The effect of temperature, farm density and foot-and-mouth disease restrictions on the 2007 UK bluetongue outbreak.

In 2006, bluetongue (BT), a disease of ruminants, was introduced into northern Europe for the first time and more than two thousand farms across five countries were affected. In 2007, BT affected more than 35,000 farms in France and Germany alone. By contrast, the UK outbreak beginning in 2007 was relatively small, with only 135 farms in southeast England affected. We use a model to investigate the effects of three factors on the scale of BT outbreaks in the UK: (1) place of introduction; (2) temperature; and (3) animal movement restrictions. Our results suggest that the UK outbreak could have been much larger had the infection been introduced into the west of England either directly or as a result of the movement of infected animals from southeast England before the first case was detected. The fact that air temperatures in the UK in 2007 were marginally lower than average probably contributed to the UK outbreak being relatively small. Finally, our results indicate that BT movement restrictions are effective at controlling the spread of infection. However, foot-and-mouth disease restrictions in place before the detection and control of BT in 2007 almost certainly helped to limit BT spread prior to its detection.

A network model of E. coli O157 transmission within a typical UK dairy herd: the effect of heterogeneity and clustering on the prevalence of infection.

Cattle are considered to be the main reservoir for Vero cytotoxin-producing Escherichia coli (VTEC) O157, a cause of food-poisoning (and even death) in humans. Here, the transmission of E. coli O157 within a typical UK dairy herd is modelled using a semi-stochastic network model. The model incorporates demographic as well as infection processes. Indirect transmission is modelled homogeneously, while direct transmission is modelled via a dynamic contact network. The aim was to investigate the effects of heterogeneity and clustering on the prevalence of infection within the herd and discover whether, particularly in terms of choosing an intervention strategy, it is necessary to include heterogeneity in direct contacts when modelling this sort of system. Results show that heterogeneity in direct contacts can make it more difficult for the pathogen to persist, particularly when the average number of contacts (per animal) in each group is small. They also show that the relationship between clustering and prevalence is not simple. For example, increasing the average number of contacts can increase clustering and prevalence. However, when the average number of contacts in each group is sufficiently high, higher clustering leads to lower prevalence. It would seem that clustering can aid the flow of infection under certain circumstances, but hinder it under others (probably by preventing wider dissemination). Further results show that indirect transmission (as it is modelled here) effectively removes the effect of heterogeneity in direct contacts. In terms of investigating proposed interventions, the results suggest that a network model would only be required if there was evidence to suggest that direct transmission was the major source of infection.

A semi-stochastic model for Salmonella infection in a multi-group herd.

A multi-group semi-stochastic model is formulated to identify possible causes of why different strains of Salmonella develop so much variation in their infection dynamics in UK dairy herds. The model includes demography (managed populations) and various types of transmission: direct, pseudovertical and indirect (via free-living infectious units in the environment). The effects of herd size and epidemiological parameters on mean prevalence of infection and mean time until fade out are investigated. Numerical simulation shows that higher pathogen-induced mortality, shorter infectious period, more persistent immune response and more rapid removal of faeces result in a lower mean prevalence of infection, a shorter mean time until fade out, and a greater probability of fade out of infection within 600 days. Combining these results and those for the deterministic counterpart could explain differences in observed epidemiological patterns and help to identify the factors inducing the decline in reported cases of epidemic strains such as DT104 in cattle. We further investigate the effect of group structure on the probability of a major outbreak by using the stochastic threshold theory in homogeneous populations and that in heterogeneous populations. Numerical studies suggest that group structure makes major outbreaks less likely than would be the case in a homogeneous population with the same basic reproduction number. Moreover, some control strategies are suggested by investigating the effect of epidemiological parameters on the probability of an epidemic.

Infection in social networks: using network analysis to identify high-risk individuals.

Simulation studies using susceptible-infectious-recovered models were conducted to estimate individuals' risk of infection and time to infection in small-world and randomly mixing networks. Infection transmitted more rapidly but ultimately resulted in fewer infected individuals in the small-world, compared with the random, network. The ability of measures of network centrality to identify high-risk individuals was also assessed. "Centrality" describes an individual's position in a population; numerous parameters are available to assess this attribute. Here, the authors use the centrality measures degree (number of contacts), random-walk betweenness (a measure of the proportion of times an individual lies on the path between other individuals), shortest-path betweenness (the proportion of times an individual lies on the shortest path between other individuals), and farness (the sum of the number of steps between an individual and all other individuals). Each was associated with time to infection and risk of infection in the simulated outbreaks. In the networks examined, degree (which is the most readily measured) was at least as good as other network parameters in predicting risk of infection. Identification of more central individuals in populations may be used to inform surveillance and infection control strategies.

A clarification of transmission terms in host-microparasite models: numbers, densities and areas.

Transmission is the driving force in the dynamics of any infectious disease. A crucial element in understanding disease dynamics, therefore, is the 'transmission term' describing the rate at which susceptible hosts are 'converted' into infected hosts by their contact with infectious material. Recently, the conventional form of this term has been increasingly questioned, and new terminologies and conventions have been proposed. Here, therefore, we review the derivation of transmission terms, explain the basis of confusion, and provide clarification. The root of the problem has been a failure to include explicit consideration of the area occupied by a host population, alongside both the number of infectious hosts and their density within the population. We argue that the terms 'density-dependent transmission' and 'frequency-dependent transmission' remain valid and useful (though a 'fuller' transmission term for the former is identified), but that the terms 'mass action', 'true mass action' and 'pseudo mass action' are all unhelpful and should be dropped. Also, contrary to what has often been assumed, the distinction between homogeneous and heterogeneous mixing in a host population is orthogonal to the distinction between density- and frequency-dependent transmission modes.

The basic depression ratio of the host: the evolution of host resistance to microparasites.

The basic reproduction ratio R0 occupies a central position in the theory of host pathogen interactions. However, this quantity stresses the role of the pathogen. This paper proposes an additional, more host-centred char acterization using the basic depression ratio D0. This quantity is the number of host individuals per infected by which the infected host population is depressed below its uninfected level. This paper shows that a baseline criterion for the evolution of host resistance to microparasites is that resistance evolves to minimize D0. This parallels the result for pathogen virulence where R0 is maximized. The tension between these two criteria is noted. The framework established allows a discussion of trade-offs between aspects of the pathogen-free host biology and the host pathogen interaction. For certain linear and convex trade-offs it is shown that the strain with the lowest transmission parameter beta wins (despite the fact that it has the lowest intrinsic birth rate a). For corresponding concave trade-offs, either the strain with minimum beta and a or the strain with maximum beta and a wins. Finally the connection with the techniques of adaptive dynamics is made. Evolutionary singular points are shown to occur at extrema of D0. The evolutionary attainment of the results is discussed.

Community dynamics, trade-offs, invasion criteria and the evolution of host resistance to microparasites.

This article discusses the community dynamics of the evolution of host resistance to microparasites. We present exact results for a model with an arbitrary number of host strains. We show that these results are identical to those inferred on the basis of invadability criteria. The long-term behaviour of the model allows monomorphism or dimorphism (but no higher polymorphisms). We invoke trade-offs between pathogen transmissibility and either host intrinsic growth rate or resistance to crowding. In the first case, convexity leads to an ESS, concavity to branching points and repellers. In the second, these roles are interchanged. We present results for fixed strain distributions and establish parallels with results using an adaptive dynamics perspective. We also establish differences. For example, if an ESS is "deleted" from the strain distribution, then adjacent-strain dimorphism is possible. The invadability criteria which we obtain can be expressed in terms of geometrical properties of the trade-offs namely, the slopes of chords and tangent to the associated function. We speculate that this result may have wider applicability than provided by the context of the present work.

Three mechanisms of host resistance to microparasites-avoidance, recovery and tolerance-show different evolutionary dynamics.

Parasite resistant hosts may avoid becoming infected, recover more quickly after infection or survive longer once infected. A model is constructed to examine the evolution of costly host resistance to directly transmitted microparasites and these three distinct mechanisms of avoidance, recovery and tolerance are compared. In each case polymorphism is more likely between very dissimilar strains and resistance (by which we mean the resistant strain alone) is always more likely to occur in hosts with high intrinsic productivity. However, the region where polymorphism occurs is relatively much smaller when resistance is through reduced pathogenicity. In particular, polymorphism with highly resistant strains requires correspondingly high costs. This is in contrast to avoidance or recovery resistance, where polymorphism can also occur when high resistance is associated with small costs due to the inability of highly resistant strains with low susceptibility or high recovery to support the parasite alone and hence resist invasion by the susceptible strain. Relatedly, resistance through avoidance and recovery is favoured in response to less pathogenic parasites.

A baseline model for the apparent competition between many host strains: the evolution of host resistance to microparasites.

The purpose of this article is to establish and analyse a baseline model for the apparent competition between many host strains attempting to avoid a uniform microparasitic population. The model is formulated and analysed using invasion criteria in the main text. The results are verified by more formal methods in the appendix. Cases in which the microparasite can invade are distinguished geometrically from those in which it cannot using threshold and strain composition conditions. A major result obtained when the pathogen persists is a competitive exclusion principle for host resistance. For non-lethal infections, the winning strain is that which affords the pathogen maximum threshold density; for possibly lethal infections, a somewhat generalized version of this criterion is presented and discussed. The tension is highlighted between these results and the baseline behaviour of many pathogen strains and a uniform host population-here the winning pathogen strain is that with minimum threshold density.

Persistence of tick-borne virus in the presence of multiple host species: tick reservoirs and parasite mediated competition.

Tick-borne viruses in tropical and temperate parts of the world have a significant impact on human, livestock and wildlife hosts both directly, through mortality/morbidity, and economically. Since the ticks have multiple life stages and can utilize a large range of host species our understanding of the dynamics of these infections is often not clear. In this paper we consider the impact of a population which is a tick host but non-viraemic on one which is both a tick host and viraemic. We present two simple deterministic models and use joint threshold density curves to illustrate the basic reproductive ratios of both the ticks and the virus. We find that the non-viraemic hosts can have considerable impact on the viraemic host. Either they amplify the tick population and cause the virus to persist, or they dilute the infection and cause it to die out. A general model framework is presented here but a special case of this model describes the red grouse-hare-Louping-ill system.

A model of disease and vaccination for infections with acute and chronic phases.

A general model is presented of a disease in which both recovered and vaccinated individuals are protected from acute disease, but are still susceptible to chronic infection. The special threshold conditions for the establishment and persistence of such a disease are derived and explained in full. The efficacies of alternative vaccination strategies are detailed and a specific example of such a disease is given by examining feline calicivirus (FCV), a cause of upper respiratory tract disease in cats.

Community structure and the interplay between interspecific infection and competition.

Our motivation is the need to understand how two different interactions between species-shared infection and interspecific competition-combine to determine community structure. We introduce a proto-typical model of two hosts sharing a pathogen and also competing directly. We discuss forces of infection, forces of competition and invasion criteria and their relevance to long-term outcomes and community structure. To understand their interplay, we consider first purely competitive and second purely infective interactions. We then investigate our full model to establish how the two forces combine and how the combination and related invasion criteria determine community structure. The forces of infection and competition do not merely add; there is a synergetic resistance to invasion. Using generalised invasion criteria and subsidiary conditions for the feasibility and stability of uninfected coexistence, we classify long-term outcomes. We distinguish two main routes to three-species coexistence. In the first, two host species, each of which would not alone support the pathogen, support it jointly if interspecific competition is relatively weak, interspecific infection strong. In the second, at least one host species would alone support the pathogen and both are invadable by the other, but subsidiary conditions yield two cases. In one, infected coexistence results when the two hosts would coexist stably purely competitively and at sufficiently high densities to support the pathogen jointly. Thus coexistence is promoted by weak interspecific competition but there is a tension between weak interspecific infection favouring invadability and strong interspecific infection promoting pathogen survival. In the other, infected coexistence results when the two hosts would not coexist in the absence of the pathogen. This pathogen-mediated host coexistence is expected where there is strong intraspecific infection (lowering densities) and weak interspecific infection (favouring invadibility) as necessary. Results are compared with previous work and apparent competition and resource- and transmission-mediated coexistence are discussed.

Host-pathogen systems in a spatially patchy environment.

A discrete model for a host-pathogen system is developed and is used to represent the dynamics in each patch within a landscape of n x n patches. These patches are linked by between-generation dispersal to neighbouring patches. Important results (compared to similar 'coupled map lattice' studies) include an increase in the likelihood of metapopulation extinction if the natural loss of pathogen particles is low, and the observation of a radial wave pattern (not previously reported) where the wavefront propagates uniformly from a central focus. This result has additional significance in that it permits the system to exhibit 'intermittency' between two quasi-stable spatial patterns: spirals and radial waves. With intermittent behaviour, the dynamics may look consistent when viewed at one time scale, but over a longer time scale they can alter dramatically and repeatedly between the two patterns. There is also evidence of clear links between spatial structure and temporal metapopulation behaviour in both the intermittent and 'pure' regions, verified by results from an algorithmic complexity measure and a spectral analysis of the temporal dynamics.

Life-history trade-offs and the evolution of pathogen resistance: competition between host strains.

The dynamics of a 'resistant' and a 'susceptible' strain of a self-regulated host species, in the presence of a directly transmitted pathogen, is investigated. The two strains trade off differences in pathogen transmissibility (as an aspect of pathogen resistance) against differences in birth rate and/or resistance to crowding. Depending on parameter values, either strain may be eliminated, or the two may coexist (along with the pathogen). Coexistence (polymorphism), unsurprisingly, requires an appropriate balance between the different advantages possessed by the two strains. The probability of coexistence through such a balance, however, varies nonlinearly with the degree of difference between the strains: coexistence is least likely between two very similar strains. Resistance is most likely to evolve in hosts with the characteristics of many insect pests. Moreover, with highly pathogenic pathogens, a 'susceptible' strain may exclude a 'resistant' strain because its higher growth rate is more effective against the pathogen than reduced transmissibility. 'Resistance' can reside in parameters other than those directly associated with the pathogen. Although no cycles arise and no chaotic behaviour is found, an oscillatory approach to equilibrium is commonly observed, signalling the possibility of observable oscillations in strain frequency in the (more variable) real world.

The population dynamics of microparasites and vertebrate hosts: the importance of immunity and recovery.

The models of Anderson and May on the dynamics of vertebrate (1979, Nature 280, 361-367) and invertebrate (1981, Philos, Trans. R. Soc. 291, 451-524) populations and their microparasites have been extended and elaborated. Hence, in a series of models the effects of a range of biological factors have been considered. These models taken together clarify in particular the effects of recovery from the disease back to a state of susceptibility and the additional effects of recovery to a state of immunity. In general recovery increases both the threshold density and the equilibrium density but does not alter the prevalence of infection or the region in parameter space in which the host is regulated. Immunity causes a further increase in the equilibrium density, does not alter either the prevalence of infection or the threshold density, but reduces the region in which there is regulation. In both cases exceptions tend to occur when there is density dependence.

Host-host-pathogen models and microbial pest control: the effect of host self regulation.

A model has been investigated of the dynamics of the interaction between two hosts that are both attacked by a common pathogen with free-living infective stages, where the hosts are also subject to self-regulation. If either host interacted with the pathogen alone, two types of dynamics would be possible: an uninfected state where the host settles at its carrying capacity, and an infected state where the host settles at, or cycles around, a density lower than the carrying capacity. The three possible combination of two hosts have been investigated: uninfected-uninfected (both hosts uninfected if alone with the pathogen), infected-uninfected and infected-infected. A range of dynamics is generated, depending on parameter values, including infected co-existence of the two hosts (arrived at by a variety of routes), uninfected co-existence of the two hosts, exclusion of one host by the other which remains in an infected state, and a number of outcomes contingent on the initial densities in the system. Free-living infective stages make uninfected co-existence more likely and introduce additional contingency into the dynamics. The implications for microbial pest control are into the dynamics. The implications for microbial pest control are markedly different from those derived from related models without host self-regulation. There appears to be little chance of a non-target host undermining pest control, relatively little chance of the non-target enhancing pest control and a small but non-negligible threat to non-targets when parameter values are appropriate. The application of the results is commended but great caution is urged.

A host-host-pathogen model with free-living infective stages, applicable to microbial pest control.

A model has been investigated of the dynamics of the interaction between two hosts which are both attacked by a common pathogen, where the pathogen has free-living infective stages the population size of which must itself be modelled explicitly, and where the host species do not interact with one another except through their shared pathogen. If either host interacted with the pathogen alone, three broad classes of dynamics would be possible: host regulation, pathogen persistence and pathogen extinction. Here, all possible types of combinations of hosts are examined: regulation-regulation (both hosts would be regulated if they interacted with the pathogen alone), regulation-persistence, regulation-extinction, persistence-persistence persistence-extinction and extinction-extinction. A wide range of dynamics is generated, including a number of patterns quite unlike those found in the one-host pathogen case (e.g. persistence in one host, elimination of the other host) and behaviour contingent on initial densities in the system. For clarity and pertinence, attention is focused on the case where one host is a pest, the pathogen is a potential microbial control agent, and the other host is a non-target species which it is undesirable to harm. The model suggests, broadly, that non-targets are unlikely to be seriously threatened in such cases, and also that non-targets, far from undermining pest control, are quite likely to contribute to its efficacy.

Field comparison of body composition techniques: hydrostatic weighing, skinfold thickness, and bioelectric impedance.

Body composition and appropriate playing weight are frequently requested by coaches. Numerous methods for estimating these figures are available, and each has its own limitation, be it technical or biological. A comparison of three common methods was made-underwater weighting (H2O, the criterion), skinfold thicknesses (SF), and commercial bioelectrical impedance analysis (BIA). Subjects were 29 professional football players measured by each of the three methods after an overnight fast. Data was collected 10 weeks preceding the players' formal training camp. There was no difference for percentage of weight as fat between SF (15.8%) and H2O (14.2%). Bioelectrical impedance analysis significantly (p < .05) overestimated percent fat (19.2%) compared to H20. Error rates when regressing SF on H2O were favorable, whether expressed for the whole sample (3.04%) or by race (1.78% or 3.56% for whites and blacks, respectively). Regression of BIA on H2O showed an elevated, overall error rate (14.12%) and elevated error rates for whites (11.57%) and blacks (13.81%). Of the two estimates of body composition on a racially mixed sample of males, SF provided the best estimate with the least amount of error. J Orthop Sports Phys Ther 1991;13(5):235-239.