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We compared the effect of cholesterol at different concentration on the phase behaviour of DMPC (1,2-dimyristoyl-sn-glycero-3-phosphocholine) multilamellar vesicles. We used pressure perturbation differential scanning calorimetry (PPC) that studies a system on the whole by giving access to relevant thermodynamic quantities, and elastic incoherent neutron scattering (EINS) that probes local motions of a system at the atomic level by allowing extraction of dynamical parameters. PPC revealed that the volume expansion coefficient of DMPC and DMPC/Cholesterol samples with 13 and 25 mol% cholesterol is a linear function of the heat capacity measured by differential scanning calorimetry. Neutron backscattering spectroscopy showed that the mean square displacements of H atoms do exhibit an increase with temperature and a decrease under increasing pressure. Cholesterol added at concentrations of 25 and 50 mol% led to suppression of the main phase transition. Taking advantage of these results, the present study aims (i) to show that calorimetry and EINS using the Bicout and Zaccai model equally permit to get access to thermodynamic quantities characterizing pure DMPC and DMPC/cholesterol mixtures, thus directly confirming the theoretical method, and (ii) to validate our approach as function of temperature and of pressure, as both are equally important and complementary thermodynamic variables.
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Colesterol/química , Dimiristoilfosfatidilcolina/química , Membrana Dobles de Lípidos/química , Presión , Termodinámica , Rastreo Diferencial de CalorimetríaRESUMEN
Highly pathogenic avian influenza (HPAI) H5N8 is currently causing an epizootic in Europe, infecting many poultry holdings as well as captive and wild bird species in more than 10 countries. Given the clear clinical manifestation, passive surveillance is considered the most effective means of detecting infected wild and domestic birds. Testing samples from new species and non-previously reported areas is key to determine the geographic spread of HPAIV H5N8 2016 in wild birds. Testing limited numbers of dead wild birds in previously reported areas is useful when it is relevant to know whether the virus is still present in the area or not, e.g. before restrictive measures in poultry are to be lifted. To prevent introduction of HPAIV from wild birds into poultry, strict biosecurity implemented and maintained by the poultry farmers is the most important measure. Providing holding-specific biosecurity guidance is strongly recommended as it is expected to have a high impact on the achieved biosecurity level of the holding. This is preferably done during peace time to increase preparedness for future outbreaks. The location and size of control and in particular monitoring areas for poultry associated with positive wild bird findings are best based on knowledge of the wider habitat and flight distance of the affected wild bird species. It is recommended to increase awareness among poultry farmers in these established areas in order to enhance passive surveillance and to implement enhanced biosecurity measures including poultry confinement. There is no scientific evidence suggesting a different effectiveness of the protection measures on the introduction into poultry holdings and subsequent spread of HPAIV when applied to H5N8, H5N1 or other notifiable HPAI viruses.
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BACKGROUND: Declared cases of exposures related to potential toxic agents are reported through a national database, the French Network of Poison Centers, and account on average for 200,000 cases per year, including 75,000 to 80,000 symptomatic cases. These data are currently used to investigate signals from local, national or international institutional partners (such as hospitals, local health authorities, and the Rapid Alert System for Food and Feed). Our objective is to complete this classical toxicovigilance activity through the automated detection of unexpected or unusual events in order to identify precociously signals representing potential threats for public health. To reach this objective, the inventory of surveillance and detection methods of unexpected events is necessary. METHODS: A literature review was conducted via Scopus(®) and Pubmed(®) databases, completed with grey literature and data available on worldwide vigilance systems' websites. RESULTS: The most commonly used methods are disproportional measures in the field of pharmacovigilance, some of which are subject to a routine detection at regular time intervals. Criteria of signal generation differ from one system to another, which have implemented data filtering strategies before or after analysis, in order to decrease the number of generated signals and improve their priority level. These signals are then transmitted to an experts committee for a clinical and epidemiological evaluation, and at times, for informing the patient's medical records. We also notice an interest in other approaches such as surveillance methods of temporal series or symbolic methods for associative rules extraction between one or more drugs and one or more adverse effects, with the possibility to include other types of variables, such a demographic data. The developments of probabilistic-based algorithms have also been recently developed, opening new opportunities. CONCLUSION: These surveillance and detection methods are of high interest for the automated detection of signals from the French toxicovigilance network. The initial step to developing these methods consists in studying the statistical quality of data and targeting the needs and expectations of the toxicovigilance network for what we want and what we can detect.
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Sistemas de Registro de Reacción Adversa a Medicamentos , Farmacovigilancia , Humanos , Vigilancia de Productos Comercializados/métodosRESUMEN
Leptospira interrogans, hantaviruses (particularly Seoul virus), hepatitis E virus (HEV), and Toxoplasma gondii are rat-associated zoonoses that are responsible for human morbidity and mortality worldwide. This study aimed to describe the infection patterns of these four pathogens in wild rats (Rattus norvegicus) across socioeconomic levels in neighbourhoods in Lyon, France. The infection or exposure status was determined using polymerase chain reaction or serology for 178 wild rats captured in 23 locations; additionally, confirmatory culture or mouse inoculation was performed. Multivariate logistic regression analyses were used to investigate whether morphological and socioeconomic data could predict the infection status of the rats. This study revealed that the rat colony's age structure may influence the prevalence of L. interrogans, hantavirus, and HEV. In addition, areas with high human population densities and low incomes may be associated with a greater number of infected rats and an increased risk of disease transmission.
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Virus de la Hepatitis E/aislamiento & purificación , Leptospira interrogans/aislamiento & purificación , Orthohantavirus/aislamiento & purificación , Enfermedades de los Roedores/epidemiología , Toxoplasma/aislamiento & purificación , Zoonosis/epidemiología , Animales , Recolección de Datos , Femenino , Francia/epidemiología , Humanos , Masculino , Reacción en Cadena de la Polimerasa , Densidad de Población , Ratas , Enfermedades de los Roedores/microbiología , Enfermedades de los Roedores/parasitología , Enfermedades de los Roedores/virología , Pruebas Serológicas , Factores Socioeconómicos , Zoonosis/microbiología , Zoonosis/parasitología , Zoonosis/virologíaRESUMEN
How long will a fluid membrane vesicle stressed with a steady ramp of micropipette last before rupture? Or conversely, how high should the surface tension be to rupture such a membrane? To answer these challenging questions we developed a theoretical framework that allows for the description and reproduction of dynamic tension spectroscopy (DTS) observations. The kinetics of the membrane rupture under ramps of surface tension is described as a succession of an initial pore formation followed by the Brownian process of the pore radius crossing the time-dependent energy barrier. We present the formalism and a derive (formal) analytical expression of the survival probability describing the fate of the membrane under DTS conditions. Using numerical simulations for the membrane prepared in an initial state with a given distribution of times for pore nucleation, we study the membrane lifetime (or inverse of rupture rate) and distribution of membrane surface tension at rupture as a function of membrane characteristics like pore nucleation rate, the energy barrier to failure, and tension loading rate. It is found that simulations reproduce the main features of DTS experiments, particularly the pore nucleation and pore-size diffusion-controlled limits of membrane rupture dynamics. This approach can be adapted and applied to processes of permeation and pore opening in membranes (electroporation, membrane disruption by antimicrobial peptides, vesicle fusion).
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Membrana Celular/química , Membrana Celular/ultraestructura , Fluidez de la Membrana , Modelos Químicos , Modelos Moleculares , Simulación por Computador , Tensión SuperficialRESUMEN
The poultry red mite Dermanyssus gallinae is a major pest and widespread ectoparasite of laying hens and other domestic and wild birds. Under optimal conditions, D. gallinae can complete its lifecycle in less than 10 days, leading to rapid proliferation of populations in poultry systems. This paper focuses on developing a theoretical model framework to describe the population dynamics of D. gallinae. This model is then used to test the efficacy and residual effect of different control options for managing D. gallinae. As well as allowing comparison between treatment options, the model also allows comparison of treatment efficacies to different D. gallinae life stages. Three different means for controlling D. gallinae populations were subjected to the model using computer simulations: mechanical cleaning (killing once at a given time all accessible population stages), sanitary clearance (starving the mite population for a given duration, e.g. between flocks) and acaricide treatment (killing a proportion of nymphs and adults during the persistence of the treatment). Simulations showed that mechanical cleaning and sanitary clearance alone could not eradicate the model D. gallinae population, although these methods did delay population establishment. In contrast, the complete eradication of the model D. gallinae population was achieved by several successive acaricide treatments in close succession, even when a relatively low treatment level was used.
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Acaricidas/farmacología , Crianza de Animales Domésticos/métodos , Ácaros/efectos de los fármacos , Ácaros/fisiología , Modelos Biológicos , Animales , Dinámica PoblacionalRESUMEN
The paper deals with the incidence of the Dengue Virus Infection (DVI) in the 18 districts of Sakon Nakhon Province, Thailand, from January 2005 to December 2007. Using a statistical and autoregressive analysis to smooth incidence data, we have constructed yearly and monthly district level maps of the DVI distribution. It is found that the DVI incidence is very correlated with weather conditions and higher occurrences are observed in the three most populated districts Wanon Niwat, Sawang Daen Din and Mueang Sakon Nakhon, and the virus transmission period spans from mid-summer to mid-rainy seasons (from April to August). Employing a Generalized Linear Model (GLM), we found that the DVI incidences were related with current meteorological (monthly minimum temperature, past 2-month cumulated rainfall) and socio-economical (population of 0-4years old, per capita number of public small water wells, and proportion of villages with primary schools) covariates. And using the GLM under the climate change conditions (A1B scenario of IPCC), we found that the higher risk of DVI spreads from the three most populated districts to less populated ones, and the period of virus transmission increases from 5 to 9months to include part of winter, summer and rainy seasons (from March to November) during which 6%, 61% and 33% of districts will be at low, medium and high risk of DVI occurrences, respectively.
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Dengue/epidemiología , Adolescente , Adulto , Anciano , Niño , Preescolar , Estudios de Cohortes , Dengue/transmisión , Monitoreo del Ambiente , Monitoreo Epidemiológico , Femenino , Humanos , Lactante , Masculino , Persona de Mediana Edad , Medición de Riesgo , Estaciones del Año , Clase Social , Tailandia/epidemiología , Tiempo (Meteorología) , Adulto JovenRESUMEN
Insect population dynamics depend strongly on environmental factors. For floodwater mosquitoes, meteorological conditions are crucial in the rhythm of mosquito abundances. Indeed, rainfall triggers the egg hatching after flooding breeding sites, and temperature controls the duration of the aquatic immature development up to adult emergence. According to this, we have developed a simple mechanistic and tractable model that describes the population dynamics of floodwater mosquitoes as a function only of the most accessible meteorological variables, rainfall and temperature. The model involves three parameters: development duration tdev of the immature aquatic stages, the adult emergence rate function f(t) (characterized by the emergence time scale tau and shaping the profile of adult population abundance), and the depletion rate, alpha, of adult disappearance. The developed model was subsequently applied to fit experimental field data of the dynamics of Aedes caspius (Pallas), the main pest mosquito in southern France. First, it was found that the emergence rate function of adult mosquitoes very well reproduce experimental data of the dynamics of immature development for all sampled temperatures. The estimated values of tdev and tau both exhibit Arrhenius behaviour as a function of temperature. Second, using the meteorological records of rainfall and temperature as inputs, the model correctly fit data from a two-site CO2 trapping survey conducted in 2004 and 2005. The estimated depletion rates (summation of the mortality and the emigration rates) were found to be a concave quadratic function of temperature with a maximum of 0.5 per days at about 22 degrees C.
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Aedes/fisiología , Modelos Biológicos , Aedes/crecimiento & desarrollo , Animales , Femenino , Larva , Masculino , Densidad de Población , Dinámica Poblacional , PupaRESUMEN
As a main vector of West Nile (WN) virus (family Flaviviridae, genus Flavivirus) in Europe, Culex modestus Ficalbi (Diptera: Culicidae) is commonly found in delta regions, lakes, and ponds. The Dombes area is located along one of the main corridors of bird migrations in France and lies 300 km north of the Camargue region, a frequent focus of WN virus circulation. It is an important breeding, wintering, and stopover site for many bird species that are putative carriers of viruses of different kinds. It is also a continental wetland with approximately =1200 fish farming ponds, scattered over the area, that provide suitable breeding sites for Cx. modestus. This article reports an entomological study based on larval surveys conducted in ponds in 2007 to assess the prevalence and abundance of Cx. modestus in the Dombes. Using the larval survey as an ecological screening test, we investigated the proportion of ponds found positive for Cx. modestus, and the relative abundance of this species was estimated in larval samples. We found that its pond distribution was more extensive in the 2007 survey than in that conducted in the 1970s. Survey methods and meteorological and anthropological factors that could account for the differences or variations between the findings of the two investigations are discussed.
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Culex/virología , Insectos Vectores/virología , Virus del Nilo Occidental/aislamiento & purificación , Animales , Aves/virología , Culex/clasificación , Francia/epidemiología , Larva/clasificación , Larva/virología , Prevalencia , Fiebre del Nilo Occidental/epidemiología , Fiebre del Nilo Occidental/transmisiónRESUMEN
The infection of wild birds by highly pathogenic strains of avian influenza (Al) virus was virtually unknown--apart from one instance of the disease appearing in common terns in South Africa in 1961--before the Asian strain of highly pathogenic AI virus (AIV), H5N1, began to expand across the world. Outbreaks of clinical disease in Eurasia have resulted in visible mortality among populations of free-ranging wild birds in a multitude of species. The circulation pattern of influenza viruses in natural ecosystems results from a selection pressure towards strains which are indirectly transmitted by droppings from water birds and contaminated fomites, and which exhibit low pathogenicity. Some of these viruses, of the subtypes H5 or H7, can mutate into highly pathogenic strains after being introduced into domestic poultry farms. The maintenance of highly pathogenic AIV (HPAIV) H5N1 in several parts of the world exposes wild birds to infected poultry, resulting in long-distance virus transmission. There is great concern that these wild birds may, in turn, propagate these HPAIV or introduce them into domestic birds. Rigorous disease control and biosecurity measures to protect poultry farms are the only solution presently available to mitigate such a risk.
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Brotes de Enfermedades/veterinaria , Subtipo H5N1 del Virus de la Influenza A/patogenicidad , Gripe Aviar/epidemiología , Animales , Animales Salvajes , Conducta Animal , Aves , Reservorios de Enfermedades/veterinaria , Reservorios de Enfermedades/virología , Europa (Continente)/epidemiología , Humanos , Subtipo H5N1 del Virus de la Influenza A/genética , Gripe Aviar/prevención & control , Gripe Aviar/transmisión , Gripe Humana/epidemiología , Gripe Humana/prevención & control , Gripe Humana/virología , Factores de RiesgoRESUMEN
BACKGROUND: Mapping a Cancer Atlas for the urban area of Grenoble revealed spatial distribution in the incidence of lung cancer among males at municipality level. Thus, our goal in this work was to use a new finer spatial scale to find out whether or not observed spatial variations might mask intramunicipality spatial variations. METHODS: The use of a Bayesian smoothing approach allowed us to overcome problems related to the very small inframunicipality scale and to take into account the spatial autocorrelation existing between neighbouring units. The relative risks were adjusted on different socioeconomic variables like the median income per consumption unit. RESULTS: After smoothing, areas with statistically significant 30 to 40% excess of cases and lack of cases were identified within the urban area of Grenoble. Median income per consumption unit appeared to be the most discriminating variable for characterizing the studied population. CONCLUSION: The inframunicipality scale enables the study of a health problem as the lung cancer within a context of strong demographic disparities.
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Neoplasias Pulmonares/epidemiología , Adolescente , Adulto , Factores de Edad , Anciano , Anciano de 80 o más Años , Teorema de Bayes , Intervalos de Confianza , Francia/epidemiología , Humanos , Incidencia , Renta , Masculino , Persona de Mediana Edad , Análisis de Regresión , Riesgo , Factores Sexuales , Factores Socioeconómicos , Población UrbanaRESUMEN
The larval survival and development times of Aedes caspius (Diptera: Culicidae) were examined in the laboratory. These life history traits were estimated using life tables constructed for two populations, one of which had been subjected to a long-term larvicide control program. Traits were evaluated for eight different population densities. The effects of population, larval stage and larval density were investigated using a general linear model. Density was positively correlated with larval survival but did not affect development time. The fourth instar and pupae had the lowest larval survival rates. First and fourth instar larvae had the longest development times. These traits were not significantly different between the two populations. The effect of larvicide control on these traits is discussed.
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Aedes/crecimiento & desarrollo , Animales , Insecticidas , Larva/crecimiento & desarrollo , Modelos Lineales , Densidad de Población , Pupa/crecimiento & desarrollo , Factores de TiempoRESUMEN
The survivorship characteristics of two populations of Aedes caspius (Pallas) (Diptera: Culicidae) were compared in the laboratory. One population was sourced from Mourgues, where larvicides have been used continuously for approximately 40 years, and the other from Pont de Gau, where there has been no consistent mosquito control. The aims of the study were to ascertain the basic life history profiles of adults and to determine whether continuous larviciding affects inherent adult survivorship. Life tables were constructed to calculate the following life expectancy parameters: mean lifetime (tau(ad)); maximum lifetime (tau(max)), and daily survival rate (p(ad)). All three parameters were higher for females than for males (paired t-test, P < or = 0.001); male mean lifetime, maximum lifetime and daily survival rate were 4.95 +/- 0.94 days, 20.50 +/- 6.66 days and 0.79 +/- 0.05, respectively; female values were 14.74 +/- 3.68 days, 49.69 +/- 16.55 days and 0.93 +/- 0.02, respectively. No differences were found between the two populations, and no correlations were found between initial adult densities and their respective survival rates. The survivorship curves for Ae. caspius were type IV for males (mortality rates higher for young adults) and type III for females (mortality rates constant).
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Aedes/crecimiento & desarrollo , Animales de Laboratorio/crecimiento & desarrollo , Sobrevida , Animales , Femenino , Francia , Masculino , Densidad de Población , Factores Sexuales , Factores de TiempoRESUMEN
West Nile virus (WNV) is a mosquito-transmitted Flavivirus with a transmission cycle involving birds as amplifying hosts. Wild birds are also believed to carry WNV over large distances and are able to introduce it into new areas during migration and dispersal. In this paper, our objective is to provide lists of birds potentially involved in the introduction, the amplification and the spread of WNV in the Camargue, a Mediterranean wetland in the south of France where several WNV outbreaks have occurred since the 1960s. Bird species were classified according to the following ecological factors: migratory status and provenance area, used biotopes, abundance and period of presence in the Camargue. The obtained lists of bird species potentially involved in the introduction, amplification and spread of WNV should prove useful to determine target species on which further studies on WNV ecology in birds could be focused.
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Enfermedades de las Aves/epidemiología , Culicidae/virología , Insectos Vectores/virología , Fiebre del Nilo Occidental/veterinaria , Virus del Nilo Occidental/aislamiento & purificación , Migración Animal , Animales , Animales Salvajes/virología , Enfermedades de las Aves/transmisión , Aves/clasificación , Brotes de Enfermedades/veterinaria , Francia/epidemiología , Vigilancia de Guardia/veterinaria , Especificidad de la Especie , Fiebre del Nilo Occidental/epidemiología , Fiebre del Nilo Occidental/transmisiónRESUMEN
Geographic information system and remote sensing technologies were used to identify landscape features associated with risk of West Nile virus transmission as defined by the presence of confirmed horse cases. SPOT-4 images of Camargue area were used to generate a map of landscape categories of epidemic foci and the geographic information system was employed to determine the proportion of landscape components surrounding 10 horse case sites and 17 control sites. The spatio-temporal analysis of the cases outbreak gave the best results for a spatial window of 9 km and a temporal window of 18 days. Two clusters were identified (relative risk=3.35), both in the wet area of Camargue, near the town "Les Saintes Maries de la Mer". The first one was 4 km radius, the second 9 km. The relationships between the presence of cases and proportions of landscape categories were analyzed using generalized linear model. The best model indicated that rice fields and dry bushes, wet "sansouire" and open water were the major components of the landscape that were associated with the presence of West Nile virus cases.
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Sistemas de Información Geográfica , Enfermedades de los Caballos/epidemiología , Enfermedades de los Caballos/transmisión , Vigilancia de Guardia/veterinaria , Fiebre del Nilo Occidental/veterinaria , Animales , Brotes de Enfermedades/veterinaria , Femenino , Francia/epidemiología , Caballos , Masculino , Medición de Riesgo , Factores de Riesgo , Agrupamiento Espacio-Temporal , Fiebre del Nilo Occidental/epidemiología , Fiebre del Nilo Occidental/transmisiónRESUMEN
After 35 yr of disease absence, West Nile virus (family Flaviviridae, genus Flavivirus, WNV) circulation has been regularly detected in the Camargue region (southern France) since 2000. WNV was isolated from Culex modestus Ficalbi, which was considered the main vector in southern France after horse outbreaks in the 1960s. Recent WNV transmissions outside of the Cx. modestus distribution suggested the existence of other vectors. To study potential WNV vectors, horse- and bird-baited traps and human landing collections of mosquitoes were carried out weekly from May to October 2004 at two Camargue sites: one site in a wet area and the other site in a dry area, both chosen for their past history of WNV transmission. At the wet site, the most abundant species in bird-baited traps were Culex pipiens L. and Cx. modestus; both species also were found in lower proportions on horses and humans. The most abundant species in horse-baited traps and human landing collections were Aedes caspius (Pallas), Aedes vexans (Meigen), and Anopheles hyrcanus (Pallas) sensu lato; some of these species were occasionally collected with avian blood at the end of the summer. Anopheles maculipennis Meigen sensu lato was an abundant horse feeder, but it was rarely collected landing on human bait and never contained avian blood. At the dry site, Cx. pipiens was the most abundant species in bird- and horse-baited traps. The seasonal and circadian dynamics of these species are analyzed, and their potential in WNV transmission in Camargue discussed.
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Conducta Animal/fisiología , Culicidae/fisiología , Insectos Vectores/fisiología , Fiebre del Nilo Occidental/transmisión , Virus del Nilo Occidental , Animales , Aves , Culicidae/clasificación , Femenino , Francia , Caballos , Humanos , Control de Mosquitos/instrumentación , Densidad de Población , Dinámica Poblacional , Lluvia , Estaciones del Año , Temperatura , Factores de Tiempo , Fiebre del Nilo Occidental/virologíaRESUMEN
Inspired by Davidson method of estimating daily survivals of a structureless population of mosquitoes, we present a model which describes the behavior of floodwater mosquitoes in terms of emergence functions following a rainfall event, blood feeding frequency and parous stages, and survival at various stages. As a generalization of the Davidson formula, we have developed an approach for dealing with the dynamics of structured population of mosquitoes, and derived various formulas allowing assessment of demographic parameters like durations of gonotrophic cycles and (apparent) daily survivals. The method was subsequently applied to field data of floodwater mosquitoes Aedes vexans arabiensis, potential vectors of Rift Valley fever in West Africa, collected during the 2003 rainy season in Barkedji, Senegal. We found that mosquitoes emerged about 3 to 4 days following an efficient rainfall, and mosquito emergences, described by a bell shaped function, lasted for about 2 days. The mean duration of the gonotrophic cycle was 3 days and the apparent daily survival about 0.87.
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Aedes/fisiología , Agresión , Insectos Vectores/fisiología , Modelos Biológicos , Lluvia , Animales , Desastres , Ecosistema , Conducta Alimentaria , Femenino , Humanos , Dinámica Poblacional , Estaciones del AñoRESUMEN
We present a model for pore stabilization in membranes without surface tension. Whereas an isolated pore is always unstable (since it either shrinks, tending to reseal, or grows without bound until membrane disintegration), it is shown that excluded volume interactions in a system of many pores can stabilize individual pores of a given size in a certain range of model parameters. For such a multipore membrane system, the distribution of pore size and associated pore lifetime are calculated within the mean-field approximation. We predict that, above the temperature T(m), when the effective line tension becomes negative, the membrane exhibits a dynamic sievelike porous structure.
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Contagious bovine pleuropneumonia (CBPP) is a cattle respiratory disease that represents one of the major threats to cattle health and production in sub-Saharan Africa. The transmission contact rate of CBPP plays a key role in the spreading dynamics of the disease. We have developed an approach based on the combination of a SEIR model describing the spread of CBPP with the dynamic of seroconversion to determine the transmission contact rate for CBPP. This method has been subsequently applied to serological diagnostic data obtained from an experimental vaccine trial. As a result, we find that the transmission contact rates for subclinical, clinical and chronic infective states are respectively, 0.084/N, 0.45 and 0.14/N per animal per day, where N is the herd population size, and the basic reproductive number corresponding to this trial (N=28) is R0=27.
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Enfermedades de los Bovinos/transmisión , Modelos Teóricos , Pleuroneumonía Contagiosa/transmisión , África/epidemiología , Animales , Bovinos , Densidad de Población , Pruebas SerológicasRESUMEN
This paper deals with the two-state (opening-closing of base pairs) model used to describe the fluctuation dynamics of a single bubble formation. We present an exact solution for the discrete and finite size version of the model that includes end effects and derive analytic expressions of the correlation function, survival probability, and lifetimes for the bubble relaxation dynamics. It is shown that the continuous and semi-infinite limit of the model becomes a good approximation to an exact result when aN <<1, where N is bubble size and a, the ratio of opening to closing rates of base pairs, is the control parameter of DNA melting.