Reproductive numbers for nonautonomous spatially distributed periodic SIS models acting on two time scales.

In this work we deal with a general class of spatially distributed periodic SIS epidemic models with two time scales. We let susceptible and infected individuals migrate between patches with periodic time dependent migration rates. The existence of two time scales in the system allows to describe certain features of the asymptotic behavior of its solutions with the help of a less dimensional, aggregated, system. We derive global reproduction numbers governing the general spatially distributed nonautonomous system through the aggregated system. We apply this result when the mass action law and the frequency dependent transmission law are considered. Comparing these global reproductive numbers to their non spatially distributed counterparts yields the following: adequate periodic migration rates allow global persistence or eradication of epidemics where locally, in absence of migrations, the contrary is expected.

Effects of density dependent sex allocation on the dynamics of a simultaneous hermaphroditic population: modelling and analysis.

In this work we present a mathematical model describing the dynamics of a population where sex allocation remains flexible throughout adult life and so can be adjusted to current environmental conditions. We consider that the fractions of immature individuals acquiring male and female sexual roles are density dependent through nonlinear functions of a weighted total population size. The main goal of this work is to understand the role of life-history parameters on the stabilization or destabilization of the population dynamics. The model turns out to be a nonlinear discrete model which is analysed by studying the existence of fixed points as well as their stability conditions in terms of model parameters. The existence of more complex asymptotic behaviours of system solutions is shown by means of numerical simulations. Females have larger fertility rate than males. On the other hand, increasing population density favours immature individuals adopting the male role. A positive equilibrium of the system exists whenever fertility and survival rates of one of the sexual roles, if shared by all adults, allow population growing while the opposite happens with the other sexual role. In terms of the female inherent net reproductive number, eta(F), it is shown that the positive equilibria are stable when eta(F) is larger and closed to 1 while for larger values of eta(F) a certain asymptotic assumption on the investment rate in the female function implies that the population density is permanent. Depending on the other parameters values, the asymptotic behaviour of solutions becomes more complex, even chaotic. In this setting the stabilization/destabilization effects of the abruptness rate in density dependence, of the survival rates and of the competition coefficients are analysed.

Reduction of slow-fast discrete models coupling migration and demography.

This work deals with a general class of two-time scales discrete nonlinear dynamical systems which are susceptible of being studied by means of a reduced system that is obtained using the so-called aggregation of variables method. This reduction process is applied to several models of population dynamics driven by demographic and migratory processes which take place at two different time scales: slow and fast. An analysis of these models exchanging the role of the slow and fast dynamics is provided: when a Leslie type demography is faster than migrations, a multi-attractor scenario appears for the reduced dynamics; on the other hand, when the migratory process is faster than demography, the reduction process gives rise to new interpretations of well known discrete models, including some Allee effect scenarios.

A method to detect variations in the wetting properties of microporous polymer membranes.

With the ability to perform dynamic experiments in the environmental scanning electron microscope (ESEM), the evaluation of microporous polymer membranes via a scanning electron microscope has advanced beyond morphological and elemental analysis. By adjusting sample temperature and environmental chamber pressure, the process of condensing water onto the porous membrane surface can be achieved. In doing so, assessments about the uniformity of wetting in hydrophilic membranes can be obtained based on how the liquid water spreads. Variations in the shape of condensed water droplets formed on non-water wetting structures will reflect the degree of hydrophobicity. This technique has proven useful in the characterization of hydrophobic spots on chemically modified hydrophilic structures and the dynamic examination of irregular wetting patterns in naturally hydrophilic membranes.

Variables aggregation in a time discrete linear model.

In this work we extend approximate aggregation methods to deal with a very general linear time discrete model. Approximate aggregation consists in describing some features of the dynamics of a general system in terms of the dynamics of a reduced system governed by a few global variables. We present a time discrete model for a structured population (i.e., the population is subdivided in subpopulations) in which we can distinguish two processes of a general nature and whose corresponding time scales are very different from each other. We transform the general system to make the global variables appear and obtain the reduced system. These global variables are, for each subpopulation, a certain linear combination of the corresponding state variables. We show that, under quite general conditions, the asymptotic behavior of the reduced system can be known in terms of the corresponding behavior for the reduced system. The general method is applied to aggregate a multiregional Leslie model in which the demographic process is supposed to be fast with respect to migration.

A discrete model with density dependent fast migration.

The aim of this work is to develop an approximate aggregation method for certain non-linear discrete models. Approximate aggregation consists in describing the dynamics of a general system involving many coupled variables by means of the dynamics of a reduced system with a few global variables. We present discrete models with two different time scales, the slow one considered to be linear and the fast one non-linear because of its transition matrix depends on the global variables. In our discrete model the time unit is chosen to be the one associated to the slow dynamics, and then we approximate the effect of fast dynamics by using a sufficiently large power of its corresponding transition matrix. In a previous work the same system is treated in the case of fast dynamics considered to be linear, conservative in the global variables and inducing a stable frequency distribution of the state variables. A similar non-linear model has also been studied which uses as time unit the one associated to the fast dynamics and has the non-linearity in the slow part of the system. In the present work we transform the system to make the global variables explicit, and we justify the quick derivation of the aggregated system. The local asymptotic behaviour of the aggregated system entails that of the general system under certain conditions, for instance, if the aggregated system has a stable hyperbolic fixed point then the general system has one too. The method is applied to aggregate a multiregional Leslie model with density dependent migration rates.

A mathematical model of growth of population of fish in the larval stage: density-dependence effects.

A mathematical model for the growth of a population of fish in the larval stage is proposed. The emphasis is put on the first part of the larval stage, when the larvae are still passive. It is assumed that during this stage, the larvae move with the phytoplankton on which they feed and share their food equally, leading to ratio-dependence. The other stages of the life cycle are modeled using simple demographic mechanisms. A distinguishing feature of the model is that the exit from the early larval stage as well as from the active one is determined in terms of a threshold to be reached by the larvae. Simplifying the model further on, the whole dynamics is reduced to a two dimensional system of state-dependent delay equations. The model is put in perspective with some of the main hypotheses proposed in the literature as an explanation to the massive destruction which occurs between the egg stage and the adult stage.

Methods of aggregation of variables in population dynamics.

In ecology, we are faced with modelling complex systems involving many variables corresponding to interacting populations structured in different compartmental classes, ages and spatial patches. Models that incorporate such a variety of aspects would lead to systems of equations with many variables and parameters. Mathematical analysis of these models would, in general, be impossible. In many real cases, the dynamics of the system corresponds to two or more time scales. For example, individual decisions can be rapid in comparison to growth of the populations. In that case, it is possible to perform aggregation methods that allow one to build a reduced model that governs the dynamics of a lower dimensional system, at a slow time scale. In this article, we present a review of aggregation methods for time continuous systems as well as for discrete models. We also present applications in population dynamics. A first example concerns a continuous time model of a single population distributed on a system of two connected patches (a logistic source and a sink), by fast migration. It is shown that under a certain condition, the total equilibrium population can be larger than the carrying capacity of the logistic source. A second example concerns a discrete model of a population distributed on two patches, still a source and a sink, connected by fast migration. The use of aggregation methods permits us to conclude that density-dependent migration can stabilize the total population.

Influence of individual aggressiveness on the dynamics of competitive populations.

Two populations are subdivided into two categories of individuals (hawks and lows). Individuals fight to have access to a resource which is necessary for their survival. Conflicts occur between individuals belonging to the same population and to different populations. We investigate the long term effects of the conflicts on the stability of the community. The model is a set of ODE's with four variables corresponding to hawk and dove individuals of the two populations. Two time scales are considered. A fast time scale is used to describe frequent encounters and fightings between individuals trying to monopolize the resource. A slow time scale is used for the demography and the long term effects of encounters. We use aggregation methods in order to reduce this model into a system of two ODE's only for the total densities of the two populations which is found to be a classical Lotka-Volterra competition model. We study different cases of proportions of hawks and doves in both populations on the global coexistence and the mutual exclusion of the two populations. Pure dove tactics in both populations are unstable. In cases of mixed hawk and dove in both populations, there is coexistence. Pure dove or mixed hawk-dove tactics in one population can coexist with pure hawks in the other one when the costs of fightings between hawks are large enough.

Linear discrete population models with two time scales in fast changing environments I: autonomous case.

In this work we consider a structured population with groups and subgroups of individuals. The intra-group dynamics is assumed to be fast in comparison with the inter-group dynamics. We study linear discrete models where the slow dynamics is represented by a single matrix and the fast dynamics is described by means of the first k terms of a converging sequence of different matrices. The number k can be interpreted as the ratio between the two time scales. The aim of this work is to extend aggregation techniques to the case of fast changing environments. The main idea of aggregation is to build up a new system, with lower dimension, that summarizes the information concerning the fast process. This "aggregated" system provides essential information on the original one. It is shown that the asymptotic behavior of the original system can be approximated by the asymptotic behavior of the aggregated system when the ratio between the two time scales is large enough. We present an example of an age structured population in a patchy environment. The migration process is assumed to be fast in comparison with the demographic process. Numerical simulations illustrate that the asymptotic growth rate and the stable age distribution of the population in the original and the aggregated systems are getting closer as the ratio k increases.

[Questionnaire for patients with ischaemic cardiopathy on their reaction to various alarm symptoms]. / Encuesta a los pacientes con cardiopatía isquémica sobre el modo de actuación ante los distintos síntomas de alarma.

OBJECTIVES: To find the degree of information that patients with ischaemic cardiopathy (IC) possess and their behaviour on alarm symptoms (thoracic pain of ischaemic profile under stress, at rest, worsening under stress and for over 20'), how they manage sub-lingual nitro-glycerine (SLNTG), and the source of their information. DESIGN: Transversal descriptive study based on personal interview and our own questionnaire, from September to December 2001. SETTING: Primary Care. Six clinics in three urban Health Areas.Participants. Randomised sample of 98 patients with IC (stable angina, unstable angina, angina with infarct). MEASUREMENTS AND RESULTS: 93 people (57 male, 36 women) were surveyed. Their average age was 71 19.34 had diagnosis of infarct. 17.2% (95% CI, 9.5%24.9%) had no SLNTG available. 78.5% (95% CI; 70.2%-86.8%) and 81.7% (95% CI; 73.8%-89.6%) of those with angina under stress or at rest, respectively, did not know when to attend the hospital Emergency department. 37.8% (95% CI, 26.8%-48.8%) with steady stress angina would attend a hospital or their doctor urgently. 100% of patients had received no information on angina at rest, under steady stress and for over 20'. There was no difference in behaviour before stress angina between patients who had been informed by Primary Care and those informed by Specialists. There was a difference, though, for good use of SLNTG between infarct and non-infarct patients (p = 0.003). CONCLUSIONS: Our cardiopaths do not recognise alarm signals quickly; and so do not benefit as well as they might from hospital treatment. No doctor (Primary Care or specialist) informed them of the different ways to confront stable and unstable angina. Only a very small number used SLNTG in stress angina properly and knew when to attend Casualty. There is an urgent need to improve the health education of our cardiopaths.

Encuesta a los pacientes con cardiopatía isquémica sobre el modo de actuación ante los distintos síntomas de alarma / Questionnaire for patients with ischaemic cardiopathy on their reaction to various alarm symptoms

Objetivo. Conocer el grado de información que tienen los pacientes con cardiopatía isquémica (CI) y su actuación ante situaciones de alarma (dolor torácico de perfil isquémico en esfuerzo, en reposo, agravamiento en esfuerzo, de más de 20 min), el manejo que hacen de la nitroglicerina sublingual (NTGSL) y la fuente de dicha información. Diseño. Estudio descriptivo transversal basado en entrevista personal y cuestionario de elaboración propia, durante septiembre-diciembre de 2001.Emplazamiento. Atención primaria. Seis consultas de tres zonas básicas de salud urbanas. Participantes. Muestra aleatoria de 98 pacientes con CI (angina estable, inestable, angina con infarto).Mediciones y resultados. Encuestados: 93 (57 varones, 36 nujeres). Edad media: 71 ñ 19.Con diagnóstico de infarto: 34. No disponen de NTGSL el 17,2 por ciento (IC del 95 por ciento: 9,5-24,9 por ciento). Desconocen cuándo acudir a urgencias hospitalarias con angina de esfuerzo y reposo el 78,5 por ciento (IC del 95 por ciento: 70,2-86,8 por ciento) y el 81,7 por ciento (IC del 95 por ciento: 73,8-89,6 por ciento), respectivamente. El 37,8 por ciento (IC del 95 por ciento: 26,848,8 por ciento) con angina de esfuerzo progresiva acudiría urgentemente a su médico o al hospital. No recibió información ante angina de reposo, esfuerzo progresivo y de más de 20 min el 100 por ciento de los pacientes. No existe diferencia sobre la actuación ante angina de esfuerzo entre pacientes informados por primaria o especializada, sí en el buen uso de NTGSL entre infartados y no infartados (p = 0,003).Conclusiones. Nuestros cardiópatas no reconocen con prontitud los síntomas de alarma; por tanto, no obtienen el máximo beneficio del tratamiento hospitalario. Ningún médico (primaria, especializada) les informó de la diferente actuación ante angina estable e inestable. Sólo una mínima parte usa bien la NTGSL en angina de esfuerzo y saben cuándo acudir a urgencias. Inminente necesidad de mejorar la educación sanitaria de nuestros cardiópatas (AU)

Estudio clínico comparativo de mupirocine tópico y cloxacilina oral en el tratamiento de infecciones cutáneas / Comparative clinique study of topical mupirocine and oral cloxacillin in the treatment of skin infections

Comparamos en un estudio randomizado la efectividad en el tratamiento de enfermedades cutáneas superficiales con mupirocine tópico y cloxacilina oral. Los resultados demostraron un a mejor respuesta con mupirocine, con 85,7 por ciento de eliminación bacteriana a la semana post-tratamiento versus un 54,5 por ciento con cloxacilina. No se reportaron efectos sistémicos colaterales con mupirocine excepto prurito y sensación de ardor