Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces.

abstract：:The Hodgkin and Huxley equations have served as the benchmark model in electrophysiology since 1950s. But it suffers from four major drawbacks. Firstly, it is only phenomenological not mechanistic. Secondly, it fails to exhibit the all-or-nothing firing mechanism for action potential generation. Thirdly, it lacks a th...

journal_title：Bulletin of mathematical biology

authors： Deng B

更新日期：2017-06-01 00:00:00

abstract：:In this paper, a simple semi-discrete (ticks' feeding is assumed to occur only during the summers of each year) model for tick population dynamics is presented. Conditions for existence, uniqueness, and stability of a positive equilibrium are found; the system is then studied numerically using parameter estimates cali...

journal_title：Bulletin of mathematical biology

authors： Ghosh M,Pugliese A

更新日期：2004-11-01 00:00:00

abstract：:Cycles in biological populations have been shown to arise from enemy-victim systems, delayed density dependence, and maternal effects. In an initial effort to model the year-to-year dynamics of natural populations of entomopathogenic nematodes and their insect hosts, we find that a simple, nonlinear, mechanistic model...

journal_title：Bulletin of mathematical biology

authors： Dugaw CJ,Hastings A,Preisser EL,Strong DR

更新日期：2004-05-01 00:00:00

abstract：:For epidemic models, it is shown that fatal infectious diseases cannot drive the host population into extinction if the incidence function is upper density-dependent. This finding holds even if a latency period is included and the time from infection to disease-induced death has an arbitrary length distribution. Howev...

journal_title：Bulletin of mathematical biology

authors： Farrell AP,Collins JP,Greer AL,Thieme HR

更新日期：2018-07-01 00:00:00

abstract：:In this paper, we present a model that explains the prepatterning of lymphatic vessel morphology in collagen gels. This model is derived using the theory of two phase rubber material due to Flory and coworkers and it consists of two coupled fourth order partial differential equations describing the evolution of the co...

journal_title：Bulletin of mathematical biology

authors： Roose T,Fowler AC

更新日期：2008-08-01 00:00:00

abstract：:A system of differential equations for the control of tumor cells growth in a cycle nonspecific chemotherapy is presented. Spontaneously acquired drug resistance is accounted for, as well as the evolution in time of normal cells. In addition, optimization of conflicting objectives forms the aim of the chemotherapeutic...

journal_title：Bulletin of mathematical biology

authors： Costa MI,Boldrini JL

更新日期：1997-07-01 00:00:00

abstract：:Analysis schemes for the classification of synergism and antagonism for mixed agents operate on the discrepancies between observed and calculated results. As such they cannot be confirmed by experiments and therefore have to be tested in terms of mathematical and logical self-consistency. The concept of independent ac...

journal_title：Bulletin of mathematical biology

authors： Lam GK

更新日期：1994-09-01 00:00:00

abstract：:Bistability and multistationarity are properties of reaction networks linked to switch-like responses and connected to cell memory and cell decision making. Determining whether and when a network exhibits bistability is a hard and open mathematical problem. One successful strategy consists of analyzing small networks ...

journal_title：Bulletin of mathematical biology

authors： Feliu E,Helmer M

更新日期：2019-04-01 00:00:00

abstract：:In this paper, we use multiple scale homogenisation to derive a set of averaged macroscale equations that describe the movement of nutrients in partially saturated soil that contains growing potato tubers. The soil is modelled as a poroelastic material, which is deformed by the growth of the tubers, where the growth o...

journal_title：Bulletin of mathematical biology

authors： Duncan SJ,Daly KR,McKay Fletcher DM,Ruiz S,Sweeney P,Roose T

更新日期：2019-10-01 00:00:00

abstract：:A kinetic model is proposed to delineate the factors that determine the coronary reactive hyperemic response (RHR) to transient ischemia. The model comprises of myocardial-interstitial (M) and vascular (V) compartments. Vasodilator metabolites (VM) are produced in the M compartment during the interval of coronary occl...

journal_title：Bulletin of mathematical biology

authors： Wong AY

更新日期：1995-01-01 00:00:00

abstract：:Understanding the life-history complex of eusociality has remained an enduring problem in evolutionary ecology, partially because natural selection models have considered traits in relative isolation. I aim for a more inclusive model that uses ecological interactions to predict the evolutionary existence of sexual rep...

journal_title：Bulletin of mathematical biology

authors： Witting L

更新日期：2007-05-01 00:00:00

abstract：:The Shapley value, a solution concept from cooperative game theory, has recently been considered for both unrooted and rooted phylogenetic trees. Here, we focus on the Shapley value of unrooted trees and first revisit the so-called split counts of a phylogenetic tree and the Shapley transformation matrix that allows f...

journal_title：Bulletin of mathematical biology

authors： Wicke K,Fischer M

更新日期：2019-02-01 00:00:00

abstract：:In special coordinates (codon position-specific nucleotide frequencies), bacterial genomes form two straight lines in 9-dimensional space: one line for eubacterial genomes, another for archaeal genomes. All the 348 distinct bacterial genomes available in Genbank in April 2007, belong to these lines with high accuracy....

journal_title：Bulletin of mathematical biology

authors： Gorban AN,Zinovyev AY

更新日期：2007-10-01 00:00:00

abstract：:We introduce here a gene evolution model which is an extension of the time-continuous stochastic IDIS model (Lèbre and Michel in J. Comput. Biol. Chem. 34:259-267, 2010) to sequence length. This new IDISL (Insertion Deletion Independent of Substitution based on sequence Length) model gives an analytical expression of ...

journal_title：Bulletin of mathematical biology

authors： Lèbre S,Michel CJ

更新日期：2012-08-01 00:00:00

abstract：:We investigate the existence of oscillatory dynamics and multiple steady-state flow rates in a network with a simple topology and in vivo microvascular blood flow constitutive laws. Unlike many previous analytic studies, we employ the most biologically relevant models of the physical properties of whole blood. Through...

journal_title：Bulletin of mathematical biology

authors： Karst NJ,Storey BD,Geddes JB

更新日期：2015-07-01 00:00:00

abstract：:We propose a new geometric buildup algorithm for the solution of the distance geometry problem in protein modeling, which can prevent the accumulation of the rounding errors in the buildup calculations successfully and also tolerate small errors in given distances. In this algorithm, we use all instead of a subset of ...

journal_title：Bulletin of mathematical biology

authors： Sit A,Wu Z,Yuan Y

更新日期：2009-11-01 00:00:00

abstract：:A coupled model is presented for simulating physical and biological dynamics in fresh water lakes. The physical model rests upon the assumption that the turbulent kinetic energy in a water column of the lake is fully contained in a mixed layer of variable depth. Below this layer the mechanical energy content is assume...

journal_title：Bulletin of mathematical biology

authors： Franke U,Hutter K,Jöhnk K

更新日期：1999-03-01 00:00:00

abstract：:A stochastic evolutionary dynamics of two strategies given by 2x 2 matrix games is studied in finite populations. We focus on stochastic properties of fixation: how a strategy represented by a single individual wins over the entire population. The process is discussed in the framework of a random walk with site depend...

journal_title：Bulletin of mathematical biology

authors： Antal T,Scheuring I

更新日期：2006-11-01 00:00:00

abstract：:A two-dimensional model for red blood cell motion is adapted to consider the dynamics of breast cancer cells in a microfluidic channel. Adjusting parameters to make the membrane stiffer, as is the case with breast cancer cells compared with red blood cells, allows the model to produce reasonable estimates of breast ca...

journal_title：Bulletin of mathematical biology

authors： Barber J,Zhu L

更新日期：2019-04-01 00:00:00

abstract：:Pseudomonas aeruginosa is a Gram-negative bacterium that is responsible for a wide range of infections in humans. Colonies employ quorum sensing (QS) to coordinate gene expression, including for virulence factors, swarming motility and complex social traits. The QS signalling system of P. aeruginosa is known to involv...

journal_title：Bulletin of mathematical biology

authors： Alfiniyah C,Bees MA,Wood AJ

更新日期：2017-06-01 00:00:00

abstract：:Advances in fluorescent labeling of cells as measured by flow cytometry have allowed for quantitative studies of proliferating populations of cells. The investigations (Luzyanina et al. in J. Math. Biol. 54:57-89, 2007; J. Math. Biol., 2009; Theor. Biol. Med. Model. 4:1-26, 2007) contain a mathematical model with fluo...

journal_title：Bulletin of mathematical biology

authors： Banks HT,Sutton KL,Thompson WC,Bocharov G,Roose D,Schenkel T,Meyerhans A

更新日期：2011-01-01 00:00:00

abstract：:In this paper we develop and extend a previous model of cell deformations, initially proposed to describe the dynamical behaviour of round-shaped cells such as keratinocytes or leukocytes, in order to take into account cell pseudopodial dynamics with large amplitude membrane deformations such as those observed in fibr...

journal_title：Bulletin of mathematical biology

authors： Stéphanou A,Chaplain MA,Tracqui P

更新日期：2004-09-01 00:00:00

abstract：:Radiation target theory has been extended to complex biochemical systems. Mathematical analyses are presented for multiple forms of biological active proteins, for the presence of large inhibitors or activators, for compounds which regulate rate or affinity and for multiple-step reactions. Several predictions of these...

journal_title：Bulletin of mathematical biology

authors： Kempner ES

更新日期：1995-11-01 00:00:00

abstract：:Bursting electrical activity is ubiquitous in excitable cells such as neurons and many endocrine cells. The technique of fast/slow analysis, which takes advantage of time scale differences, is typically used to analyze the dynamics of bursting in mathematical models. Two classes of bursting oscillations that have been...

journal_title：Bulletin of mathematical biology

authors： Teka W,Tsaneva-Atanasova K,Bertram R,Tabak J

更新日期：2011-06-01 00:00:00

abstract：:We develop a model for describing the dynamics of imatinib-treated chronic myelogenous leukemia. Our model is based on replacing the recent agent-based model of Roeder et al. (Nat. Med. 12(10):1181-1184, 2006) by a system of deterministic difference equations. These difference equations describe the time-evolution of ...

journal_title：Bulletin of mathematical biology

authors： Kim PS,Lee PP,Levy D

更新日期：2008-04-01 00:00:00

abstract：:Cell polarization is an important part of the response of eukaryotic cells to stimuli, and forms a primary step in cell motility, differentiation, and many cellular functions. Among the important biochemical players implicated in the onset of intracellular asymmetries that constitute the early phases of polarization a...

journal_title：Bulletin of mathematical biology

authors： Walther GR,Marée AF,Edelstein-Keshet L,Grieneisen VA

更新日期：2012-11-01 00:00:00

abstract：:Temporal evolution of a clonal bacterial population is modelled taking into account reversible mutation and selection mechanisms. For the mutation model, an efficient algorithm is proposed to verify whether experimental data can be explained by this model. The selection-mutation model has unobservable fitness paramete...

journal_title：Bulletin of mathematical biology

authors： Bayliss CD,Fallaize C,Howitt R,Tretyakov MV

更新日期：2019-03-01 00:00:00

abstract：:Collective dynamics of migrating cell populations drive key processes in tissue formation and maintenance under normal and diseased conditions. Collective cell behavior at the tissue level is typically characterized by considering cell density patterns such as clusters and moving cell fronts. However, there are also i...

journal_title：Bulletin of mathematical biology

authors： Mente C,Voss-Böhme A,Deutsch A

更新日期：2015-04-01 00:00:00

abstract：:Logical modeling of biological regulatory networks gives rise to a representation of the system's dynamics as a so-called state transition graph. Analysis of such a graph in its entirety allows for a comprehensive understanding of the functionalities and behavior of the modeled system. However, the size of the vertex ...

journal_title：Bulletin of mathematical biology

authors： Lorenz T,Siebert H,Bockmayr A

更新日期：2013-06-01 00:00:00

abstract：:Microtubules (MTs) are protein filaments found in all eukaryotic cells which are crucial for many cellular processes including cell movement, cell differentiation, and cell division. Due to their role in cell division, they are often used as targets for chemotherapy drugs used in cancer treatment. Experimental studies...

journal_title：Bulletin of mathematical biology

authors： Honoré S,Hubert F,Tournus M,White D

更新日期：2019-03-01 00:00:00