Glenn Marion

Environmental Brownian noise suppresses explosions in population dynamics

Population systems are often subject to environmental noise, and our aim is to show that (surprisingly) the presence of even a tiny amount can suppress a potential population explosion. To prove this intrinsically interesting result, we stochastically perturb the multivariate deterministic system into the Ito form dx(t)=f(x(t)) dt+g(x(t)) dw(t), and show that although the solution to the original ordinary differential equation may explode to infinity in a finite time, with probability one that of the associated stochastic differential equation does not.

Predicting Impacts of Climate Change on Fasciola hepatica Risk

Fasciola hepatica (liver fluke) is a physically and economically devastating parasitic trematode whose rise in recent years has been attributed to climate change. Climate has an impact on the free-living stages of the parasite and its intermediate host Lymnaea truncatula, with the interactions between rainfall and temperature having the greatest influence on transmission efficacy. There have been a number of short term climate driven forecasts developed to predict the following seasons infection risk, with the Ollerenshaw index being the most widely used. Through the synthesis of a modified Ollerenshaw index with the UKCP09 fine scale climate projection data we have developed long term seasonal risk forecasts up to 2070 at a 25 km square resolution. Additionally UKCIP gridded datasets at 5 km square resolution from 1970-2006 were used to highlight the climate-driven increase to date. The maps show unprecedented levels of future fasciolosis risk in parts of the UK, with risk of serious epidemics in Wales by 2050. The seasonal risk maps demonstrate the possible change in the timing of disease outbreaks due to increased risk from overwintering larvae. Despite an overall long term increase in all regions of the UK, spatio-temporal variation in risk levels is expected. Infection risk will reduce in some areas and fluctuate greatly in others with a predicted decrease in summer infection for parts of the UK due to restricted water availability. This forecast is the first approximation of the potential impacts of climate change on fasciolosis risk in the UK. It can be used as a basis for indicating where active disease surveillance should be targeted and where the development of improved mitigation or adaptation measures is likely to bring the greatest benefits.

Species' range: adaptation in space and time.

Populations living in a spatially and temporally changing environment can adapt to the changing optimum and/or migrate toward favorable habitats. Here we extend previous analyses with a static optimum to allow the environment to vary in time as well as in space. The model follows both population dynamics and the trait mean under stabilizing selection, and the outcomes can be understood by comparing the loads due to genetic variance, dispersal, and temporal change. With fixed genetic variance, we obtain two regimes: (1) adaptation that is uniform along the environmental gradient and that responds to the moving optimum as expected for panmictic populations and when the spatial gradient is sufficiently steep, and (2) a population with limited range that adapts more slowly than the environmental optimum changes in both time and space; the population therefore becomes locally extinct and migrates toward suitable habitat. We also use a population‐genetic model with many loci to allow genetic variance to evolve, and we show that the only solution now has uniform adaptation.

Estimation of multiple transmission rates for epidemics in heterogeneous populations

One of the principal challenges in epidemiological modeling is to parameterize models with realistic estimates for transmission rates in order to analyze strategies for control and to predict disease outcomes. Using a combination of replicated experiments, Bayesian statistical inference, and stochastic modeling, we introduce and illustrate a strategy to estimate transmission parameters for the spread of infection through a two-phase mosaic, comprising favorable and unfavorable hosts. We focus on epidemics with local dispersal and formulate a spatially explicit, stochastic set of transition probabilities using a percolation paradigm for a susceptible–infected (S–I) epidemiological model. The S–I percolation model is further generalized to allow for multiple sources of infection including external inoculum and host-to-host infection. We fit the model using Bayesian inference and Markov chain Monte Carlo simulation to successive snapshots of damping-off disease spreading through replicated plant populations that differ in relative proportions of favorable and unfavorable hosts and with time-varying rates of transmission. Epidemiologically plausible parametric forms for these transmission rates are compared by using the deviance information criterion. Our results show that there are four transmission rates for a two-phase system, corresponding to each combination of infected donor and susceptible recipient. Knowing the number and magnitudes of the transmission rates allows the dominant pathways for transmission in a heterogeneous population to be identified. Finally, we show how failure to allow for multiple transmission rates can overestimate or underestimate the rate of spread of epidemics in heterogeneous environments, which could lead to marked failure or inefficiency of control strategies.

Bayesian estimation for percolation models of disease spread in plant populations

Statistical methods are formulated for fitting and testing percolation-based, spatio-temporal models that are generally applicable to biological or physical processes that evolve in spatially distributed populations. The approach is developed and illustrated in the context of the spread of Rhizoctonia solani, a fungal pathogen, in radish but is readily generalized to other scenarios. The particular model considered represents processes of primary and secondary infection between nearest-neighbour hosts in a lattice, and time-varying susceptibility of the hosts. Bayesian methods for fitting the model to observations of disease spread through space and time in replicate populations are developed. These use Markov chain Monte Carlo methods to overcome the problems associated with partial observation of the process. We also consider how model testing can be achieved by embedding classical methods within the Bayesian analysis. In particular we show how a residual process, with known sampling distribution, can be defined. Model fit is then examined by generating samples from the posterior distribution of the residual process, to which a classical test for consistency with the known distribution is applied, enabling the posterior distribution of the P-value of the test used to be estimated. For the Rhizoctonia-radish system the methods confirm the findings of earlier non-spatial analyses regarding the dynamics of disease transmission and yield new evidence of environmental heterogeneity in the replicate experiments.

Livestock Helminths in a Changing Climate: Approaches and Restrictions to Meaningful Predictions.

Simple Summary Parasitic helminths represent one of the most pervasive challenges to livestock, and their intensity and distribution will be influenced by climate change. There is a need for long-term predictions to identify potential risks and highlight opportunities for control. We explore the approaches to modelling future helminth risk to livestock under climate change. One of the limitations to model creation is the lack of purpose driven data collection. We also conclude that models need to include a broad view of the livestock system to generate meaningful predictions. Abstract Climate change is a driving force for livestock parasite risk. This is especially true for helminths including the nematodes Haemonchus contortus, Teladorsagia circumcincta, Nematodirus battus, and the trematode Fasciola hepatica, since survival and development of free-living stages is chiefly affected by temperature and moisture. The paucity of long term predictions of helminth risk under climate change has driven us to explore optimal modelling approaches and identify current bottlenecks to generating meaningful predictions. We classify approaches as correlative or mechanistic, exploring their strengths and limitations. Climate is one aspect of a complex system and, at the farm level, husbandry has a dominant influence on helminth transmission. Continuing environmental change will necessitate the adoption of mitigation and adaptation strategies in husbandry. Long term predictive models need to have the architecture to incorporate these changes. Ultimately, an optimal modelling approach is likely to combine mechanistic processes and physiological thresholds with correlative bioclimatic modelling, incorporating changes in livestock husbandry and disease control. Irrespective of approach, the principal limitation to parasite predictions is the availability of active surveillance data and empirical data on physiological responses to climate variables. By combining improved empirical data and refined models with a broad view of the livestock system, robust projections of helminth risk can be developed.

Control of bovine tuberculosis in British livestock: there is no 'silver bullet'.

Bovine tuberculosis (bTB; Mycobacterium bovis) is a bacterial infection of cattle that also affects certain wildlife species. Culling badgers (Meles meles), the principal wildlife host, results in perturbation of the badger population and an increased level of disease in cattle. Therefore, the priority for future management must be to minimize the risk of disease transmission by finding new ways to reduce the contact rate among the host community. At the farm level, targeting those individuals that represent an elevated risk of transmission might prove to be effective. At the landscape level, risk mapping can provide the basis for targeted surveillance of the host community. Here, we review the current evidence for bTB persistence in Britain and make recommendations for future management and research.

Evaluating the tuberculosis hazard posed to cattle from wildlife across Europe

Tuberculosis (TB) caused by infection with Mycobacterium bovis (M. bovis) and other closely related members of the M. tuberculosis complex (MTC) infects many domestic and wildlife species across Europe. Transmission from wildlife species to cattle complicates the control of disease in cattle. By determining the level of TB hazard for which a given wildlife species is responsible, the potential for transmission to the cattle population can be evaluated. We undertook a quantitative review of TB hazard across Europe on a country-by-country basis for cattle and five widely-distributed wildlife species. Cattle posed the greatest current and potential TB hazard other cattle for the majority of countries in Europe. Wild boar posed the greatest hazard of all the wildlife species, indicating that wild boar have the greatest ability to transmit the disease to cattle. The most common host systems for TB hazards in Europe are the cattle-deer-wild boar ones. The cattle-roe deer-wild boar system is found in 10 countries, and the cattle-red deer-wild boar system is found in five countries. The dominance of cattle with respect to the hazards in many regions confirms that intensive surveillance of cattle for TB should play an important role in any TB control programme. The significant contribution that wildlife can make to the TB hazard to cattle is also of concern, given current population and distribution increases of some susceptible wildlife species, especially wild boar and deer, and the paucity of wildlife TB surveillance programmes.

A Systematic Bayesian Integration of Epidemiological and Genetic Data

Genetic sequence data on pathogens have great potential to inform inference of their transmission dynamics ultimately leading to better disease control. Where genetic change and disease transmission occur on comparable timescales additional information can be inferred via the joint analysis of such genetic sequence data and epidemiological observations based on clinical symptoms and diagnostic tests. Although recently introduced approaches represent substantial progress, for computational reasons they approximate genuine joint inference of disease dynamics and genetic change in the pathogen population, capturing partially the joint epidemiological-evolutionary dynamics. Improved methods are needed to fully integrate such genetic data with epidemiological observations, for achieving a more robust inference of the transmission tree and other key epidemiological parameters such as latent periods. Here, building on current literature, a novel Bayesian framework is proposed that infers simultaneously and explicitly the transmission tree and unobserved transmitted pathogen sequences. Our framework facilitates the use of realistic likelihood functions and enables systematic and genuine joint inference of the epidemiological-evolutionary process from partially observed outbreaks. Using simulated data it is shown that this approach is able to infer accurately joint epidemiological-evolutionary dynamics, even when pathogen sequences and epidemiological data are incomplete, and when sequences are available for only a fraction of exposures. These results also characterise and quantify the value of incomplete and partial sequence data, which has important implications for sampling design, and demonstrate the abilities of the introduced method to identify multiple clusters within an outbreak. The framework is used to analyse an outbreak of foot-and-mouth disease in the UK, enhancing current understanding of its transmission dynamics and evolutionary process.

Modelling Parasite Transmission in a Grazing System: The Importance of Host Behaviour and Immunity

Parasitic helminths present one of the most pervasive challenges to grazing herbivores. Many macro-parasite transmission models focus on host physiological defence strategies, omitting more complex interactions between hosts and their environments. This work represents the first model that integrates both the behavioural and physiological elements of gastro-intestinal nematode transmission dynamics in a managed grazing system. A spatially explicit, individual-based, stochastic model is developed, that incorporates both the hosts’ immunological responses to parasitism, and key grazing behaviours including faecal avoidance. The results demonstrate that grazing behaviour affects both the timing and intensity of parasite outbreaks, through generating spatial heterogeneity in parasite risk and nutritional resources, and changing the timing of exposure to the parasites’ free-living stages. The influence of grazing behaviour varies with the host-parasite combination, dependent on the development times of different parasite species and variations in host immune response. Our outputs include the counterintuitive finding that under certain conditions perceived parasite avoidance behaviours (faecal avoidance) can increase parasite risk, for certain host-parasite combinations. Through incorporating the two-way interaction between infection dynamics and grazing behaviour, the potential benefits of parasite-induced anorexia are also demonstrated. Hosts with phenotypic plasticity in grazing behaviour, that make grazing decisions dependent on current parasite burden, can reduce infection with minimal loss of intake over the grazing season. This paper explores how both host behaviours and immunity influence macro-parasite transmission in a spatially and temporally heterogeneous environment. The magnitude and timing of parasite outbreaks is influenced by host immunity and behaviour, and the interactions between them; the incorporation of both regulatory processes is required to fully understand transmission dynamics. Understanding of both physiological and behavioural defence strategies will aid the development of novel approaches for control.