Coevolution fails to maintain genetic variation in a host-parasite model with constant finite population size.

Coevolutionary negative frequency-dependent selection has been hypothesized to maintain genetic variation in host and parasites. Despite the extensive literature pertaining to host-parasite coevolution, the temporal dynamics of genetic variation have not been examined in a matching-alleles model (MAM) with a finite population size relative to the expectation under neutral genetic drift alone. The dynamics of the MA coevolution in an infinite population, in fact, suggests that genetic variation in these coevolving populations behaves neutrally. By comparing host heterozygosity to the expectation in a single-species model of neutral genetic drift we find that while this is also largely true in finite populations two additional phenomena arise. First, reciprocal natural selection acting on stochastic perturbations in host and pathogen allele frequencies results in a slight increase or decrease in genetic variation depending on the parameter conditions. Second, following the fixation of an allele in the parasite, selection in the MAM becomes directional, which then rapidly erodes genetic variation in the host. Hence, rather than maintain it, we find that, on average, matching-alleles coevolution depletes genetic variation.

Rapid simulation of spatial epidemics: a spectral method.

Spatial structure and hence the spatial position of host populations plays a vital role in the spread of infection. In the majority of situations, it is only possible to predict the spatial spread of infection using simulation models, which can be computationally demanding especially for large population sizes. Here we develop an approximation method that vastly reduces this computational burden. We assume that the transmission rates between individuals or sub-populations are determined by a spatial transmission kernel. This kernel is assumed to be isotropic, such that the transmission rate is simply a function of the distance between susceptible and infectious individuals; as such this provides the ideal mechanism for modelling localised transmission in a spatial environment. We show that the spatial force of infection acting on all susceptibles can be represented as a spatial convolution between the transmission kernel and a spatially extended 'image' of the infection state. This representation allows the rapid calculation of stochastic rates of infection using fast-Fourier transform (FFT) routines, which greatly improves the computational efficiency of spatial simulations. We demonstrate the efficiency and accuracy of this fast spectral rate recalculation (FSR) method with two examples: an idealised scenario simulating an SIR-type epidemic outbreak amongst N habitats distributed across a two-dimensional plane; the spread of infection between US cattle farms, illustrating that the FSR method makes continental-scale outbreak forecasting feasible with desktop processing power. The latter model demonstrates which areas of the US are at consistently high risk for cattle-infections, although predictions of epidemic size are highly dependent on assumptions about the tail of the transmission kernel.

Strategies for controlling non-transmissible infection outbreaks using a large human movement data set.

Prediction and control of the spread of infectious disease in human populations benefits greatly from our growing capacity to quantify human movement behavior. Here we develop a mathematical model for non-transmissible infections contracted from a localized environmental source, informed by a detailed description of movement patterns of the population of Great Britain. The model is applied to outbreaks of Legionnaires' disease, a potentially life-threatening form of pneumonia caused by the bacteria Legionella pneumophilia. We use case-report data from three recent outbreaks that have occurred in Great Britain where the source has already been identified by public health agencies. We first demonstrate that the amount of individual-level heterogeneity incorporated in the movement data greatly influences our ability to predict the source location. The most accurate predictions were obtained using reported travel histories to describe movements of infected individuals, but using detailed simulation models to estimate movement patterns offers an effective fast alternative. Secondly, once the source is identified, we show that our model can be used to accurately determine the population likely to have been exposed to the pathogen, and hence predict the residential locations of infected individuals. The results give rise to an effective control strategy that can be implemented rapidly in response to an outbreak.

Silent spread of H5N1 in vaccinated poultry.

International debate on the merits of vaccinating poultry against the H5N1 influenza A virus has raised concerns about the possibility of an increased risk of between-flock transmission before outbreaks are detected. Here we show that this 'silent spread' can occur because of incomplete protection at the flock level, even if a vaccine is effective in individual birds. The use of unvaccinated sentinels can mitigate, although not completely eliminate, the problem.

Feedback between coevolution and epidemiology can help or hinder the maintenance of genetic variation in host-parasite models.

Antagonistic coevolution has long been suggested to help maintain host genetic variation. Although ecological and epidemiological feedbacks are known to have important consequences on coevolutionary allele-frequency dynamics, their effects on the maintenance of genetic variation remains poorly understood. Here, we extend previous work on the maintenance of genetic variation in a classic matching alleles coevolutionary model by exploring the effects of ecological and epidemiological feedbacks, where both allele frequencies and population sizes are allowed to vary over time. We find that coevolution rarely maintains more host genetic variation than expected under neutral genetic drift alone. When and if coevolution maintains or depletes genetic variation relative to neutral drift is determined, predominantly, by two factors: the deterministic stability of the Red Queen allele-frequency cycles and the chance of allele fixation in the pathogen, as this results in directional selection and depletion of genetic variation in the host. Compared to purely coevolutionary models with constant host and pathogen population sizes, ecological and epidemiological feedbacks stabilize Red Queen cycles deterministically, but population fluctuations in the pathogen increase the rate of allele fixation in the pathogen, especially in epidemiological models. Our results illustrate the importance of considering the ecological and epidemiological context in which coevolution occurs when examining the impact of Red Queen cycles on genetic variation.

INFERENCE FOR INDIVIDUAL-LEVEL MODELS OF INFECTIOUS DISEASES IN LARGE POPULATIONS.

Individual Level Models (ILMs), a new class of models, are being applied to infectious epidemic data to aid in the understanding of the spatio-temporal dynamics of infectious diseases. These models are highly flexible and intuitive, and can be parameterised under a Bayesian framework via Markov chain Monte Carlo (MCMC) methods. Unfortunately, this parameterisation can be difficult to implement due to intense computational requirements when calculating the full posterior for large, or even moderately large, susceptible populations, or when missing data are present. Here we detail a methodology that can be used to estimate parameters for such large, and/or incomplete, data sets. This is done in the context of a study of the UK 2001 foot-and-mouth disease (FMD) epidemic.

Reducing respiratory syncytial virus (RSV) hospitalization in a lower-income country by vaccinating mothers-to-be and their households.

Respiratory syncytial virus is the leading cause of lower respiratory tract infection among infants. RSV is a priority for vaccine development. In this study, we investigate the potential effectiveness of a two-vaccine strategy aimed at mothers-to-be, thereby boosting maternally acquired antibodies of infants, and their household cohabitants, further cocooning infants against infection. We use a dynamic RSV transmission model which captures transmission both within households and communities, adapted to the changing demographics and RSV seasonality of a low-income country. Model parameters were inferred from past RSV hospitalisations, and forecasts made over a 10-year horizon. We find that a 50% reduction in RSV hospitalisations is possible if the maternal vaccine effectiveness can achieve 75 days of additional protection for newborns combined with a 75% coverage of their birth household co-inhabitants (~7.5% population coverage).

Effect of data quality on estimates of farm infectiousness trends in the UK 2001 foot-and-mouth disease epidemic.

Most of the mathematical models that were developed to study the UK 2001 foot-and-mouth disease epidemic assumed that the infectiousness of infected premises was constant over their infectious periods. However, there is some controversy over whether this assumption is appropriate. Uncertainty about which farm infected which in 2001 means that the only method to determine if there were trends in farm infectiousness is the fitting of mechanistic mathematical models to the epidemic data. The parameter values that are estimated using this technique, however, may be influenced by missing and inaccurate data. In particular to the UK 2001 epidemic, this includes unreported infectives, inaccurate farm infection dates and unknown farm latent periods. Here, we show that such data degradation prevents successful determination of trends in farm infectiousness.

Topographic determinants of foot and mouth disease transmission in the UK 2001 epidemic.

BACKGROUND: A key challenge for modelling infectious disease dynamics is to understand the spatial spread of infection in real landscapes. This ideally requires a parallel record of spatial epidemic spread and a detailed map of susceptible host density along with relevant transport links and geographical features. RESULTS: Here we analyse the most detailed such data to date arising from the UK 2001 foot and mouth epidemic. We show that Euclidean distance between infectious and susceptible premises is a better predictor of transmission risk than shortest and quickest routes via road, except where major geographical features intervene. CONCLUSION: Thus, a simple spatial transmission kernel based on Euclidean distance suffices in most regions, probably reflecting the multiplicity of transmission routes during the epidemic.

Disease transmission promotes evolution of host spatial patterns.

Ecological dynamics can produce a variety of striking patterns. On ecological time scales, pattern formation has been hypothesized to be due to the interaction between a species and its local environment. On longer time scales, evolutionary factors must be taken into account. To examine the evolutionary robustness of spatial pattern formation, we construct a spatially explicit model of vegetation in the presence of a pathogen. Initially, we compare the dynamics for vegetation parameters that lead to competition induced spatial patterns and those that do not. Over ecological time scales, banded spatial patterns dramatically reduced the ability of the pathogen to spread, lowered its endemic density and hence increased the persistence of the vegetation. To gain an evolutionary understanding, each plant was given a heritable trait defining its resilience to competition; greater competition leads to lower vegetation density but stronger spatial patterns. When a disease is introduced, the selective pressure on the plant's resilience to the competition parameter is determined by the transmission of the disease. For high transmission, vegetation that has low resilience to competition and hence strong spatial patterning is an evolutionarily stable strategy. This demonstrates a novel mechanism by which striking spatial patterns can be maintained by disease-driven selection.

Testing the hypothesis of preferential attachment in social network formation.

The hypothesis of preferential attachment (PA) - whereby better connected individuals make more connections - is hotly debated, particularly in the context of epidemiological networks. The simplest models of PA, for example, are incompatible with the eradication of any disease through population-level control measures such as random vaccination. Typically, evidence has been sought for the presence or absence of preferential attachment via asymptotic power-law behaviour. Here, we present a general statistical method to test directly for evidence of PA in count data and apply this to data for contacts relevant to the spread of respiratory diseases. We find that while standard methods for model selection prefer a form of PA, careful analysis of the best fitting PA models allows for a level of contact heterogeneity that in fact allows control of respiratory diseases. Our approach is based on a flexible but numerically cheap likelihood-based model that could in principle be applied to other integer data where the hypothesis of PA is of interest.

The interplay between determinism and stochasticity in childhood diseases.

An important issue in the history of ecology has been the study of the relative importance of deterministic forces and processes noise in shaping the dynamics of ecological populations. We address this question by exploring the temporal dynamics of two childhood infections, measles and whooping cough, in England and Wales. We demonstrate that epidemics of whooping cough are strongly influenced by stochasticity; fully deterministic approaches cannot achieve even a qualitative fit to the observed data. In contrast, measles dynamics are extremely well explained by a deterministic model. These differences are shown to be caused by their contrasting responses to dynamical noise due to different infectious periods.

An inter-laboratory validation of a real time PCR assay to measure host excretion of bacterial pathogens, particularly of Mycobacterium bovis.

Advances in the diagnosis of Mycobacterium bovis infection in wildlife hosts may benefit the development of sustainable approaches to the management of bovine tuberculosis in cattle. In the present study, three laboratories from two different countries participated in a validation trial to evaluate the reliability and reproducibility of a real time PCR assay in the detection and quantification of M. bovis from environmental samples. The sample panels consisted of negative badger faeces spiked with a dilution series of M. bovis BCG Pasteur and of field samples of faeces from badgers of unknown infection status taken from badger latrines in areas with high and low incidence of bovine TB (bTB) in cattle. Samples were tested with a previously optimised methodology. The experimental design involved rigorous testing which highlighted a number of potential pitfalls in the analysis of environmental samples using real time PCR. Despite minor variation between operators and laboratories, the validation study demonstrated good concordance between the three laboratories: on the spiked panels, the test showed high levels of agreement in terms of positive/negative detection, with high specificity (100%) and high sensitivity (97%) at levels of 10(5) cells g(-1) and above. Quantitative analysis of the data revealed low variability in recovery of BCG cells between laboratories and operators. On the field samples, the test showed high reproducibility both in terms of positive/negative detection and in the number of cells detected, despite low numbers of samples identified as positive by any laboratory. Use of a parallel PCR inhibition control assay revealed negligible PCR-interfering chemicals co-extracted with the DNA. This is the first example of a multi-laboratory validation of a real time PCR assay for the detection of mycobacteria in environmental samples. Field studies are now required to determine how best to apply the assay for population-level bTB surveillance in wildlife.

Modelling the many-wrongs principle: the navigational advantages of aggregation in nomadic foragers.

We develop a simple individual-based model to gain an understanding of the drivers of aggregation behaviour in nomadic foragers. The model incorporates two key elements influencing nomadic foragers in variable environments: uncertainty regarding the location of food sources and variability in the spatio-temporal distribution of ephemeral food sources. A genetic algorithm is used to evolve parameters describing an individual's movement and aggregation strategy. We apply the aggregation model to a case study of the Bornean bearded pig (Sus barbatus). Bearded pigs are ideal for considering the foraging advantages of aggregation, because they are highly mobile and exhibit a variety of aggregation strategies, ranging from solitary and sedentary to mass aggregation and wide ranging migration. Our model demonstrates the "many-wrongs principle", and shows that environmental variability, uncertainty in the location of food sources, and local population density drive aggregation behaviour.