Cattle farmer psychosocial profiles and their association with control strategies for bovine viral diarrhea.

Bovine viral diarrhea (BVD) is endemic in the United Kingdom and causes major economic losses. Control is largely voluntary for individual farmers and is likely to be influenced by psychosocial factors, such as altruism, trust, and psychological proximity (feeling close) to relevant "others," such as farmers, veterinarians, the government, and their cows. These psychosocial factors (factors with both psychological and social aspects) are important determinants of how people make decisions related to their own health, many of which have not been studied in the context of infectious disease control by farmers. Farmer psychosocial profiles were investigated using multiple validated measures in an observational survey of 475 UK cattle farmers using the capability, opportunity, motivation-behavior (COM-B) framework. Farmers were clustered by their BVD control practices using latent class analysis. Farmers were split into 5 BVD control behavior classes, which were tested for associations with the psychosocial and COM-B factors using multinomial logistic regression, with doing nothing as the baseline class. Farmers who were controlling disease both for themselves and others were more likely to do something to control BVD (e.g., test, vaccinate). Farmers who did not trust other farmers, had high psychological capability (knowledge and understanding of how to control disease), and had high physical opportunity (time and money to control disease) were more likely to have a closed, separate herd and test. Farmers who did not trust other farmers were also more likely to undertake many prevention strategies with an open herd. Farmers with high automatic motivation (habits and emotions) and reflective motivation (decisions and goals) were more likely to vaccinate and test, alone or in combination with other controls. Farmers with high psychological proximity (feeling of closeness) to their veterinarian were more likely to undertake many prevention strategies in an open herd. Farmers with high psychological proximity to dairy farmers and low psychological proximity to beef farmers were more likely to keep their herd closed and separate and test or vaccinate and test. Farmers who had a lot of trust in other farmers and invested in them, rather than keeping everything for themselves, were more likely to be careful introducing new stock and test. In conclusion, farmer psychosocial factors were associated with strategies for BVD control in UK cattle farmers. Psychological proximity to veterinarians was a novel factor associated with proactive BVD control and was more important than the more extensively investigated trust. These findings highlight the importance of a close veterinarian-farmer relationship and are important for promoting effective BVD control by farmers, which has implications for successful nationwide BVD control and eradication schemes.

Aggregation dynamics explain vegetation patch-size distributions.

Vegetation patch-size distributions have been an intense area of study for theoreticians and applied ecologists alike in recent years. Of particular interest is the seemingly ubiquitous nature of power-law patch-size distributions emerging in a number of diverse ecosystems. The leading explanation of the emergence of these power-laws is due to local facilitative mechanisms. There is also a common transition from power law to exponential distribution when a system is under global pressure, such as grazing or lack of rainfall. These phenomena require a simple mechanistic explanation. Here, we study vegetation patches from a spatially implicit, patch dynamic viewpoint. We show that under minimal assumptions a power-law patch-size distribution appears as a natural consequence of aggregation. A linear death term also leads to an exponential term in the distribution for any non-zero death rate. This work shows the origin of the breakdown of the power-law under increasing pressure and shows that in general, we expect to observe a power law with an exponential cutoff (rather than pure power laws). The estimated parameters of this distribution also provide insight into the underlying ecological mechanisms of aggregation and death.

Mathematical modelling of infectious diseases.

INTRODUCTION: Mathematical models allow us to extrapolate from current information about the state and progress of an outbreak, to predict the future and, most importantly, to quantify the uncertainty in these predictions. Here, we illustrate these principles in relation to the current H1N1 epidemic. SOURCES OF DATA: Many sources of data are used in mathematical modelling, with some forms of model requiring vastly more data than others. However, a good estimation of the number of cases is vitally important. AREAS OF AGREEMENT: Mathematical models, and the statistical tools that underpin them, are now a fundamental element in planning control and mitigation measures against any future epidemic of an infectious disease. Well-parameterized mathematical models allow us to test a variety of possible control strategies in computer simulations before applying them in reality. AREAS OF CONTROVERSY: The interaction between modellers and public-health practitioners and the level of detail needed for models to be of use. GROWING POINTS: The need for stronger statistical links between models and data. AREAS TIMELY FOR DEVELOPING RESEARCH: Greater appreciation by the medical community of the uses and limitations of models and a greater appreciation by modellers of the constraints on public-health resources.

Implications of vaccination and waning immunity.

For infectious diseases where immunization can offer lifelong protection, a variety of simple models can be used to explain the utility of vaccination as a control method. However, for many diseases, immunity wanes over time and is subsequently enhanced (boosted) by asymptomatic encounters with the infection. The study of this type of epidemiological process requires a model formulation that can capture both the within-host dynamics of the pathogen and immune system as well as the associated population-level transmission dynamics. Here, we parametrize such a model for measles and show how vaccination can have a range of unexpected consequences as it reduces the natural boosting of immunity as well as reducing the number of naive susceptibles. In particular, we show that moderate waning times (40-80 years) and high levels of vaccination (greater than 70%) can induce large-scale oscillations with substantial numbers of symptomatic cases being generated at the peak. In addition, we predict that, after a long disease-free period, the introduction of infection will lead to far larger epidemics than that predicted by standard models. These results have clear implications for the long-term success of any vaccination campaign and highlight the need for a sound understanding of the immunological mechanisms of immunity and vaccination.

Efficient methods for studying stochastic disease and population dynamics.

Stochastic ecological and epidemiological models are now routinely used to inform management and decision making throughout conservation and public-health. A difficulty with the use of such models is the need to resort to simulation methods when the population size (and hence the size of the state space) becomes large, resulting in the need for a large amount of computation to achieve statistical confidence in results. Here we present two methods that allow evaluation of all quantities associated with one- (and higher) dimensional Markov processes with large state spaces. We illustrate these methods using SIS disease dynamics and studying species that are affected by catastrophic events. The methods allow the possibility of extending exact Markov methods to real-world problems, providing techniques for efficient parameterisation and subsequent analysis.

Disease extinction and community size: modeling the persistence of measles.

A basic issue in ecology is the relation between extinction and population size. One of the clearest manifestations of a population threshold for extinction is the critical community size below which infections like measles do not persist. The current generation of stochastic models overestimates the observed critical community size for measles, generating much less persistence of infection than is observed. The inclusion of a more biologically realistic model for the duration of infection produced a much closer fit to the actual critical community size and explains previously undescribed high-frequency oscillations in measles incidence.

Reinterpreting space, time lags, and functional responses in ecological models.

Natural enemy-victim interactions are of major applied importance and of fundamental interest to ecologists. A key question is what stabilizes these interactions, allowing the long-term coexistence of the two species. Three main theoretical explanations have been proposed: behavioral responses, time-dependent factors such as delayed density dependence, and spatial heterogeneity. Here, using the powerful moment-closure technique, we show a fundamental equivalence between these three elements. Limited movement by organisms is a ubiquitous feature of ecological systems, allowing spatial structure to develop; we show that the effects of this can be naturally described in terms of time lags or within-generation functional responses.

Dynamics of the 2001 UK foot and mouth epidemic: stochastic dispersal in a heterogeneous landscape.

Foot-and-mouth is one of the world's most economically important livestock diseases. We developed an individual farm-based stochastic model of the current UK epidemic. The fine grain of the epidemiological data reveals the infection dynamics at an unusually high spatiotemporal resolution. We show that the spatial distribution, size, and species composition of farms all influence the observed pattern and regional variability of outbreaks. The other key dynamical component is long-tailed stochastic dispersal of infection, combining frequent local movements with occasional long jumps. We assess the history and possible duration of the epidemic, the performance of control strategies, and general implications for disease dynamics in space and time.

The Role of Movement Restrictions in Limiting the Economic Impact of Livestock Infections.

Movements are essential for the economic success of the livestock industry. These movements however bring the risk of long-range spread of infection, potentially bringing infection to previously disease-free areas where subsequent localised transmission can be devastating. Mechanistic predictive models usually consider controls that minimize the number of livestock affected without considering other costs of an ongoing epidemic. However, it is more appropriate to consider the economic burden, as movement restrictions have major consequences for the economic revenue of farms. Using mechanistic models of foot-and-mouth disease (FMD), bluetongue virus (BTV) and bovine tuberculosis (bTB) in the UK, we contrast the economically optimal control strategies for these diseases. We show that for FMD, the optimal strategy is to ban movements in a small radius around infected farms; the balance between disease control and maintaining 'business as usual' varies between regions. For BTV and bTB, we find that the cost of any movement ban is more than the epidemiological benefits due to the low within-farm prevalence and slow rate of disease spread. This work suggests that movement controls need to be carefully matched to the epidemiological and economic consequences of the disease, and optimal movement bans are often far shorter than existing policy.

On methods for studying stochastic disease dynamics.

Models that deal with the individual level of populations have shown the importance of stochasticity in ecology, epidemiology and evolution. An increasingly common approach to studying these models is through stochastic (event-driven) simulation. One striking disadvantage of this approach is the need for a large number of replicates to determine the range of expected behaviour. Here, for a class of stochastic models called Markov processes, we present results that overcome this difficulty and provide valuable insights, but which have been largely ignored by applied researchers. For these models, the so-called Kolmogorov forward equation (also called the ensemble or master equation) allows one to simultaneously consider the probability of each possible state occurring. Irrespective of the complexities and nonlinearities of population dynamics, this equation is linear and has a natural matrix formulation that provides many analytical insights into the behaviour of stochastic populations and allows rapid evaluation of process dynamics. Here, using epidemiological models as a template, these ensemble equations are explored and results are compared with traditional stochastic simulations. In addition, we describe further advantages of the matrix formulation of dynamics, providing simple exact methods for evaluating expected eradication (extinction) times of diseases, for comparing expected total costs of possible control programmes and for estimation of disease parameters.

Spatiotemporal patterns and risks of herd breakdowns in pigs with postweaning multisystemic wasting syndrome.

A retrospective cohort study of 116 British pig farms was undertaken to investigate the epidemiological risk factors associated with herd breakdowns with postweaning multisystemic wasting syndrome (PMWS). Farmers reported the PMWS status of their herd (case definition 1) and, where applicable, when the disease was first suspected and what they observed; they described a prolonged increase in mortality in six to 16-week-old pigs that was not attributable to any disease known to be on their farm. There was over 90 per cent agreement on the farmers' PMWS status between the farmers and their veterinarians. Approximately 70 per cent of the breakdowns were confirmed at the laboratory (case definition 2) except during the outbreak of foot-and-mouth disease (FMD) in 2001 when it was reduced to 30 per cent. Porcine circovirus type 2 antigen was detected in pigs examined postmortem (case definition 3) in approximately 90 per cent of the farms with increased mortality. The breakdowns occurred initially in the south of England and spread west and north, as well as locally in a radial pattern from the affected farms, and there was strong statistical evidence that there was non-random space-time clustering. The risk of herd breakdowns with PMWS was not constant; therefore, for each case definition, three survival models were developed with outcome variable time to breakdown of between January 2000 and January 2001, February 2001 to September 2001 (during FMD) or October 2001 to December 2003. Exposures with a bivariable significance of P<0.20 were tested in three multivariable Cox proportional hazard models. From January 2000 to January 2001 the risk of a herd breakdown with PMWS for definitions 1, 2 and 3 was greater for farms with 600 or more breeding sows, and for definitions 1 and 3 there was an increased risk associated with the purchase of replacement gilts rather than using homebred replacements. For definitions 1 and 3 the farms where the nearest pig farm had no breeding pigs were at greater risk of a breakdown than those where the nearest farm had breeding stock, as were the farms where visitors were not requested to avoid pigs for more than three days before visiting the farm during the FMD outbreak. From October 2001, the associated risks were identical for all three case definitions; farms were at greater risk when they had 600 or more breeding sows, if visitors had not avoided contact with pigs for more than three days before visiting the farm, and when there was a farm with PMWS less than five miles away. The affected farms were more likely to have disease associated with porcine parvovirus, porcine reproduction and respiratory syndrome virus, erysipelas, Escherichia coli and salmonella. These exposures were positively associated with large herds and the farm being close to other pig farms, but did not remain in the final models for breakdown with PMWS, indicating that such farms may be at greater risk of many infectious diseases.

Data-driven models to predict the elimination of sleeping sickness in former Equateur province of DRC.

Approaching disease elimination, it is crucial to be able to assess progress towards key objectives using quantitative tools. For Gambian human African trypanosomiasis (HAT), the ultimate goal is to stop transmission by 2030, while intermediary targets include elimination as a public health problem - defined as <1 new case per 10,000 inhabitants in 90% of foci, and <2000 reported cases by 2020. Using two independent mathematical models, this study assessed the achievability of these goals in the former Equateur province of the Democratic Republic of Congo, which historically had endemic levels of disease. The two deterministic models used different assumptions on disease progression, risk of infection and non-participation in screening, reflecting biological uncertainty. To validate the models a censor-fit-uncensor procedure was used to fit to health-zone level data from 2000 to 2012; initially the last six years were censored, then three and the final step utilised all data. The different model projections were used to evaluate the expected transmission and reporting for each health zone within each province under six intervention strategies using currently available tools. In 2012 there were 197 reported HAT cases in former Equateur reduced from 6828 in 2000, however this reflects lower active testing for HAT (1.3% of the population compared to 7.2%). Modelling results indicate that there are likely to be <300 reported cases in former Equateur in 2020 if screening continues at the mean level for 2000-2012 (6.2%), and <120 cases if vector control is introduced. Some health zones may fail to achieve <1 new case per 10,000 by 2020 without vector control, although most appear on track for this target using medical interventions alone. The full elimination goal will be harder to reach; between 39 and 54% of health zones analysed may have to improve their current medical-only strategy to stop transmission completely by 2030.

Fractal measures of spatial pattern as a heuristic for return rate in vegetative systems.

Measurement of population persistence is a long-standing problem in ecology; in particular, whether it is possible to gain insights into persistence without long time-series. Fractal measurements of spatial patterns, such as the Korcak exponent or boundary dimension, have been proposed as indicators of the persistence of underlying dynamics. Here we explore under what conditions a predictive relationship between fractal measures and persistence exists. We combine theoretical arguments with an aerial snapshot and time series from a long-term study of seagrass. For this form of vegetative growth, we find that the expected relationship between the Korcak exponent and persistence is evident at survey sites where the population return rate can be measured. This highlights a limitation of the use of power-law patch-size distributions and other indicators based on spatial snapshots. Moreover, our numeric simulations show that for a single species and a range of environmental conditions that the Korcak-persistence relationship provides a link between temporal dynamics and spatial pattern; however, this relationship is specific to demographic factors, so we cannot use this methodology to compare between species.

Modelling the persistence of measles.

For vaccination programs to be effective, it is important to understand and predict the persistence of the disease. By considering the process at different scales (from the individual to the population level), several models allow the persistence of diseases, such as measles, to be captured.

Age- and bite-structured models for vector-borne diseases.

The biology and behaviour of biting insects is a vitally important aspect in the spread of vector-borne diseases. This paper aims to determine, through the use of mathematical models, what effect incorporating vector senescence and realistic feeding patterns has on disease. A novel model is developed to enable the effects of age- and bite-structure to be examined in detail. This original PDE framework extends previous age-structured models into a further dimension to give a new insight into the role of vector biting and its interaction with vector mortality and spread of disease. Through the PDE model, the roles of the vector death and bite rates are examined in a way which is impossible under the traditional ODE formulation. It is demonstrated that incorporating more realistic functions for vector biting and mortality in a model may give rise to different dynamics than those seen under a more simple ODE formulation. The numerical results indicate that the efficacy of control methods that increase vector mortality may not be as great as predicted under a standard host-vector model, whereas other controls including treatment of humans may be more effective than previously thought.

Eight challenges in modelling infectious livestock diseases.

The transmission of infectious diseases of livestock does not differ in principle from disease transmission in any other animals, apart from that the aim of control is ultimately economic, with the influence of social, political and welfare constraints often poorly defined. Modelling of livestock diseases suffers simultaneously from a wealth and a lack of data. On the one hand, the ability to conduct transmission experiments, detailed within-host studies and track individual animals between geocoded locations make livestock diseases a particularly rich potential source of realistic data for illuminating biological mechanisms of transmission and conducting explicit analyses of contact networks. On the other hand, scarcity of funding, as compared to human diseases, often results in incomplete and partial data for many livestock diseases and regions of the world. In this overview of challenges in livestock disease modelling, we highlight eight areas unique to livestock that, if addressed, would mark major progress in the area.

Deterministic limits to stochastic spatial models of natural enemies.

Stochastic spatial models are becoming an increasingly popular tool for understanding ecological and epidemiological problems. However, due to the complexities inherent in such models, it has been difficult to obtain any analytical insights. Here, we consider individual-based, stochastic models of both the continuous-time Lotka-Volterra system and the discrete-time Nicholson-Bailey model. The stability of these two stochastic models of natural enemies is assessed by constructing moment equations. The inclusion of these moments, which mimic the effects of spatial aggregation, can produce either stabilizing or destabilizing influences on the population dynamics. Throughout, the theoretical results are compared to numerical models for the full distribution of populations, as well as stochastic simulations.

The effects of local spatial structure on epidemiological invasions.

Predicting the likely success of invasions is vitally important in ecology and especially epidemiology. Whether an organism can successfully invade and persist in the short-term is highly dependent on the spatial correlations that develop in the early stages of invasion. By modelling the correlations between individuals, we are able to understand the role of spatial heterogeneity in invasion dynamics without the need for large-scale computer simulations. Here, a natural methodology is developed for modelling the behaviour of individuals in a fixed network. This formulation is applied to the spread of a disease through a structured network to determine invasion thresholds and some statistical properties of a single epidemic.

Bubonic plague: a metapopulation model of a zoonosis.

Bubonic plague (Yersinia pestis) is generally thought of as a historical disease; however, it is still responsible for around 1000-3000 deaths each year worldwide. This paper expands the analysis of a model for bubonic plague that encompasses the disease dynamics in rat, flea and human populations. Some key variables of the deterministic model, including the force of infection to humans, are shown to be robust to changes in the basic parameters, although variation in the flea searching efficiency, and the movement rates of rats and fleas will be considered throughout the paper. The stochastic behaviour of the corresponding metapopulation model is discussed, with attention focused on the dynamics of rats and the force of infection at the local spatial scale. Short-lived local epidemics in rats govern the invasion of the disease and produce an irregular pattern of human cases similar to those observed. However, the endemic behaviour in a few rat subpopulations allows the disease to persist for many years. This spatial stochastic model is also used to identify the criteria for the spread to human populations in terms of the rat density. Finally, the full stochastic model is reduced to the form of a probabilistic cellular automaton, which allows the analysis of a large number of replicated epidemics in large populations. This simplified model enables us to analyse the spatial properties of rat epidemics and the effects of movement rates, and also to test whether the emergent metapopulation behaviour is a property of the local dynamics rather than the precise details of the model.

Correlation models for childhood epidemics.

One of the simplest set of equations for the description of epidemics (the SEIR equations) has been much studied, and produces reasonable approximations to the dynamics of communicable disease. However, it has long been recognized that spatial and social structure are important if we are to understand the long-term persistence and detailed behaviour of disease. We will introduce three pair models which attempt to capture the underlying heterogeneous structure by studying the connections and correlations between individuals. Although modelling the correlations necessarily leads to more complex equations, this pair formulation naturally incorporates the local dynamical behaviour generating more realistic persistence. In common with other studies on childhood diseases we will focus our attention on measles, for which the case returns are particularly well documented and long running.