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Usage and management alter the dynamics of soil organic carbon (SOC). The aim of this study was to compare the CO2 emissions in a Typic Humudept under different uses, and to relate the effects of CO2 emissions to the organic carbon content of the soil. Soil samples were collected from the 0-0.05, 0.05-0.10, 0.10-0.15 and 0.15-0.20 m layers under the following agricultural systems: no-tillage (NT), conventional (CT) and fruit orchard (FO). Samples were also collected from an area of native forest (NF) adopted as reference. The variables under evaluation were CO2 emissions and SOC content. Interaction between the usage or management systems and the soil layers influenced CO2 emissions in the soil. However, there was a difference in CO2 emissions between the soil layers under NF and CT only. In the 0-0.20 m layer, there was no difference in CO2 emissions under FO or CT, however these were greater than under NF or NT. In turn, the emissions under NT were lower than under NF at this layer. Furthermore, the systems with greater CO2 emissions showed less SOC. As such, in a Typic Humudept, the no-tillage management system results in reduced CO2 emissions. Greater SOC mineralisation has a direct impact on higher CO2 emissions.

Conventional epidemiological studies of infections spreading through trade networks, e.g., via livestock movements, generally show that central large-size holdings (hubs) should be preferentially surveyed and controlled in order to reduce epidemic spread. However, epidemiological strategies alone may not be economically optimal when costs of control are factored in together with risks of market disruption from targeting core holdings in a supply chain. Using extensive data on animal movements in supply chains for cattle and swine in France, we introduce a method to identify effective strategies for preventing outbreaks with limited budgets while minimizing the risk of market disruptions. Our method involves the categorization of holdings based on position along the supply chain and degree of market share. Our analyses suggest that trade has a higher risk of propagating epidemics through cattle networks, which are dominated by exchanges involving wholesalers, than for swine. We assess the effectiveness of contrasting interventions from the perspectives of regulators and the market, using percolation analysis. We show that preferentially targeting minor, non-central agents can outperform targeting of hubs when the costs to stakeholders and the risks of market disturbance are considered. Our study highlights the importance of assessing joint economic-epidemiological risks in networks underlying pathogen propagation and trade., (© 2016 The Authors.)

Market trade-routes can support infectious-disease transmission, impacting biological populations and even disrupting trade that conduces the disease. Epidemiological models increasingly account for reductions in infectious contact, such as risk-aversion behaviour in response to pathogen outbreaks. However, responses in market dynamics clearly differ from simple risk aversion, as are driven by other motivation and conditioned by "friction" constraints (a term we borrow from labour economics). Consequently, the propagation of epidemics in markets of, for example livestock, is frictional due to time and cost limitations in the production and exchange of potentially infectious goods. Here we develop a coupled economic-epidemiological model where transient and long-term market dynamics are determined by trade friction and agent adaptation, and can influence disease transmission. The market model is parameterised from datasets on French cattle and pig exchange networks. We show that, when trade is the dominant route of transmission, market friction can be a significantly stronger determinant of epidemics than risk-aversion behaviour. In particular, there is a critical level of friction above which epidemics do not occur, which suggests some epidemics may not be sustained in highly frictional markets. In addition, friction may allow for greater delay in removal of infected agents that still mitigates the epidemic and its impacts. We suggest that policy for minimising contagion in markets could be adjusted to the level of market friction, by adjusting the urgency of intervention or by increasing friction through incentivisation of larger-volume less-frequent transactions that would have limited effect on overall trade flow. Our results are robust to model specificities and can hold in the presence of non-trade disease-transmission routes., (Copyright © 2015 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Knowledge of the incubation period of infectious diseases (time between host infection and expression of disease symptoms) is crucial to our epidemiological understanding and the design of appropriate prevention and control policies. Plant diseases cause substantial damage to agricultural and arboricultural systems, but there is still very little information about how the incubation period varies within host populations. In this paper, we focus on the incubation period of soilborne plant pathogens, which are difficult to detect as they spread and infect the hosts underground and above-ground symptoms occur considerably later. We conducted experiments on Rhizoctonia solani in sugar beet, as an example patho-system, and used modelling approaches to estimate the incubation period distribution and demonstrate the impact of differing estimations on our epidemiological understanding of plant diseases. We present measurements of the incubation period obtained in field conditions, fit alternative probability models to the data, and show that the incubation period distribution changes with host age. By simulating spatially-explicit epidemiological models with different incubation-period distributions, we study the conditions for a significant time lag between epidemics of cryptic infection and the associated epidemics of symptomatic disease. We examine the sensitivity of this lag to differing distributional assumptions about the incubation period (i.e. exponential versus Gamma). We demonstrate that accurate information about the incubation period distribution of a pathosystem can be critical in assessing the true scale of pathogen invasion behind early disease symptoms in the field; likewise, it can be central to model-based prediction of epidemic risk and evaluation of disease management strategies. Our results highlight that reliance on observation of disease symptoms can cause significant delay in detection of soil-borne pathogen epidemics and mislead practitioners and epidemiologists about the timing, extent, and viability of disease control measures for limiting economic loss.

Invasive soilborne plant pathogens cause substantial damage to crops and natural populations, but our understanding of how to prevent their epidemics or reduce their damage is limited. A key and experimentally-tested concept in the epidemiology of soilborne plant diseases is that of a threshold spacing between hosts below which epidemics (invasive spread) can occur. We extend this paradigm by examining how plant-root growth may alter the conditions for occurrence of soilborne pathogen epidemics in plant populations. We hypothesise that host-root growth can 1) increase the probability of pathogen transmission between neighbouring plants and, consequently, 2) decrease the threshold spacing for epidemics to occur. We predict that, in systems initially below their threshold conditions, root growth can trigger soilborne pathogen epidemics through a switch from non-invasive to invasive behaviour, while in systems above threshold conditions root growth can enhance epidemic development. As an example pathosystem, we studied the fungus Rhizoctonia solani on sugar beet in field experiments. To address hypothesis 1, we recorded infections within inoculum-donor and host-recipient pairs of plants with differing spacing. We translated these observations into the individual-level concept of pathozone, a host-centred form of dispersal kernel. To test hypothesis 2 and our prediction, we used the pathozone to parameterise a stochastic model of pathogen spread in a host population, contrasting scenarios of spread with and without host growth. Our results support our hypotheses and prediction. We suggest that practitioners of agriculture and arboriculture account for root system expansion in order to reduce the risk of soilborne-disease epidemics. We discuss changes in crop design, including increasing plant spacing and using crop mixtures, for boosting crop resilience to invasion and damage by soilborne pathogens. We speculate that the disease-induced root growth observed in some pathosystems could be a pathogen strategy to increase its population through host manipulation.

Exotic pathogens and pests threaten ecosystem service, biodiversity, and crop security globally. If an invasive agent can disperse asymptomatically over long distances, multiple spatial and temporal scales interplay, making identification of effective strategies to regulate, monitor, and control disease extremely difficult. The management of outbreaks is also challenged by limited data on the actual area infested and the dynamics of spatial spread, due to financial, technological, or social constraints. We examine principles of landscape epidemiology important in designing policy to prevent or slow invasion by such organisms, and use Phytophthora ramorum, the cause of sudden oak death, to illustrate how shortfalls in their understanding can render management applications inappropriate. This pathogen has invaded forests in coastal California, USA, and an isolated but fast-growing epidemic focus in northern California (Humboldt County) has the potential for extensive spread. The risk of spread is enhanced by the pathogen's generalist nature and survival. Additionally, the extent of cryptic infection is unknown due to limited surveying resources and access to private land. Here, we use an epidemiological model for transmission in heterogeneous landscapes and Bayesian Markov-chain-Monte-Carlo inference to estimate dispersal and life-cycle parameters of P. ramorum and forecast the distribution of infection and speed of the epidemic front in Humboldt County. We assess the viability of management options for containing the pathogen's northern spread and local impacts. Implementing a stand-alone host-free "barrier" had limited efficacy due to long-distance dispersal, but combining curative with preventive treatments ahead of the front reduced local damage and contained spread. While the large size of this focus makes effective control expensive, early synchronous treatment in newly-identified disease foci should be more cost-effective. We show how the successful management of forest ecosystems depends on estimating the spatial scales of invasion and treatment of pathogens and pests with cryptic long-distance dispersal., (© 2012 Filipe et al.)

Background: The persistence of malaria as an endemic infection and one of the major causes of childhood death in most parts of Africa has lead to a radical new call for a global effort towards eradication. With the deployment of a highly effective vaccine still some years away, there has been an increased focus on interventions which reduce exposure to infection in the individual and -by reducing onward transmission-at the population level. The development of appropriate monitoring of these interventions requires an understanding of the timescales of their effect., Methods & Findings: Using a mathematical model for malaria transmission which incorporates the acquisition and loss of both clinical and parasite immunity, we explore the impact of the trade-off between reduction in exposure and decreased development of immunity on the dynamics of disease following a transmission-reducing intervention such as insecticide-treated nets. Our model predicts that initially rapid reductions in clinical disease incidence will be observed as transmission is reduced in a highly immune population. However, these benefits in the first 5-10 years after the intervention may be offset by a greater burden of disease decades later as immunity at the population level is gradually lost. The negative impact of having fewer immune individuals in the population can be counterbalanced either by the implementation of highly-effective transmission-reducing interventions (such as the combined use of insecticide-treated nets and insecticide residual sprays) for an indefinite period or the concurrent use of a pre-erythrocytic stage vaccine or prophylactic therapy in children to protect those at risk from disease as immunity is lost in the population., Conclusions: Effective interventions will result in rapid decreases in clinical disease across all transmission settings while population-level immunity is maintained but may subsequently result in increases in clinical disease many years later as population-level immunity is lost. A dynamic, evolving intervention programme will therefore be necessary to secure substantial, stable reductions in malaria transmission.

The broad-spectrum antiparasitic drug ivermectin was licensed for use against onchocerciasis in 1987, yet the mechanisms by which it exerts a fast decrease and long-lasting suppression of Onchocerca volvulus microfilaridermia, and inhibition of microfilarial release by female worms remain largely unknown. A better understanding of the effects of ivermectin on O volvulus microfilariae and macrofilariae is crucial to improve our ability to predict the long-term effect of treatment. We did a systematic review of individual and population-based ivermectin trials to investigate the temporal dynamics of the drug's microfilaricidal and embryostatic efficacy after administration of a single, standard dose (150 microg/kg). Meta-analyses on data from 26 microfilarial and 15 macrofilarial studies were linked by a mathematical model describing the dynamics of potentially fertile female parasites to skin microfilariae. The model predicts that after treatment, microfilaridermia would be reduced by half after 24 h, by 85% after 72 h, by 94% after 1 week, and by 98-99% after 1-2 months, the latter also corresponding to the time when the fraction of females harbouring live microfilariae is at its lowest (reduced by around 70% from its original value). Our results provide a baseline microfilarial skin repopulation curve against which to compare studies done after long-term treatment.

Background: The durations of untreated stage 1 (early stage, haemo-lymphatic) and stage 2 (late stage, meningo-encephalitic) human African trypanosomiasis (sleeping sickness) due to Trypanosoma brucei gambiense are poorly quantified, but key to predicting the impact of screening on transmission. Here, we outline a method to estimate these parameters., Methods: We first model the duration of stage 1 through survival analysis of untreated serological suspects detected during Médecins Sans Frontières interventions in Uganda and Sudan. We then deduce the duration of stage 2 based on the stage 1 to stage 2 ratio observed during active case detection in villages within the same sites., Results: Survival in stage 1 appears to decay exponentially (daily rate = 0.0019; mean stage 1 duration = 526 days [95%CI 357 to 833]), possibly explaining past reports of abnormally long duration. Assuming epidemiological equilibrium, we estimate a similar duration of stage 2 (500 days [95%CI 345 to 769]), for a total of nearly three years in the absence of treatment., Conclusion: Robust estimates of these basic epidemiological parameters are essential to formulating a quantitative understanding of sleeping sickness dynamics, and will facilitate the evaluation of different possible control strategies.

Gambiense human African trypanosomiasis (HAT, sleeping sickness) is widely assumed to be 100% pathogenic and fatal. However, reports to the contrary exist, and human trypano-tolerance has been postulated. Furthermore, there is uncertainty about the actual duration of both stage 1 and stage 2 infection, particularly with respect to how long a patient remains infectious. Understanding such basic parameters of HAT infection is essential for optimising control strategies based on case detection. We considered the potential existence and relevance of human trypano-tolerance, and explored the duration of infectiousness, through a review of published evidence on the natural progression of gambiense HAT in the absence of treatment, and biological considerations. Published reports indicate that most gambiense HAT cases are fatal if untreated. Self-resolving and asymptomatic chronic infections probably constitute a minority if they do indeed exist. Chronic carriage, however, deserves further study, as it could seed renewed epidemics after control programmes cease.

Acquisition of partially protective immunity is a dominant feature of the epidemiology of malaria among exposed individuals. The processes that determine the acquisition of immunity to clinical disease and to asymptomatic carriage of malaria parasites are poorly understood, in part because of a lack of validated immunological markers of protection. Using mathematical models, we seek to better understand the processes that determine observed epidemiological patterns. We have developed an age-structured mathematical model of malaria transmission in which acquired immunity can act in three ways ("immunity functions"): reducing the probability of clinical disease, speeding the clearance of parasites, and increasing tolerance to subpatent infections. Each immunity function was allowed to vary in efficacy depending on both age and malaria transmission intensity. The results were compared to age patterns of parasite prevalence and clinical disease in endemic settings in northeastern Tanzania and The Gambia. Two types of immune function were required to reproduce the epidemiological age-prevalence curves seen in the empirical data; a form of clinical immunity that reduces susceptibility to clinical disease and develops with age and exposure (with half-life of the order of five years or more) and a form of anti-parasite immunity which results in more rapid clearance of parasitaemia, is acquired later in life and is longer lasting (half-life of >20 y). The development of anti-parasite immunity better reproduced observed epidemiological patterns if it was dominated by age-dependent physiological processes rather than by the magnitude of exposure (provided some exposure occurs). Tolerance to subpatent infections was not required to explain the empirical data. The model comprising immunity to clinical disease which develops early in life and is exposure-dependent, and anti-parasite immunity which develops later in life and is not dependent on the magnitude of exposure, appears to best reproduce the pattern of parasite prevalence and clinical disease by age in different malaria transmission settings. Understanding the effector mechanisms underlying these two immune functions will assist in the design of transmission-reducing interventions against malaria.

1. The transient dynamics and stability of a population are determined by the interplay between species density, its spatial distribution and the positive and negative density-dependent processes regulating population growth. 2. Using the human-helminth parasite system as an example, we propose that the life-stage upon which negative density dependence operates will influence the rate of host reinfection following anthelmintic chemotherapy, and the likely success of control programmes. 3. Simple deterministic models are developed which highlight how a parasite species whose population size is down-regulated by density-dependent establishment will reinfect a host population at a faster rate than a species with density-dependent parasite fecundity. 4. Different forms of density dependence can produce the same equilibrium behaviour but different transient dynamics. Under-representing the nature and magnitude of density-dependent mechanisms, and in particular those operating upon establishing life-stages, may cause the resilience of the parasite population to a control perturbation to be underestimated.

Severe adverse events (SAEs) following ivermectin treatment may occur in people harbouring high Loa loa microfilarial (mf) densities. In the context of mass ivermectin distribution for onchocerciasis control in Africa, it is crucial to define precisely the geographical distribution of L. loa in relation to that of Onchocerca volvulus and predict the prevalence of heavy infections. To this end, we analysed the distribution of mf loads in 4183 individuals living in 36 villages of central Cameroon. Mf loads were assessed quantitatively by calibrated blood smears, collected prior to ivermectin distribution. We explored the pattern of L. loa mf aggregation by fitting the (zero-truncated) negative binomial distribution and estimating its overdispersion parameter k by maximum likelihood. The value of k varied around 0.3 independently of mf intensity, host age, village and endemicity level. Based on these results, we developed a semi-empirical model to predict the prevalence of heavy L. loa mf loads in a community given its overall mf prevalence. If validated at the continental scale and linked to predictive spatial models of loiasis distribution, this approach would be particularly useful for optimizing the identification of areas at risk of SAEs and providing estimates of populations at risk in localities where L. loa and O. volvulus are co-endemic.

Ivermectin treatment may induce severe adverse reactions in some individuals heavily infected with Loa loa. This hampers the implementation of mass ivermectin treatment against onchocerciasis in areas where Onchocerca volvulus and L. loa are co-endemic. In order to identify factors, including co-infections, which may explain the presence of high L. loa microfilaraemia in some individuals, we analysed data collected in 19 villages of central Cameroon. Two standardized skin snips and 30 mul of blood were obtained from each of 3190 participants and the microfilarial (mf) loads of both O. volvulus and L. loa were quantified. The data were analysed using multivariate hierarchical models. Individual-level variables were: age, sex, mf presence, and mf load; village-related variables included the endemicity levels for each infection. The two species show a certain degree of ecological separation in the study area. However, for a given individual host, the presence of microfilariae of one species was positively associated with the presence of microfilariae of the other (OR=1.79, 95% CI [1.43-2.24]). Among individuals harbouring Loa microfilariae, there was a slight positive relationship between the L. loa and O. volvulus mf loads which corresponded to an 11% increase in L. loa mf load per 100 O. volvulus microfilariae. Co-infection with O. volvulus is not sufficient to explain the very high L. loa mf loads harboured by some individuals.

Background: Botulism is a rare but potentially lethal disease in which ophthalmic signs and symptoms are among the very earliest manifestations. The aim of this study was to investigate the epidemiological and clinical features of botulism-infected patients admitted to a general hospital in Porto, Portugal., Methods: We performed a retrospective chart review of all botulism patients admitted to São João Hospital between January 1998 and January 2003. We excerpted data on epidemiology, ophthalmic and non-ophthalmic manifestations, and treatment., Results: We identified 18 patients in nine registered outbreaks. In two patients (11%), ophthalmic manifestations preceded systemic manifestations; in six patients (33%), ophthalmic and systemic manifestations occurred simultaneously; in ten patients (56%), systemic manifestations occurred first. Ophthalmologists had examined only seven patients and made the correct diagnosis in five. The most common ocular symptoms were blurred near vision (100%), blurred distant vision (94%), and diplopia (44%). Accommodation impairment was documented in all seven patients examined by ophthalmologists., Conclusions: Ophthalmic manifestations were among the earliest and most prominent manifestations of botulism in this series, as in earlier reports. The diagnosis should be suspected when impaired accommodation and gastrointestinal symptoms occur together.

Here we analyze patterns of human infection with Onchocerca volvulus (the cause of river blindness) in different continents and ecologies. In contrast with some geohelminths and schistosome parasites whose worm burdens typically exhibit a humped pattern with host age, patterns of O. volvulus infection vary markedly with locality. To test the hypothesis that such differences are partly due to heterogeneity in exposure to vector bites, we develop an age- and sex-structured model for intensity of infection, with parasite regulation within humans and vectors. The model is fitted to microfilarial data from savannah villages of northern Cameroon, coffee fincas of central Guatemala, and forest-dwelling communities of southern Venezuela that were recorded before introducing ivermectin treatment. Estimates of transmission and infection loads are compared with entomological and epidemiological field data. Host age- and sex-heterogeneous exposure largely explains locale-specific infection patterns in onchocerciasis (whereas acquired protective immunity has been invoked for other helminth infections). The basic reproductive number, R0, ranges from 5 to 8, which is slightly above estimates for other helminth parasites but well below previously presented values.

Bystander effects, whereby cells that are not directly exposed to ionizing radiation exhibit adverse biological effects, have been observed in a number of experimental systems. A novel stochastic model of the radiation-induced bystander effect is developed that takes account of spatial location, cell killing and repopulation. The ionizing radiation dose- and time-responses of this model are explored, and it is shown to exhibit pronounced downward curvature in the high dose-rate region, similar to that observed in many experimental systems, reviewed in the paper. It is also shown to predict the augmentation of effect after fractionated delivery of dose that has been observed in certain experimental systems. It is shown that the generally intractable solution of the full stochastic system can be considerably simplified by assumption of pairwise conditional dependence that varies exponentially over time.

Epidemiologists are interested in using models that incorporate the effects of clustering in the spatial pattern of disease on epidemic dynamics. Bolker (1999, Bull. Math. Biol. 61, 849-874) has developed an approach to study such models based on a moment closure assumption. We show that the assumption works above a threshold initial level of disease that depends on the spatial dispersal of the pathogen. We test an alternative assumption and show that it does not have this limitation. We examine the relation between lattice and continuous-medium implementations of the approach.

Spatial interactions are key determinants in the dynamics of many epidemiological and ecological systems; therefore it is important to use spatio-temporal models to estimate essential parameters. However, spatially-explicit data sets are rarely available; moreover, fitting spatially-explicit models to such data can be technically demanding and computationally intensive. Thus non-spatial models are often used to estimate parameters from temporal data. We introduce a method for fitting models to temporal data in order to estimate parameters which characterise spatial epidemics. The method uses semi-spatial models and pair approximation to take explicit account of spatial clustering of disease without requiring spatial data. The approach is demonstrated for data from experiments with plant populations invaded by a common soilborne fungus, Rhizoctonia solani. Model inferences concerning the number of sources of disease and primary and secondary infections are tested against independent measures from spatio-temporal data. The applicability of the method to a wide range of host-pathogen systems is discussed.

Aims: To study the mechanism and the means of preventing soccer eye injuries., Methods: Kicked soccer ball velocities were measured for a range of ages and experience. Soccer balls (sizes 3, 4, and 5), inflated to 3, 6, and 9 psi, were impacted onto an artificial orbit and the results analysed at 1000 frames per second. Protective eyewear was fitted to a headform then impacted and evaluated., Results: The mean peak ball velocity was 20.4 (SD 6.2) m/s. Soccer balls at 18 m/s entered the orbit between 7.5 and 8.7 mm. There was no significant difference in orbital penetration as a result of ball size or pressure. The soccer ball stayed in the orbit approximately 10 ms and appeared to have a suction effect as it withdrew. Protective eyewear that complied with sports protective eyewear standard ASTM F803 prevented contact of the ball to the eye., Conclusions: The soccer ball causes eye injury by entering the orbit. Protectors that pass ASTM F803 would prevent orbital intrusion.

The nature of pathogen transport mechanisms strongly determines the spatial pattern of disease and, through this, the dynamics and persistence of epidemics in plant populations. Up to recently, the range of possible mechanisms or interactions assumed by epidemic models has been limited: either independent of the location of individuals (mean-field models) or restricted to local contacts (between nearest neighbours or decaying exponentially with distance). Real dispersal processes are likely to lie between these two extremes, and many are well described by long-tailed contact kernels such as power laws. We investigate the effect of different spatial dispersal mechanisms on the spatio-temporal spread of disease epidemics by simulating a stochastic Susceptible-infective model motivated by previous data analyses. Both long-term stationary behaviour (in the presence of a control or recovery process) and transient behaviour (which varies widely within and between epidemics) are examined. We demonstrate the relationship between epidemic size and disease pattern (characterized by spatial autocorrelation), and its dependence on dispersal and infectivity parameters. Special attention is given to boundary effects, which can decrease disease levels significantly relative to standard, periodic geometries in cases of long-distance dispersal. We propose and test a definition of transient duration which captures the dependence of transients on dispersal mechanisms. We outline an analytical approach that represents the behaviour of the spatially-explicit model, and use it to prove that the epidemic size is predicted exactly by the mean-field model (in the limit of an infinite system) when dispersal is sufficiently long ranged (i.e. when the power-law exponent a

Aims: To determine the severity and long term sequelae of eye injuries caused by modern sports that could be responsible for significant ocular trauma in the future., Methods: Prospective observational study of 24 (25 eyes) athletes with sports related ocular injuries from health clubs, war games, adventure, radical and new types of soccer, presenting to an eye emergency department between 1992 and 2002 (10 years)., Results: Modern sports were responsible for 8.3% of the 288 total sports eye injuries reported. Squash (29.2%) was the most common cause, followed by paintball (20.8%) and motocross (16.6%). The most common diagnosis during the follow up period was retinal breaks (20%). 18 (75%) patients sustained a severe injury. The final visual acuity remained <20/100 in two paintball players., Conclusions: Ocular injuries resulting from modern sports are often severe. Adequate instruction of the participants in the games, proper use of eye protectors, and a routine complete ophthalmological examination after an eye trauma should be mandatory.

We consider a model for surface deposition in one dimension, in the presence of both precursor-layer diffusion and desorption. The model is a generalization that includes random sequential adsorption (RSA), accelerated RSA, and growth-and-coalescence models as special cases. Exact solutions are obtained for the model for both its lattice and continuum versions. Expressions are obtained for physically important quantities such as the surface coverage, average island size, mass-adsorption efficiency, and the process efficiency. The connection between a limiting case of the model and epidemic models is discussed.

Many biologists use population models that are spatial, stochastic and individual based. Analytical methods that describe the behaviour of these models approximately are attracting increasing interest as an alternative to expensive computer simulation. The methods can be employed for both prediction and fitting models to data. Recent work has extended existing (mean field) methods with the aim of accounting for the development of spatial correlations. A common feature is the use of closure approximations for truncating the set of evolution equations for summary statistics. We investigate an analytical approach for spatial and stochastic models where individuals interact according to a generic function of their distance; this extends previous methods for lattice models with interactions between close neighbours, such as the pair approximation. Our study also complements work by Bolker and Pacala (BP) [Theor. Pop. Biol. 52 (1997) 179; Am. Naturalist 153 (1999) 575]: it treats individuals as being spatially discrete (defined on a lattice) rather than as a continuous mass distribution; it tests the accuracy of different closure approximations over parameter space, including the additive moment closure (MC) used by BP and the Kirkwood approximation. The study is done in the context of an susceptible-infected-susceptible epidemic model with primary infection and with secondary infection represented by power-law interactions. MC is numerically unstable or inaccurate in parameter regions with low primary infection (or density-independent birth rates). A modified Kirkwood approximation gives stable and generally accurate transient and long-term solutions; we argue it can be applied to lattice and to continuous-space models as a substitute for MC. We derive a generalisation of the basic reproduction ratio, R(0), for spatial models.

Objective: To outline the severity and long-term sequelae of eye injuries in soccer., Design: Prospective observational study of 163 patients who sustained soccer-related ocular injuries between April 1, 1992, and March 31, 2000 (8 years)., Methods: Patients were observed at a sports ophthalmology unit located in the largest university hospital of the northern region of the country and central to all major soccer fields in town. The data were recorded using the United States Eye Injury Registry report forms for initial and follow-up observation., Main Outcome Measures: (1) Self-reported history surrounding the ocular trauma, initial visual acuity, diagnosis, and operations and (2) final visual acuity, late diagnosis, and additional operations., Results: Injuries occurred predominantly in young men (mean +/- SD age, 23.2 +/- 8.8 years) practicing indoor soccer (50.9%) or outdoor soccer (47.2%), and most resulted from a kicked ball (79.1%) near the goal post (60.1%). Angle recession and peripheral vitreoretinal lesions were more likely to occur in the superotemporal quadrant (54.7%; 95% confidence interval, 44.2%-65.0%; and 57.6%; 95% confidence interval, 48.4%-66.4%; respectively). Vitreoretinal lesions were present in 42.2% (95% confidence interval, 33.1%-51.8%) of patients with "normal" visual acuity (> or =20/40) and in 50.0% (95% confidence interval, 38.1%-61.8%) of patients without hyphema. No significant association was found between severity of injury and age, sex, type of soccer, level of athletic expertise, or player position., Conclusions: Severe ocular lesions can occur in soccer players without symptoms and at all skill levels. The development of laboratory models will be essential to explain the tendency for lesions to be in the superotemporal quadrant. The data support the need for protective eyewear designed specifically for soccer.

Spectral analysis of heart rate variability has become a noninvasive standard method for assessment of autonomic nervous system activity in athletes. The effect of exercise training on autonomic regulation of pupillary light reflex is not known. The purpose of this study was to evaluate pupil autonomic function in athletes. We studied 46 highly trained athletes practicing gymnastics, swimming, long-distance running, soccer, and 51 healthy control subjects, using a portable infrared pupillometry. Five left pupil light response curves were recorded for each subject; the 485 pupillogram records were processed by a computer system. The following pupillometric parameters calculated were significantly higher (P<0.05) in runners than in controls: reflex amplitude (2.1 mm; 95% CI, 1.9-2.3 vs. 1.8 mm; 95% CI, 1.7-1.9), mean percent reflex amplitude of initial diameter (34%; 95% CI, 32-37 vs. 30%, 95% CI, 28-31) and mean time at which pupil redilated 75% of reflex amplitude (2.15 s; 95% CI, 1.99-2.31 vs. 1.86 s; 95% CI, 1.78-1.93). Sex, age, height, weight, body mass index and years of sports practice had no significant influence in the evaluated parameters. The results were consistent with an increased parasympathetic activity and a reduced sympathetic activity of pupillary light reflex in endurance-trained runners, supporting the hypothesis of a generalized "dysautonomy" associated with this type of training.

We consider a model for single-season disease epidemics, with a delay (latent period) in the onset of infectivity and a decay ("quenching") in host susceptibility described by time-varying rates of primary and secondary infections. The classical susceptible-exposed-infected (SEI) model of epidemiology is a special case with constant rates. The decaying rates force the epidemics to slow down, and eventually stop in a "quenched transient" state that depends on the full history of the epidemic including its initial state. This equilibrium state is neutrally stable (i.e., has zero-value eigenvalues), and cannot be studied using standard equilibrium analysis. We introduce a method that gives an approximate analytical solution for the quenched state. The method uses an interpolation between two exactly solvable limits and applies to the whole, five-dimensional parameter space of the model. Some applications of the solutions for analysis of epidemics are given.

1. The contractile capacity of smooth muscle cells depends on the cytoskeletal framework of the cell. The aim of this study was to determine the functional importance of both the actin and the tubulin components of the cytoskeleton in contractile responses of the bovine isolated iris sphincter muscle. 2. In each preparation, two contractions to the muscarinic agonist carbachol were obtained. The maximum responses of the first contractions were taken as 100%. The second contractions to carbachol were elicited in the presence of either cytochalasin B (50 and 5 microm), an inhibitor of the actin cytoskeleton, or colchicine (100 microm), an inhibitor of the tubulin cytoskeleton (30 min incubation). 3. Cytochalasin B, at a concentration of 50 microm, significantly decreased the contractions induced by carbachol, with the maximum response reduced to 21.8 +/- 6.6% (n = 12) of the initial maximum. The maximal contractions to carbachol in the presence of colchicine reached 96.2 +/- 7.9% (n = 9) of the initial contraction, which was not significantly different from control second responses to carbachol with neither drug present, which reached 113.3 +/- 7.6% (n = 7). 4. The effect of cytochalasin B was dose-dependent, since at a lower concentration of 5 microm, the drug decreased the maximum contraction to carbachol to 60.3 +/- 8.8% (n = 6). The effect of cytochalasin B was at least partially reversible, since after the use of the higher concentration of 50 microm, contractions to carbachol increased to 62.3 +/- 15.5% (n = 4) of the maximal response, after 1 h repeated washing of the preparations. 5. Cytochalasin D, at a concentration of 50 microm, completely abolished the contractions induced by carbachol (n = 4). 6. These findings suggest that in bovine iris sphincter muscle, contractions to carbachol are highly dependent, from a functional point of view, on actin polymerization, and not, to any important degree, on the polymerization of tubulin., (Copyright 2002 American Health Foundation and Elsevier Science (USA))

Analytical methods for predicting and exploring the dynamics of stochastic, spatially interacting populations have proven to have useful application in epidemiology and ecology. An important development has been the increasing interest in spatially explicit models, which require more advanced analytical techniques than the usual mean-field or mass-action approaches. The general principle is the derivation of differential equations describing the evolution of the expected population size and other statistics. As a result of spatial interactions no closed set of equations is obtained. Nevertheless, approximate solutions are possible using closure relations for truncation. Here we review and report recent progress on closure approximations applicable to lattice models with nearest-neighbour interactions, including cluster approximations and elaborations on the pair (or pairwise) approximation. This study is made in the context of an SIS model for plant-disease epidemics introduced in Filipe and Gibson (1998, Studying and approximating spatio-temporal models for epidemic spread and control, Phil. Trans. R. Soc. Lond. B 353, 2153-2162) of which the contact process [Harris, T. E. (1974), Contact interactions on a lattice, Ann. Prob. 2, 969] is a special case. The various methods of approximation are derived and explained and their predictions are compared and tested against simulation. The merits and limitations of the various approximations are discussed. A hybrid pairwise approximation is shown to provide the best predictions of transient and long-term, stationary behaviour over the whole parameter range of the model.

Purpose: The authors performed a sports-related ocular injuries evaluation with periodic patient observation and follow-up, to outline the severity and long-term sequelae of eye injuries in sports., Methods: A prospective study was conducted of 84 consecutive patients (85 injured eyes) with sports-related eye injuries examined at the Eye Emergency Department of Porto S. João Hospital, between April 1992 and March 1995. The ophthalmologic examination was recorded using the United States Eye Injury Registry report forms, and the follow-up ranged from 3 months to 3 years., Results: Injuries occurred predominantly in young males (mean age, 24.8 +/- 9.6 years). The type of sport and the mechanism most frequently responsible for injuries were, respectively, outdoor and indoor soccer (72.6%) and ball trauma (64.3%). Of 45 patients presenting with hyphema, 24 (53.3%) had vitreous and/or retina (V/R) lesions (95% confidence interval [CI], 35.8-67.5) compared with 13 of 39 (33.3%) patients with no hyphema (95% CI, 20.0-49.1). Angle recession was significantly more common in the presence of hyphema (55.6%; 95% CI, 41.0-69.5 vs. 10.3%; 95% CI, 3.3-22.9; P < 0.00005), and retinal tears were more common in the presence of vitreous hemorrhage (P = 0.004). Nineteen of 58 (32.8%) patients with "normal" visual acuity (> or = 20/40) presented with V/R lesions. Hyphemas were significantly more frequent in soccer players (38/61 vs. 7/23, P = 0.018)., Conclusion: These results highlighted the serious nature of outdoor and indoor soccer injuries. The severity of the anterior segment injury was not a good predictor of posterior segment damage. Ophthalmologists can help prevent delayed consequences by including regular gonioscopy and peripheral retinal examination in all cases of blunt trauma. The United States Eye Injury Registry report forms adapted to sports proved to be a useful tool for collecting detailed information and sharing a common database.

Bungee jumping is becoming a popular sport in the Western world with some cases of ophthalmic complications being reported in recent literature. The authors reported a case of a 23-year-old healthy female who presented retinal complications following a bungee jumping. Her fundi showed superficial retinal hemorrhages in the right eye and a sub-internal limiting membrane hemorrhage affecting the left eye. A general examination, including a full neurological examination, was normal and laboratorial investigations were all within normal values. More studies are necessary to identify risk factors and the true incidence of related ocular lesions, but until then, we think this sport activity should be desencouraged, especially to those that are not psychological and physically fit.