HOSPICIJ-POTREBA HUMANOG DRUŠTVA

Hrvatsko zakonodavstvo i regulativa palijativne skrbi imaju postavljene neke smjernice za razvoj u Republici Hrvatskoj. Međutim, da uhvatimo korak s razvijenim zemljama treba puno toga pravno i organizacijski urediti. Imamo znanje, imamo volju , imamo svijest nesebičnog djelovanja, ali nemamo financijske mogućnosti u ovom trenutku.O palijativnoj skrbi svaki pojedinac počinje razmišljati tek onda kada mu se razboli član njegove obitelji. Da smo u stanju podići ovu djelatnost u prioritete, našla bi se i sredstva za nju. Da bismo mogli iskoristiti znanje koje imamo treba odmah djelovati. To neće biti jednostavan proces, no u svijetu postoji puno modela i primjera, pa bi se uz iskustvo drugih, naš stručni kadar, te djelovanje na fleksibilnost hrvatske birokracije, okolnosti mogle promijeniti u pozitivnom smislu. Ne zbog nas, ali možda i za nas

The importance of census times in discrete-time growth-dispersal models.

Dispersal has been the focus of spatial ecology for a few decades. What should be a proper theoretical framework for understanding and modelling of dispersal processes remains a controversial issue though. Integrodifference equations (IDE) model the spatial dynamics of a population with distinct growth and dispersal stages in their life cycle. Depending on the stage observed, the equations take on different forms, only one of which is usually studied in the literature. Here we reveal that while these different forms are mathematically equivalent, the biological conclusions drawn from the different forms may differ considerably. We provide a summary of similarities and differences and point out the greatest potential caveats when applying IDE

SPATIO-TEMPORAL CHAOS IN AN ECOLOGICAL COMMUNITY AS A RESPONSE TO UNFAVOURABLE ENVIRONMENTAL CHANGES

The impact of ecological chaos on population dynamics has been an issue of intense discussion over the last decade. While many authors consider chaotic dynamics as a favourable factor facilitating species biodiversity, there is also a strong opinion that chaos may enhance population extinction. In this paper we show that chaotic spatio-temporal dynamics in an ecological community can arise as a response of the community to unfavourable environmental changes. Appearing in that way, chaos can prevent species extinction in a situation when it would be inevitable otherwise. We also show that an essential consequence of chaotic dynamics is that the issue of species extinction is subject to the size of the domain inhabited by the population, the extinction more likely happens in a small domain than in a large one.Population dynamics, prey-predator interaction, reaction-diffusion system, spatio-temporal chaos, species extinction

Analysing the impact of trap shape and movement behaviour of ground-dwelling arthropods on trap efficiency

The most reliable estimates of the population abundance of ground-dwelling arthropods are obtained almost entirely through trap counts. Trap shape can be easily controlled by the researcher, commonly the same trap design is employed in all sites within a given study. Few researchers really try to compare abundances (numbers of collected individuals) between studies because these are heavily influenced by environmental conditions, e.g. temperature, habitat structure and food sources available, directly affecting insect movement activity. We propose that useful insights can be obtained from a theoretical-based approach. We focus on the interplay between trap shape (circle, square, slot), the underlying movement behaviour and the subsequent effect on captures. We simulate trap counts within these different geometries whilst considering movement processes with clear distinct properties, such as Brownian motion (BM), the correlated random walk (CRW) and the Lévy walk (LW). (a) We find that slot shaped traps are far less efficient than circular or square traps assuming same perimeter length, with differences which can exceed more than two-fold. Such impacts of trap geometry are only realized if insect mobility is sufficiently large, which is known to significantly vary depending on type of habitat. (b) If the movement pattern incorporates localized forward persistence then trap counts accumulate at a much slower rate, and this rate decreases further with higher persistency. (c) If the movement behaviour is of Lévy type, then fastest catch rates are recorded in the case of circular trap, and the slowest for the slot trap, indicating that trap counts can strongly depend on trap shape. Lévy walks exacerbate the impact of geometry while CRW make these differences more inconsequential. In this study we reveal trap efficiencies and how movement type can alter capture rates. Such information contributes towards improved trap count interpretations, as required in ecological studies which make use of trapping systems

Statistical mechanics of animal movement: Animals's decision-making can result in superdiffusive spread

Peculiarities of individual animal movement and dispersal have been a major focus of recent research as they are thought to hold the key to the understanding of many phenomena in spatial ecology. Superdiffusive spread and long-distance dispersal have been observed in different species but the underlying biological mechanisms often remain obscure. In particular, the effect of relevant animal behavior has been largely unaddressed. In this paper, we show that a superdiffusive spread can arise naturally as a result of animal behavioral response to small-scale environmental stochasticity. Surprisingly, the emerging fast spread does not require the standard assumption about the fat tail of the dispersal kernel

Interaction of human migration and wealth distribution

Dynamics of human populations depends on various economical and social factors. Their migration is partially determined by the economical conditions and it can also influence these conditions. This work is devoted to the analysis of the interaction of human migration and wealth distribution. The model consists of a system of equations for the population density and for the wealth distribution with conventional diffusion terms and with cross diffusion terms describing human migration determined by the wealth gradient and wealth flux determined by human migration. Wealth production and consumption depend on the population density while the natality and mortality rates depend on the level of wealth. In the absence of cross diffusion terms, dynamics of solutions is described by travelling wave solutions of the corresponding reaction-diffusion systems of equations. We show persistence of such solutions for sufficiently small cross diffusion coefficients. This result is based on the perturbation methods and on the spectral properties of the linearized operators

On the Consistency of the Reaction-Telegraph Process Within Finite Domains

Reaction-telegraph equation (RTE) is a mathematical model that has often been used to describe natural phenomena, with specific applications ranging from physics to social sciences. In particular, in the context of ecology, it is believed to be a more realistic model to describe animal movement than the more traditional approach based on the reaction-diffusion equations. Indeed, the reaction-telegraph equation arises from more realistic microscopic assumptions about individual animal movement (the correlated random walk) and hence could be expected to be more relevant than the diffusion-type models that assume the simple, unbiased Brownian motion. However, the RTE has one significant drawback as its solutions are not positively defined. It is not clear at which stage of the RTE derivation the realism of the microscopic description is lost and/or whether the RTE can somehow be ‘improved’ to guarantee the solutions positivity. Here we show that the origin of the problem is twofold. Firstly, the RTE is not fully equivalent to the Cattaneo system from which it is obtained; the equivalence can only be achieved in a certain parameter range and only for the initial conditions containing a finite number of Fourier modes. Secondly, the Dirichlet type boundary conditions routinely used for reaction-diffusion equations appear to be meaningless if used for the RTE resulting in solutions with unrealistic properties. We conclude that, for the positivity to be regained, one has to use the Cattaneo system with boundary conditions of Robin type or Neumann type, and we show how relevant classes of solutions can be obtained

The mathematics behind biological invasions

This book investigates the mathematical analysis of biological invasions. Unlike purely qualitative treatments of ecology, it draws on mathematical theory and methods, equipping the reader with sharp tools and rigorous methodology. Subjects include invasion dynamics, species interactions, population spread, long-distance dispersal, stochastic effects, risk analysis, and optimal responses to invaders. While based on the theory of dynamical systems, including partial differential equations and integrodifference equations, the book also draws on information theory, machine learning, Monte Carlo methods, optimal control, statistics, and stochastic processes. Applications to real biological invasions are included throughout. Ultimately, the book imparts a powerful principle: that by bringing ecology and mathematics together, researchers can uncover new understanding of, and effective response strategies to, biological invasions. It is suitable for graduate students and established researchers in mathematical ecology