176 research outputs found
Limiting the spread of disease through altered migration patterns
We consider a model for an epidemic in a population that occupies
geographically distinct locations. The disease is spread within subpopulations
by contacts between infective and susceptible individuals, and is spread
between subpopulations by the migration of infected individuals. We show how
susceptible individuals can act collectively to limit the spread of disease
during the initial phase of an epidemic, by specifying the distribution that
minimises the growth rate of the epidemic when the infectives are migrating so
as to maximise the growth rate. We also give an explicit strategy that
minimises the basic reproduction number, which is also shown be optimal in
terms of the probability of extinction and total size of the epidemic
Local approximation of a metapopulation's equilibrium
We consider the approximation of the equilibrium of a metapopulation model,
in which a finite number of patches are randomly distributed over a bounded
subset of Euclidean space. The approximation is good when a large
number of patches contribute to the colonization pressure on any given
unoccupied patch, and when the quality of the patches varies little over the
length scale determined by the colonization radius. If this is the case, the
equilibrium probability of a patch at being occupied is shown to be close
to , the equilibrium occupation probability in Levins's model, at any
point not too close to the boundary, if the local colonization
pressure and extinction rates appropriate to are assumed. The approximation
is justified by giving explicit upper and lower bounds for the occupation
probabilities, expressed in terms of the model parameters. Since the patches
are distributed randomly, the occupation probabilities are also random, and we
complement our bounds with explicit bounds on the probability that they are
satisfied at all patches simultaneously
A metapopulation model with Markovian landscape dynamics
We study a variant of Hanski's incidence function model that allows habitat
patch characteristics to vary over time following a Markov process. The widely
studied case where patches are classified as either suitable or unsuitable is
included as a special case. For large metapopulations, we determine a recursion
for the probability that a given habitat patch is occupied. This recursion
enables us to clarify the role of landscape dynamics in the survival of a
metapopulation. In particular, we show that landscape dynamics affects the
persistence and equilibrium level of the metapopulation primarily through its
effect on the distribution of a local population's life span.Comment: This manuscript version is made available under the CC-BY-NC-ND 4.0
license http://creativecommons.org/licenses/by-nc-nd/4.0
Connecting deterministic and stochastic metapopulation models
In this paper, we study the relationship between certain stochastic and
deterministic versions of Hanski's incidence function model and the spatially
realistic Levins model. We show that the stochastic version can be well
approximated in a certain sense by the deterministic version when the number of
habitat patches is large, provided that the presence or absence of individuals
in a given patch is influenced by a large number of other patches. Explicit
bounds on the deviation between the stochastic and deterministic models are
given.Comment: The final publication is available at Springer via
http://dx.doi.org/10.1007/s00285-015-0865-
The limiting behaviour of Hanski's incidence function metapopulation model
Hanski's incidence function model is one of the most widely used metapopulation models in ecology. It models the presence/absence of a species at spatially distinct habitat patches as a discrete-time Markov chain whose transition probabilities are determined by the physical landscape. In this analysis, the limiting behaviour of the model is studied as the number of patches increases and the size of the patches decreases. Two different limiting cases are identified depending on whether or not the metapopulation is initially near extinction. Basic properties of the limiting models are derived
Cholinergic receptor pathways involved in apoptosis, cell proliferation and neuronal differentiation
Acetylcholine (ACh) has been shown to modulate neuronal differentiation during early development. Both muscarinic and nicotinic acetylcholine receptors (AChRs) regulate a wide variety of physiological responses, including apoptosis, cellular proliferation and neuronal differentiation. However, the intracellular mechanisms underlying these effects of AChR signaling are not fully understood. It is known that activation of AChRs increase cellular proliferation and neurogenesis and that regulation of intracellular calcium through AChRs may underlie the many functions of ACh. Intriguingly, activation of diverse signaling molecules such as Ras-mitogen-activated protein kinase, phosphatidylinositol 3-kinase-Akt, protein kinase C and c-Src is modulated by AChRs. Here we discuss the roles of ACh in neuronal differentiation, cell proliferation and apoptosis. We also discuss the pathways involved in these processes, as well as the effects of novel endogenous AChRs agonists and strategies to enhance neuronal-differentiation of stem and neural progenitor cells. Further understanding of the intracellular mechanisms underlying AChR signaling may provide insights for novel therapeutic strategies, as abnormal AChR activity is present in many diseases
Mineral deficiency and the presence of Pinus sylvestris on mires during the mid- to late Holocene: Palaeoecological data from Cadogan's Bog, Mizen Peninsula, Co. Cork, southwest Ireland
Pollen records across parts of Ireland, England and northern Scotland show a dramatic collapse in Pinus pollen percentages at approximately 4000 radiocarbon years BP. This phenomenon has attracted much palaeoecological interest and several hypotheses have been put forward to account for this often synchronous and rapid reduction in pine from mid-Holocene woodland. Explanations for the 'pine decline' include prehistoric human activity, climatic change, in particular a substantial increase in precipitation resulting in increased mire wetness, and airborne pollution associated with the deposition of tephra. Hitherto, one largely untested hypothesis is that mineral deficiency could adversely affect pine growth and regeneration on mire surfaces. The discovery of pine-tree remains (wood pieces, stumps and trunks) within a peat located at Cadogan's Bog on the Mizen Peninsula, southwest Ireland, provided an opportunity to investigate the history of Pinus sylvestris and also to assess the importance of mineral nutrition in maintaining pine growth on mires. Pollen, plant macrofossils, microscopic charcoal and geochemical data are presented from a radiocarbon dated monolith extracted from this peat together with tree ring-width data and radiocarbon dated age estimates from subfossil wood. Analyses of these data suggest that peat accumulation commenced at the site around 6000 years BP when pine was the dominant local tree. Thereafter Pinus pollen percentages diminish in two stages, with the second decline taking place around 4160 ± 50 years BP. Concomitant with this decline in Pinus pollen, there is a noticeable, short-lived increase in wet-loving mire taxa and a decrease in the concentration of phosphorus, potassium, magnesium, calcium, sodium, iron and zinc. These results suggest that increased mire surface wetness, possibly the result of a change in climate, created conditions unsuitable for pine growth c. 4000 years BP. Mire surface wetness, coupled with a period of associated nutrient deficiency, appears to be a possible explanation for a lack of subsequent pine-seedling establishment for most of the later Holocene
Optimal Allocation Of Effort In Packet Switching Networks With Generally Distributed Transmission Times
: We consider the problem of how best to assign resources in a packet switching network with generally distributed transmission times so as to minimize the average delay under a cost constraint. For such networks there are typically no analytical formulae for the delay distributions. Thus, we shall approach the optimal allocation problem using an approximation technique, namely the residual-life approximation [9]. This work extends previous work of author [10] and generalizes results of Kleinrock [6], who studied networks with exponentially distributed service times. 1. INTRODUCTION In contrast to circuit switched networks, where one or more circuits are held simultaneously on several links connecting source and destination nodes, only one link is used at any given time by transmissions in a message or packet switched network; transmissions are received in their entirety at a given node before being transmitted along the next link in their path through the network. If the link is bus..
Integrals for continuous-time Markov chains
This paper presents a method of evaluating the expected value of a path integral for a general Markov chain on a countable state space. We illustrate the method with reference to several models, including birth-death processes and the birth, death and catastrophe process. (C) 2002 Elsevier Science Inc. All rights reserved
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