Showing papers in "Bulletin of Mathematical Biology in 2004"

TL;DR: This short treatise presents a concise history of the study of solid tumour growth, illustrating the development of mathematical approaches from the early decades of the twentieth century to the present time, showing the crucial relationship between experimental and theoretical approaches.

TL;DR: A model of stochastic evolutionary game dynamics in finite populations which is similar to the familiar replicator dynamics for infinite populations is introduced and the conditions for selection favoring the invasion and/or fixation of new phenotypes are focused on.

TL;DR: Given a qualitative model of a genetic regulatory network, consisting of a system of PL differential equations and inequality constraints on the parameter values, the method produces a graph of qualitative states and transitions between qualitative states, summarizing the qualitative dynamics of the system.

TL;DR: Lyapunov functions for basic virus dynamics models are introduced, and global stability of the models are thereby established.

TL;DR: A continuum model of cell motility in ameboid cells based on a viscoelastic description of the cytoplasm and active stress generation controlled by extracellular signals is developed and analyzed.

TL;DR: It is demonstrated how habitat movement, coupled with edge effects, can open up a new niche for invaders that would be otherwise excluded in a moving habitat.

TL;DR: This work applies a circular random walk model to the process of angiogenesis, and thus allows the cells to move independently of a lattice; the results display good agreement with empirical observations.

TL;DR: A qualitative simulation method is used to model the sporulation network and simulate the response of the cell to nutrient deprivation, and reproduce essential features of the choice between vegetative growth and sporulation.

TL;DR: This work describes one implementation of the phantom bursting mechanism in which intracellular Ca2+ controls the oscillations through both direct and indirect negative feedback pathways, and shows how the model dynamics can be understood through an extension of the fast/slow analysis that is typically employed for bursting oscillations.

TL;DR: This paper generalizes an earlier spatial model to incorporate an immune response against the infected tumor cells and estimates of some unknown parameters provide some implications for the delivery of treatment.

TL;DR: An immunological model that considers the dynamics of CD4+ T cells interacting with free virions, reverse transcriptase inhibiting drugs and protease inhibited drugs finds that insufficient dosing of either drug corresponds to high viral load and a large population of infectious T cells.

TL;DR: In this article, a sensitivity analysis is performed on a delay differential equation model for the viral dynamics of an in vivo HIV infection during protease inhibitor therapy, and the results support the claim that the presence of a nonzero delay has a major impact on the model dynamics.

TL;DR: This paper uses the Gray code representation of the genetic code C = 00, U = 10, G = 11 and A = 01 to generate a sequence of genetic code-based matrices and presents an explicit decomposition formula for the genetic Code-based matrix in terms of permutation matrices, which provides a hypercube representation ofThe genetic code.

TL;DR: A model for the evolution of positive HIV population and manifestation of AIDS (acquired immunideficiency syndrome) is introduced in a fuzzy model that preserves the biological meaning and nature of the transference rate λ.

TL;DR: Analysis of the Gierer-Meinhardt model revealed that a change in a single parameter can explain two effects of FGF on limb mesenchyme cells—reinforcement of lateral inhibition and earlier appearance of pattern.

TL;DR: This study addresses natural selection’s role in tumor evolution by developing and exploring a mathematical model of a heterogenous primary neoplasm and suggests that parenchyma cell diversity can be maintained by a tissue-like integration of cells specialized to provide different services.

TL;DR: This paper characterize the fluorescence recovery curves for diffusing nuclear proteins undergoing binding events with an approximate spatially homogeneous structure and shows how the two models, describing the same type of dynamics using different approaches, relate and share common ground.

TL;DR: A detailed description of a mathematical model of the process which is able to reproduce several qualitative and quantitative features of in vitro vascularization experiments is given, whose possible area of application is the design of properly vascularized artificial tissues.

TL;DR: The research presented here include simulations of two processes—cell proliferation and cell fusion which both play a crucial role in the growth and development of the trophoblast tissue and the computed results of simulations of both processes running independently as well as simultaneously are presented.

TL;DR: This paper presents two existing phenology models, the distributed delay model and the Sharpe and DeMichele model, and develops an alternate approach, called the Extended von Foerster model, based on the age-structured McKendrick-von Foersters partial differential model, which exhibits the highest correlation between theory and observation.

TL;DR: Simulations predict that short-term viral suppression with varying interruptions strategies does not guarantee long-term clinical benefit and dynamics occurring below the limit of detection are influenced by these factors, and contribute to reemergence or suppression of virus during interruptions.

TL;DR: Results of biological significance include: the change of behaviour by the CSW’s has a more direct effect on the spread of HIV than that of the male customers; the basic reproduction number is obtained by considering all possible infection cycles of the heterosexual transmission of HIV which indicates the importance of understanding the sexual networking in heterosexual transmissionof HIV.

TL;DR: It is shown that a Hopf bifurcation can occur implying that if the carrying capacity is made sufficiently large by enrichment of the environment, the model predicts the eventual extinction of the predator providing strong support for the so-called ‘paradox of enrichment’.

TL;DR: Analysis of a simple semi-discrete model for tick population dynamics reveals that a ‘dilution effect’ occurs both for competent and for incompetent hosts; this means that, besides a lower threshold for host densities for infection to persist, there exists also an upper threshold: ifHost densities were higher than the upper threshold, the infection would go to extinction.

TL;DR: This paper presents an alternative analysis of a previously presented stochastic model for an epidemic in continuous space and investigates the dependence of the epidemic threshold on host spatial distribution and pathogen dispersal.

TL;DR: The present study involves a stochastic generalization of the original idea described by Kier, which concerned the use of molecular negentropies in QSAR, and concludes that the approach described here seems to be a promising 3D-QSAR tool based on the mathematical theory of Stochastic processes.

TL;DR: Numerical simulations of the stochastic model show that coexistence cases predicted by the deterministic model are an unlikely occurrence in the stoChastic model even for short time periods.

TL;DR: This work summarizes relative fitness and treatment efficacy via two simple parameters, and demonstrates that invasion of resistance depends critically on a trade-off between them.

TL;DR: The model makes a potentially significant prediction about animal behaviour in the area of kleptoparasitism, that a searcher, when it meets a handler, will only decline to attack that handler when α < 1/2 i.e. when the defender is more likely to win.

TL;DR: Stable LCO can emerge in coupled nephrons for sufficiently large gains and delays, however, these LCO may emerge at lower values of the feedback gain, relative to a single (i.e., uncoupled) nephron, or at shorter delays, provided the delays are sufficiently close.