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1.
We study the positive steady state distributions and dynamical behavior of reaction-diffusion equation with weak Allee effect
type growth, in which the growth rate per capita is not monotonic as in logistic type, and the habitat is assumed to be a
heterogeneous bounded region. The existence of multiple steady states is shown, and the global bifurcation diagrams are obtained.
Results are applied to a reaction-diffusion model with type II functional response, and also a model with density-dependent
diffusion of animal aggregation.
J. S. is partially supported by United States NSF grants DMS-0314736 and EF-0436318, College of William and Mary summer grants,
and a grant from Science Council of Heilongjiang Province, China. 相似文献
2.
Journal of Mathematical Biology - A SIR epidemic model is analyzed with respect to identification of its parameters, based upon reported case data from public health sources. The objective of the... 相似文献
3.
In this paper we develop a model of intracellular transport of cell organelles and vesicles along the axon of a nerve cell. These particles are moving alternately by processive motion along a microtubule with the aid of motor proteins, and by diffusion. The model involves a degenerate system of diffusion equations. We prove a maximum principle and establish existence and behavior of a unique solution. Numerical results show how the transportation of mass depends on the relevant parameters of the model. 相似文献
4.
Ayati BP 《Journal of mathematical biology》2006,52(1):93-114
In this paper we present continuous age- and space-structured models and numerical computations of Proteus mirabilis swarm-colony development. We base the mathematical representation of the cell-cycle dynamics of Proteus mirabilis on those developed by Esipov and Shapiro, which are the best understood aspects of the system, and we make minimum assumptions
about less-understood mechanisms, such as precise forms of the spatial diffusion. The models in this paper have explicit age-structure
and, when solved numerically, display both the temporal and spatial regularity seen in experiments, whereas the Esipov and
Shapiro model, when solved accurately, shows only the temporal regularity.
The composite hyperbolic-parabolic partial differential equations used to model Proteus mirabilis swarm-colony development are relevant to other biological systems where the spatial dynamics depend on local physiological
structure. We use computational methods designed for such systems, with known convergence properties, to obtain the numerical
results presented in this paper. 相似文献
5.
Dendrites of nerve cells have membranes with spatially distributed densities of ionic channels and hence non-uniform conductances. These conductances are usually represented as constant parameters in neural models because of the difficulty in experimentally estimating them locally. In this paper we investigate the inverse problem of recovering a single spatially distributed conductance parameter in a one-dimensional diffusion (cable) equation through a new use of a boundary control method. We also outline how our methodology can be extended to cable theory on finite tree graphs. The reconstruction is unique. 相似文献
6.
This paper analyses travelling-wave behaviour in a recently-formulated multiphase model for the growth of biological tissue
that comprises motile cells and water inside a porous scaffold. The model arises in the context of tissue engineering, and
its purpose is to study how cells migrate and proliferate inside porous biomaterials. In suitable limits, tissue growth in
the model is shown to occur in the form of travelling waves that can propagate either forwards or backwards, depending on
the values of the parameters. In the case where the drag force between the scaffold and the cells is non-zero, the growth
of the aggregate can be analysed in terms of the propagation of a constant-speed wavefront in a semi-infinite domain. A numerical
(shooting) method is described for calculating the wave speed, and detailed results for how the speed varies with respect
to the parameters are given. In the case where the drag force is zero, the size of the aggregate is shown either to grow or
to shrink exponentially with time. These results may be of importance in determining the experimental factors that control
tissue invasiveness in scaffolds thereby allowing greater control over engineered tissue growth. 相似文献
7.
We consider a mathematical model for the indirect transmission via a contaminated environment of a microparasite between two spatially distributed host populations having non-coincident spatial domains. The parasite is benign in a first population and lethal in the second one. Global existence results are given for the resulting reaction-diffusion system coupled with an ordinary differential equation. Then, invasion and persistence of the parasite are studied. A simplified model for the transmission of a hantavirus from bank vole to human populations is then analysed. 相似文献
8.
C. C. Chicone Z. -S. Cai P. D. King E. L. Forker 《Journal of mathematical biology》1993,31(3):273-289
We develop a simple mathematical model for bile formation and analyze some features of the model that suggest the design for future physiological experiments. The mathematical model results in a boundary value problem for a system of functional differential equations depending on several physical parameters. From the observability of the boundary values we can identify, both qualitatively and quantitatively, some of these physical parameters. This identification then suggests physical experiments from which one could infer some of the bile transport phenomena that are not, at present, directly observable. The mathematical parameter identification problem is solved by converting the boundary value problem to a transition time problem for a quadratic system of ordinary differential equations on the plane where we are able to employ some special properties of quadratic systems in order to obtain a solution.The author was supported by the Air Force Office of Scientific Research and the National Science Foundation under the grants AF-AFOSR-89-0078 and DMS-9022621The author was supported by National Institutes of Health under grant number R37 DK-27623 相似文献
9.
This work is concerned with a reaction-diffusion system that has been proposed as a model to describe acid-mediated cancer invasion. More precisely, we consider the properties of travelling waves that can be supported by such a system, and show that a rich variety of wave propagation dynamics, both fast and slow, is compatible with the model. In particular, asymptotic formulae for admissible wave profiles and bounds on their wave speeds are provided. 相似文献
10.
Geometry and membrane properties of the dendrites crucially determine input–output relations in neurons. Unlike geometry often available in detail from computer reconstruction, the membrane resistivity is fragmentarily known if at all. Moreover, it varies during ongoing activity. In this study we address the question: what is the impact of the variation in membrane resistivity on the transfer properties of dendrites? Following a standard approach of the control system theory, we derive and explore the sensitivity functions complementary to the transfer functions of the passive dendrites with arbitrary geometrical parameters (length and diameter) and boundary conditions. We use the location-dependent somatopetal current transfer ratio (the reciprocal of the somatofugal voltage) as the transfer function, and its membrane resistivity derivatives, as the sensitivity functions. In the dendrites, at every path distance from the origin, the sensitivity function in a common form relates the transfer function, membrane resistivity, characteristic input conductance of semi-infinite cable and directional somatofugal input conductances at the given internal site and origin, and the length. Plotted in membrane resistivity versus path distance coordinates, the sensitivity functions display common features: along any coordinate there are low and high ranges, in which the sensitivity, respectively, increases and decreases. The ranges and corresponding rates depend on morphology and boundary conditions in a characteristic manner. These features predict existence of the geometry-dependent range of membrane resistivity (the earlier unattended mid-conductance state), such that the dendrites with a given metrical asymmetry are most distinguished in their transfer properties and electrical states if membrane resistivity is within the range and are not otherwise. 相似文献
11.
The somatic shunt model, a generalized version of the Rall equivalent cylinder model, is used commonly to describe the passive electrotonic properties of neurons. Procedures for determining the parameters of the somatic shunt model that best describe a given neuron typically rely on the response of the cell to a small step of hyperpolarizing current injected by an intrasomatic recording electrode. In this study it is shown that the problem of estimating model parameters for the somatic shunt model using physiological data is ill-posed, in that very small errors in measured data can lead to large and unpredictable errors in parameter estimates. If the somatic shunt is assumed to be a real property of the intact neuron, the effects of these errors are not severe when predicting EPSP waveshapes resulting from synaptic input at a given location. However, if the somatic shunt is assumed to be a consequence of a leakage pathway around the recording electrode, and a correction for the shunt is applied, then the instability of the inverse problem can introduce large errors in estimates of EPSP waveshape as a function of synaptic location in the intact cell. Morphological constraints can be used to improve the accuracy of the inversion procedure in terms of both parameter estimates and predicted EPSP responses. 相似文献
12.
It is well known that in many scalar models for the spread of a fitter phenotype or species into the territory of a less fit one, the asymptotic spreading speed can be characterized as the lowest speed of a suitable family of traveling waves of the model. Despite a general belief that multi-species (vector) models have the same property, we are unaware of any proof to support this belief. The present work establishes this result for a class of multi-species model of a kind studied by Lui [Biological growth and spread modeled by systems of recursions. I: Mathematical theory, Math. Biosci. 93 (1989) 269] and generalized by the authors [Weinberger et al., Analysis of the linear conjecture for spread in cooperative models, J. Math. Biol. 45 (2002) 183; Lewis et al., Spreading speeds and the linear conjecture for two-species competition models, J. Math. Biol. 45 (2002) 219]. Lui showed the existence of a single spreading speed c(*) for all species. For the systems in the two aforementioned studies by the authors, which include related continuous-time models such as reaction-diffusion systems, as well as some standard competition models, it sometimes happens that different species spread at different rates, so that there are a slowest speed c(*) and a fastest speed c(f)(*). It is shown here that, for a large class of such multi-species systems, the slowest spreading speed c(*) is always characterized as the slowest speed of a class of traveling wave solutions. 相似文献
13.
Bekkal Brikci F Clairambault J Ribba B Perthame B 《Journal of mathematical biology》2008,57(1):91-110
We present a nonlinear model of the dynamics of a cell population divided into proliferative and quiescent compartments. The
proliferative phase represents the complete cell cycle (G
1−S−G
2−M) of a population committed to divide at its end. The model is structured by the time spent by a cell in the proliferative
phase, and by the amount of Cyclin D/(CDK4 or 6) complexes. Cells can transit from one compartment to the other, following transition rules which differ according to the
tissue state: healthy or tumoral. The asymptotic behaviour of solutions of the nonlinear model is analysed in two cases, exhibiting
tissue homeostasis or tumour exponential growth. The model is simulated and its analytic predictions are confirmed numerically. 相似文献
14.
This work presents an example of a cooperative system of truncated linear recursions in which the interaction between species
causes one of the species to have an anomalous spreading speed. By this we mean that this species spreads at a speed which
is strictly greater than its spreading speed in isolation from the other species and the speeds at which all the other species
actually spread. An ecological implication of this example is discussed in Sect. 5. Our example shows that the formula for
the fastest spreading speed given in Lemma 2.3 of our paper (Weinberger et al. in J Math Biol 45:183–218, 2002) is incorrect.
However, we find an extra hypothesis under which the formula for the faster spreading speed given in (Weinberger et al. in
J Math Biol 45:183–218, 2002) is valid. We also show that the hypotheses of all but one of the theorems of (Weinberger et al.
in J Math Biol 45:183–218, 2002) whose proofs rely on Lemma 2.3 imply this extra hypothesis, so that all but one of the theorems
of (Weinberger et al. in J Math Biol 45:183–218, 2002) and all the examples given there are valid as they stand. 相似文献
15.
An idea used by Thieme (J. Math. Biol. 8, 173-187, 1979) is extended to show that a class of integro-difference models for a periodically varying habitat has a spreading speed and a formula for it, even when the recruitment function R(u, x) is not nondecreasing in u, so that overcompensation occurs. Numerical simulations illustrate the behavior of solutions of the recursion whose initial values vanish outside a bounded set. 相似文献
16.
The goal of this work is to formulate a general Holling-type functional, or behavioral, response for continuous physiologically structured populations, where both the predator and the prey have physiological densities and certain rules apply to their interactions. The physiological variable can be, for example, a development stage, weight, age, or a characteristic length. The model leads to a Fredholm integral equation for the functional response, and, when inserted into population balance laws, it produces a coupled system of partial differential-integral equations for the two species, with a nonlocal integral term that arises from rules of interaction in the functional response. The general model is, typically, analytically intractable, but specialization to a structured prey-unstructured predator model leads to some analytic results that reveal interesting and unexpected dynamics caused by the presence of size-dependent handling times in the functional response. In this case, steady-states are shown to exist over long times, similar to the stable age-structure solutions for the McKendick-von Foerster model with exponential growth rates determined by the Euler-Lotka equation. But, for type II responses, there are early transient oscillations in the number of births that bifurcate in a few generations into either the decaying or growing steady-state. The bifurcation parameter is the initial level of prey. This special case is applied to a problem of the biological control of a structured pest population (e.g., aphids) by a predator (e.g., lady beetles). 相似文献
17.
In this paper, we use singular perturbation methods to study the structure of travelling waves for some reaction-diffusion
models obtained from the Martiel-Goldbeter and Goldbeter-Segel's models of cAMP signalling in Dictyostelium discoideum. As a consequence, we derive analytic formulae for quantities like wave speed, maximum concentration and other magnitudes
in terms of the different biochemical constants that appear in the model. 相似文献
18.
19.
A model of competition for two complementary nutrients between plasmid-bearing and plasmid-free organisms in a chemostat is proposed. A rigorous mathematical analysis of the global asymptotic behavior of the model is presented. The work extends the model of competition for a single-limited nutrient studied by Stephanopoulos and Lapidus [Chem. Engng. Sci. 443 (1988) 49] and Hsu, Waltman and Wolkowicz [J. Math. Biol. 32 (1994) 731]. 相似文献
20.
A stochastic model for prostate-specific antigen levels 总被引:1,自引:0,他引:1
We introduce a continuous stochastic model for the prostate-specific antigen (PSA) levels following radiotherapy and derive solutions for the associated partial differential (Kolmogorov-Chapman) equation. The solutions describe the evolution of the time-dependent density for PSA levels which take into account an absorbing condition along the boundary and various initial conditions. We include implications for single-dose and multi-dose radiation treatment regimens and discuss parameter estimation and sensitivity issues. 相似文献