共查询到20条相似文献,搜索用时 31 毫秒
1.
H. L. Smith 《Journal of mathematical biology》1997,35(5):545-556
It is proved that the periodically forced Droop model for phytoplankton growth in a chemostat has precisely two dynamic regimes
depending on a threshold condition involving the dilution rate. If the dilution rate is such that the sub-threshold condition
holds, the phytoplankton population is washed out of the chemostat. If the super-threshold condition holds, then there is
a unique periodic solution, having the same period as the forcing, characterized by the presence of the phytoplankton population,
to which all solutions approach asymptotically. Furthermore, this result holds for a general class of models with monotone
growth rate and monotone uptake rate, the latter possibly depending on the cell quota.
Received 10 October 1995; received in revised form 26 March 1996 相似文献
2.
We describe and analyze a numerical method for an S-I-R type epidemic model. We prove that it is unconditionally convergent
and that solutions it produces share many qualitative and quantitative properties of the solution of the differential problem
being approximated. Finally, we establish explicit sufficient conditions for the unique endemic steady state of the system
to be unstable and we use our numerical algorithm to approximate the solution in such cases and discover that it can be periodic,
just as suggested by the instability of the endemic steady state.
Received: 1 September 1995 / Revised version: 30 April 1997 相似文献
3.
Stephen P. Ellner Akira Sasaki Yoshihiro Haraguchi Hirotsugu Matsuda 《Journal of mathematical biology》1998,36(5):469-484
We propose a simple approach to approximating the speed of invasion in lattice population models. Approximate critical parameter
values for successful invasion are then found by solving for zero wave speed. The approximation is based on describing the
occupied region by the ordinary pair approximation, and using quasi-steady-state pair approximations to describe the leading
edge of the wave front. We illustrate this idea using the basic contact process on the 1 and 2 dimensional lattice (with and
without nearest-neighbor migration), finding very good agreement between the approximation and simulation results. The approximate
critical values obtained by our approximation are significantly more accurate than those obtained by the ordinary pair approximation.
Received 4 September 1996 相似文献
4.
Roguing and replanting is a widely adopted control strategy of infectious diseases in orchards. Little is known about the
effect of this type of management on the dynamics of the infectious disease. In this paper we analyze a structured population
model for the dynamics of an S-I-R type epidemic under roguing and replanting management. The model is structured with respect
to the total number of infections and the number of post-infectious infections on a tree. Trees are assumed to be rogued,
and replaced by uninfected trees, when the total number of infections on the tree reaches a threshold value. Stability analysis
and numerical exploration of the model show that for specific parameter combinations the internal equilibrium can become unstable
and large amplitude periodic fluctuations arise. Several hypothesis on the mechanism causing the destabilisation of the steady-state
are considered. The mechanism leading to the large amplitude fluctuations is identified and biologically interpreted.
Received 2 September 1994 相似文献
5.
A hierarchically structured population model with a dependence of the vital rates on a function of the population density
(environment) is considered. The existence, uniqueness and the asymptotic behaviour of the solutions is obtained transforming the original
non-local PDE of the model into a local one. Under natural conditions, the global asymptotical stability of a nontrivial equilibrium
is proved. Finally, if the environment is a function of the biomass distribution, the existence of a positive total biomass
equilibrium without a nontrivial population equilibrium is shown.
Received 16 February 1996; received in revised form 16 September 1996 相似文献
6.
A model for the transmission of dengue fever with variable human population size is analyzed. We find three threshold parameters
which govern the existence of the endemic proportion equilibrium, the increase of the human population size, and the behaviour
of the total number of human infectives. We prove the global asymptotic stability of the equilibrium points using the theory
of competitive systems, compound matrices, and the center manifold theorem.
Received: 3 November 1997 / Revised version: 3 July 1998 相似文献
7.
In this paper, we build up an individual-based model (IBM) that describes the aggregative behavior in phytoplankton. The processes in play at the individual level (an individual=a phytoplankton cell) are: a random dispersal, a displacement due to the net effect of cells present in a suitable neighborhood (spatial interactions) and a branching (cell division and death). The IBM model provides a virtual world where phytoplankton cells appear to form clusters. Using this model, we explore the spatial structure of phytoplankton and present some numerical simulations that help the understanding of the aggregation phenomenon. 相似文献
8.
Morihiro Notohara 《Journal of mathematical biology》1997,36(2):188-200
The distribution of the number of segregating sites among randomly sampled DNA sequences from a geographically structured
population is studied. We assume the infinitely-many-sites model of neutral genes and no recombination. Employing the genealogical
process, we derive an equation for the generating function of the distribution of the number of segregating sites. First we
study the strong-migration limit and prove that the distribution converges to that for a panmictic population. We also study
the case of two sampled DNA sequences in the d-dimensional torus model with homogeneous migration.
Received 13 July 1995; received in revised form 21 April 1997 相似文献
9.
Helen M. Byrne 《Journal of mathematical biology》1999,39(1):59-89
In this paper we study a mathematical model that describes the growth of an avascular solid tumour. Our analysis concentrates
on the stability of steady, radially-symmetric model solutions with respect to perturbations taken from the class of spherical
harmonics. Using weakly nonlinear analysis, previous results are extended to show how the amplitudes of the asymmetric modes
interact. Attention focuses on a special case for which the model equations simplify. Analysis of the simplified model equations
leads to the identification of a two-parameter family of asymmetric steady solutions, the dimensions of whose stable and unstable
manifolds depend on the system parameters. The asymmetric steady solutions limit the basin of attraction of the radially-symmetric
steady state when it is linearly stable. On the basis of these numerical and analytical results we postulate the existence
of fully nonlinear steady solutions which are stable with respect to time-dependent perturbations.
Received: 25 October 1998 / Revised version: 20 June 1998 相似文献
10.
Odo Diekmann Mats Gyllenberg J. A. J. Metz Horst R. Thieme 《Journal of mathematical biology》1998,36(4):349-388
—We define a linear physiologically structured population model by two rules, one for reproduction and one for “movement”
and survival. We use these ingredients to give a constructive definition of next-population-state operators. For the autonomous
case we define the basic reproduction ratio R
0 and the Malthusian parameter r and we compute the resolvent in terms of the Laplace transform of the ingredients. A key feature of our approach is that
unbounded operators are avoided throughout. This will facilitate the treatment of nonlinear models as a next step.
Received 26 July 1996; received in revised form 3 September 1997 相似文献
11.
A model for macroparasitic infection with variable aggregation is considered. The starting point is an immigration-and-death
process for parasites within a host, as in [3]; it is assumed however that infections will normally occur with several larvae
at the same time. Starting from here, a four-dimensional, where free-living larvae are explicitly considered, and a three-dimensional
model are obtained with same methods used in [26]. The equilibria of these models are found, their stability is discussed,
as well as some qualitative features. It has been found that the assumption of “clumped” infections may have dramatic effects
on the aggregation exhibited by these models. Infections with several larvae at the same time also increases the stability
of the endemic equilibria of these models, and makes the occurrence of subcritical bifurcations (and consequently multiple
equilibria) slightly more likely.
The results of the low-dimensional model have also been compared to numerical simulations of the infinite system that describes
the immigration-and-death process. It appears that the results of the systems are, by and large, in close correspondence,
except for a parameter region where the four-dimensional model exhibits unusual properties, such as the occurrence of multiple
disease-free equilibria, that do not appear to be shared by the infinite system.
Received 28 October 1996; in revised form 11 April 1997 相似文献
12.
This article focuses on the analysis of coastal fish communities along the Norwegian Skagerrak coast. Species numbers are
estimated based on annual samples of the fish communities within 12 fjords from 1953 to 1994. On this basis, a community dynamics
model (incorporating both community-intrinsic and community-extrinsic processes) was developed and analyzed. This model is
then discussed on the basis of other community models available through the literature, both phenomenologically oriented and
process-oriented models.
Received: January 17, 2002 / Accepted: May 13, 2002
Acknowledgments We thank Dr. Masakado Kawata for the invi-tation to present this paper at the 19th Symposium of the Society of Population
Ecology held in Yamagata, Japan, October 26–28, 2001: “Evolution of Biodiversity: Theories and Facts.” Valuable input was
provided after the presentation at this meeting, which we greatly appreciated. The reformulation of the model in terms of
ΔS was kindly suggested to us by Prof. Joan Roughgarden. Thanks to Dr. Hildegunn Viljugrein for advice on the BUGS analyses
and to two anonymous reviewers for constructive comments. This work has been supported by grants from the Norwegian Science
Council (NFR).
Correspondence to:N.C. Stenseth 相似文献
13.
Thomas Nagylaki 《Journal of mathematical biology》1997,35(4):409-431
The diffusion approximation is derived for migration and selection at a multiallelic locus in a partially selfing plant population
subdivided into a lattice of colonies. Generations are discrete and nonoverlapping; both pollen and seeds disperse. In the
diffusion limit, the genotypic frequencies at each point are those determined at equilibrium by the local rate of selfing
and allelic frequencies. If the drift and diffusion coefficients are taken as the appropriate linear combination of the corresponding
coefficients for pollen and seeds, then the migration terms in the partial differential equation for the allelic frequencies
have the standard form for a monoecious animal population. The selection term describes selection on the local genotypic frequencies.
The boundary conditions and the unidimensional transition conditions for a geographical barrier and for coincident discontinuities
in the carrying capacity and migration rate have the standard form. In the diallelic case, reparametrization renders the entire
theory of clines and of the wave of advance of favorable alleles directly applicable to plant populations.
Received 30 August 1995; received in revised form 23 February 1996 相似文献
14.
Analysis of an SEIRS epidemic model with two delays 总被引:29,自引:0,他引:29
A disease transmission model of SEIRS type with exponential demographic structure is formulated. All newborns are assumed
susceptible, there is a natural death rate constant, and an excess death rate constant for infective individuals. Latent and
immune periods are assumed to be constants, and the force of infection is assumed to be of the standard form, namely proportional
to I(t)/N(t) where N(t) is the total (variable) population size and I(t) is the size of the infective population. The model consists of a set of integro-differential equations. Stability of the
disease free proportion equilibrium, and existence, uniqueness, and stability of an endemic proportion equilibrium, are investigated.
The stability results are stated in terms of a key threshold parameter. More detailed analyses are given for two cases, the
SEIS model (with no immune period), and the SIRS model (with no latent period). Several threshold parameters quantify the
two ways that the disease can be controlled, by forcing the number or the proportion of infectives to zero.
Received 8 May 1995; received in revised form 7 November 1995 相似文献
15.
A. Suzuki 《Trees - Structure and Function》2000,14(6):329-333
The patterns of vegetative growth and reproduction in relation to orders of terminal branches were examined in the evergreen
woody plant, Eurya japonica. The branch order number was determined centrifugally. The trunk was given order number 1; branches issuing directly from
the trunk were order 2; branches growing on order 2 branches were order 3, and so on. The results of this study show the differential
patterns of vegetative growth and reproduction in relation to the branch orders. Lower-order shoots of terminal branches grew
more, but produced few flowers. On the other hand, for the higher-order terminal branches, shoot growth was very limited but
flowering was more intense. The results show that a tree can be interpreted not as a mere population of equivalent modules
but as a spatially structured population. Thus, it is essential to consider the position of modules within the branch system
when patterns of vegetative growth and reproduction are examined. It is hypothesized that the difference in the opportunity
cost in relation to the branch orders is the main cause of the spatial structure for patterns of vegetative growth and reproduction.
Furthermore, for same-order terminal branches, current-year shoot elongation was independent of flowering intensity. These
results suggest that this species only invests resources in reproduction that are surplus to its requirements for the functions
associated with survival, such as growth and/or storage.
Received: 22 July 1999 / Accepted: 12 January 2000 相似文献
16.
Sarah A. Wilson Shashank N. Maindarkar Michelle C. McKee Michael Vilkhovoy Michael A. Henson Susan C. Roberts 《Biotechnology progress》2020,36(2):e2932
Cellular aggregation in plant suspension cultures directly affects the accumulation of high value products, such as paclitaxel from Taxus. Through application of mechanical shear by repeated, manual pipetting through a 10 ml pipet with a 1.6 mm aperture, the mean aggregate size of a Taxus culture can be reduced without affecting culture growth. When a constant level of mechanical shear was applied over eight generations, the sheared population was maintained at a mean aggregate diameter 194 μm lower than the unsheared control, but the mean aggregate size fluctuated by over 600 μm, indicating unpredictable culture variability. A population balance model was developed to interpret and predict disaggregation dynamics under mechanical shear. Adjustable parameters involved in the breakage frequency function of the population balance model were estimated by nonlinear optimization from experimentally measured size distributions. The optimized model predictions were in strong agreement with measured size distributions. The model was then used to determine the shear requirements to successfully reach a target aggregate size distribution. This model will be utilized in the future to maintain a culture with a constant size distribution with the goal of decreasing culture variability and increasing paclitaxel yields. 相似文献
17.
Dickinson RB 《Journal of mathematical biology》2000,40(2):97-135
A generalized transport model is derived for cell migration in an anisotropic environment and is applied to the specific
cases of biased cell migration in a gradient of a stimulus (taxis; e.g., chemotaxis or haptotaxis) or along an axis of anisotropy (e.g., contact guidance). The model accounts for spatial or directional dependence of cell speed and cell turning behavior to predict a constitutive
cell flux equation with drift velocity and diffusivity tensor (termed random motility tensor) that are explicit functions of the parameters of the underlying random walk model. This model provides the connection between
cell locomotion and the resulting persistent random walk behavior to the observed cell migration on longer time scales, thus
it provides a framework for interpreting cell migration data in terms of underlying motility mechanisms.
Received: 8 April 1999 相似文献
18.
Phototolerance of lichens, mosses and higher plants in an alpine environment: analysis of photoreactions 总被引:8,自引:0,他引:8
Adaptation to excessive light is one of the requirements of survival in an alpine environment particularly for poikilohydric
organisms which in contrast to the leaves of higher plants tolerate full dehydration. Changes in modulated chlorophyll fluorescence
and 820-nm absorption were investigated in the lichens Xanthoria elegans (Link) Th. Fr. and Rhizocarpon geographicum (L.) DC, in the moss Grimmia alpestris Limpr. and the higher plants Geum montanum L., Gentiana lutea L. and Pisum sativum L., all collected at altitudes higher than 2000 m above sea level. In the dehydrated state, chlorophyll fluorescence was
very low in the lichens and the moss, but high in the higher plants. It increased on rehydration in the lichens and the moss,
but decreased in the higher plants. Light-induced charge separation in photosystem II was indicated by pulse-induced fluorescence
increases only in dried leaves, not in the dry moss and dry lichens. Strong illumination caused photodamage in the dried leaves,
but not in the dry moss and dry lichens. Light-dependent increases in 820-nm absorption revealed formation of potential quenchers
of chlorophyll fluorescence in all dehydrated plants, but energy transfer to quenchers decreased chlorophyll fluorescence
only in the moss and the lichens, not in the higher plants. In hydrated systems, coupled cyclic electron transport is suggested
to occur concurrently with linear electron transport under strong actinic illumination particularly in the lichens because
far more electrons became available after actinic illumination for the reduction of photo-oxidized P700 than were available
in the pool of electron carriers between photosystems II and I. In the moss Grimmia, but not in the lichens or in leaves, light-dependent quenching of chlorophyll fluorescence was extensive even under nitrogen,
indicating anaerobic thylakoid acidification by persistent cyclic electron transport. In the absence of actinic illumination,
acidification by ca. 8% CO2 in air quenched the initial chlorophyll fluorescence yield Fo only in the hydrated moss and the lichens, not in leaves of the higher plants. Under the same conditions, 8% CO2 reduced the maximal fluorescence yield Fm strongly in the poikilohydric organisms, but only weakly or not at all in leaves. The data indicate the existence of deactivation
pathways which enable poikilohydric organisms to avoid photodamage not only in the hydrated but also in the dehydrated state.
In the hydrated state, strong nonphotochemical quenching of chlorophyll fluorescence indicated highly sensitive responses
to excess light which facilitated the harmless dissipation of absorbed excitation energy into heat. Protonation-dependent
fluorescence quenching by cyclic electron transport, P700 oxidation and, possibly, excitation transfer between the photosystems
were effectively combined to produce phototolerance.
Received: 10 December 1999 / Accepted: 13 April 2000 相似文献
19.
Multiparametric bifurcations for a model in epidemiology 总被引:1,自引:0,他引:1
In the present paper we make a bifurcation analysis of an SIRS epidemiological model depending on all parameters. In particular
we are interested in codimension-2 bifurcations.
Received 8 April 1994; received in revised form 29 June 1995 相似文献
20.
Analysis of a mathematical model for the growth of tumors 总被引:13,自引:0,他引:13
In this paper we study a recently proposed model for the growth of a nonnecrotic, vascularized tumor. The model is in the form of a free-boundary problem whereby the tumor grows (or shrinks) due to cell proliferation or death according to the level of a diffusing nutrient concentration.
The tumor is assumed to be spherically symmetric, and its boundary is an unknown function r=s(t). We concentrate on the case where at the boundary of the tumor the birth rate of cells exceeds their death rate, a necessary
condition for the existence of a unique stationary solution with radius r=R
0 (which depends on the various parameters of the problem). Denoting by c the quotient of the diffusion time scale to the tumor doubling time scale, so that c is small, we rigorously prove that
(i) lim inf
t→∞
s(t)>0, i.e. once engendered, tumors persist in time. Indeed, we further show that
(ii) If c is sufficiently small then s(t)→R
0 exponentially fast as t→∞, i.e. the steady state solution is globally asymptotically stable. Further,
(iii) If c is not “sufficiently small” but is smaller than some constant γ determined explicitly by the parameters of the problem, then
lim sup
t→∞
s(t)<∞; if however c is “somewhat” larger than γ then generally s(t) does not remain bounded and, in fact, s(t)→∞ exponentially fast as t→∞.
Received: 25 February 1998 / Revised version: 30 April 1998 相似文献