descriptive statistics for the obtained search space samples are contrasted and commented on. The LON features are also used in linear mixed models and random forest regression for predicting heuristic optimisation performance of two prominent heuristics for the QAP on the underlying combinatorial problems. The model results are then used to make deductions about the sampling algorithms’ utility. We also propose a specific set of LON metrics for use in future predictive models alongside previously-proposed network metrics, demonstrating the payoff in doing so

Modelling norovirus dynamics within oysters emphasises potential food safety issues associated with current testing & depuration protocols

Norovirus is a significant global cause of viral gastroenteritis, with raw oyster consumption often linked to such outbreaks due to their filter-feeding in harvest waters. National water quality and depuration/relaying times are often classified using Escherichia coli, a poor proxy for norovirus levels in shellfish. The current norovirus assay is limited to only the digestive tracts of oysters, meaning the total norovirus load of an oyster may differ from reported results. These limitations motivated this work, building upon previous modelling by the authors, and considers the sequestration of norovirus into observed and cryptic (unobservable) compartments within each oyster. Results show that total norovirus levels in shellfish batches exhibit distinct peaks during the early depuration stages, with each peak's magnitude dependent on the proportion of cryptic norovirus. These results are supported by depuration trial data and other studies, where viral levels often exhibit multiphase decays. This work's significant result is that any future norovirus legislation needs to consider not only the harvest site's water classification but also the total viral load present in oysters entering the market. We show that 62 h of depuration should be undertaken before any norovirus testing is conducted on oyster samples, being the time required for cryptic viral loads to have transited into the digestive tracts where they can be detected by current assay, or have exited the oyster

Cross-sectional telephone surveys as a tool to study epidemiological factors and monitor seasonal influenza activity in Malta

Background Seasonal influenza has major implications for healthcare services as outbreaks often lead to high activity levels in health systems. Being able to predict when such outbreaks occur is vital. Mathematical models have extensively been used to predict epidemics of infectious diseases such as seasonal influenza and to assess effectiveness of control strategies. Availability of comprehensive and reliable datasets used to parametrize these models is limited. In this paper we combine a unique epidemiological dataset collected in Malta through General Practitioners (GPs) with a novel method using cross-sectional surveys to study seasonal influenza dynamics in Malta in 2014–2016, to include social dynamics and self-perception related to seasonal influenza. Methods Two cross-sectional public surveys (n = 406 per survey) were performed by telephone across the Maltese population in 2014–15 and 2015–16 influenza seasons. Survey results were compared with incidence data (diagnosed seasonal influenza cases) collected by GPs in the same period and with Google Trends data for Malta. Information was collected on whether participants recalled their health status in past months, occurrences of influenza symptoms, hospitalisation rates due to seasonal influenza, seeking GP advice, and other medical information. Results We demonstrate that cross-sectional surveys are a reliable alternative data source to medical records. The two surveys gave comparable results, indicating that the level of recollection among the public is high. Based on two seasons of data, the reporting rate in Malta varies between 14 and 22%. The comparison with Google Trends suggests that the online searches peak at about the same time as the maximum extent of the epidemic, but the public interest declines and returns to background level. We also found that the public intensively searched the Internet for influenza-related terms even when number of cases was low. Conclusions Our research shows that a telephone survey is a viable way to gain deeper insight into a population’s self-perception of influenza and its symptoms and to provide another benchmark for medical statistics provided by GPs and Google Trends. The information collected can be used to improve epidemiological modelling of seasonal influenza and other infectious diseases, thus effectively contributing to public health