Showing papers in "Bulletin of Mathematical Biology in 2016"

TL;DR: A review of some research areas in mathematical immunology that evolved over the last 10 years and a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales.

TL;DR: This case study explores multistationarity, model comparison, dynamics within regions of the state space, identifiability, and parameter estimation, from a geometric point of view using current methods from computational algebraic geometry, polyhedral geometry, and combinatorics.

TL;DR: The exact master equations of the propagation process are derived for an arbitrary hypergraph given by its incidence matrix, and moment closure approximation and mean-field models are introduced and compared to individual-based stochastic simulations.

TL;DR: This review presents the progress in mathematical modelling of bacterial quorum sensing, highlighting the various theoretical approaches that have been used and discussing some of the insights that have emerged.

TL;DR: In this paper, the authors developed a physiological model of granulopoiesis which includes explicit modelling of the kinetics of the cytokine granulocyte colony-stimulating factor (G-CSF) incorporating both the freely circulating concentration and the concentration of cytokine bound to mature neutrophils.

TL;DR: An SIR model for an epidemic, including vital dynamics, from an underlying stochastic process is developed, showing how fractional differential operators arise naturally in these models whenever the recovery time from the disease is power-law distributed.

TL;DR: The structural and practical identifiability of a nested immuno-epidemiological model of arbovirus diseases, where host–vector transmission rate, host recovery, and disease-induced death rates are governed by the within-host immune system is discussed.

TL;DR: In this article, a class of continuous-time Markov chain models for biochemical interaction systems with non-mass action kinetics whose network satisfies a certain constraint is studied. And the stationary distributions of these models can be computed explicitly.

TL;DR: This paper is an attempt to estimate the risk of infection importation and exportation by travelers in two countries: one disease-free country and one visited or source country with a running endemic or epidemic infectious disease.

TL;DR: A concept from ecology, the Allee effect, is used to help explain tumor extinction in a model of tumor growth that incorporates feedback regulation of stem cell dynamics, which occurs in many tumor types where certain signaling molecules, such as Wnts, are upregulated.

TL;DR: It is shown that the class of tree-child networks is precisely the classof tree-based networks with the property that every embedded phylogenetic tree is a base tree.

TL;DR: In this article, the authors decompose the resulting travelling wave solution into neutral genetic components to analyse the spatio-temporal dynamics of its genetic structure and show that range expansions and range shifts under slow climate change preserve genetic diversity.

TL;DR: An integro-difference equation model that describes the spatial dynamics of a species in an expanding or contracting habitat and conditions under which the species disperses to a region of poor quality where the species eventually becomes extinct is studied.

TL;DR: An individual-based model of cell migration and proliferation that includes neighbour-dependent proliferation and death is developed using a spatial moment dynamics approach, which allows insight into the two-way interaction between spatial structure and population dynamics that cannot be captured by traditional mean-field models.

TL;DR: An image-based modelling approach to investigating how the internal structure of the node affects the fluid flow pathways within the node shows that the flow predominantly takes a direct path between the afferent and efferent lymphatics and that fluid is both filtered and absorbed across the blood vessel boundaries.

TL;DR: The novel state space truncation and error analysis methods developed here can be used to ensure accurate direct solutions to the dCME for a large number of stochastic networks.

TL;DR: Three mathematical models are presented, in which vector transmission of the virus, sexual contact transmission and migration are considered, showing that sexual transmission influences the magnitude of the outbreaks and migration generates outbreaks over time, each of lower intensity than the previous.

TL;DR: This work uses a simple model to examine the fundamental roles of broad demographic and spatial structures in epidemic initiation, growth and control and shows that the key factors are local dilution, characterised by the vector–host ratio, and spatial connectivity, characterising by the extent of habitually variable movement patterns.

TL;DR: The development of cervical cells from normal cells infected by human papillomavirus into invasive cancer cells can be modeled using population dynamics of the cells and free virus and the boundary between initial conditions of solutions is investigated.

TL;DR: A general mathematical model incorporating multiple infection stages and various drug classes that can interfere with specific stages of the viral life cycle can explain the viral load decline in HIV patients treated with raltegravir-containing regimens.

TL;DR: This article generalises the Luria–Delbrück model to different types of wild-type population growth, with mutants evolving as a birth–death branching process, and proves that the long-time limit of the clone size distribution has a general two-parameter form, whose tail decays as a power-law.

TL;DR: The results indicate that the initial density of mosquitoes, the quantities of mosquitoes released in augmentations and their sex ratios have impacts on whether or not the strategies of population suppression or replacement can be achieved.

TL;DR: A previously derived system of 12 first-order coupled differential equations that describe the transport between, and storage in, different tissues of the human body is used to solve the model numerically, separately simulating each individual tissue as insulin resistant, and draws three main conclusions.

TL;DR: A game-theoretical model in which individuals choose their own level of protection against mosquito bites in order to maximize their own benefits is presented, effectively balancing the cost of protection and the risk of contracting the dengue fever.

TL;DR: In this paper, the authors present two PDE models describing lymphangiogenesis according to these two different hypotheses and include the effect of advection due to interstitial flow and lymph flow coming from open capillaries.

TL;DR: The study implies that the smaller size colony invests its resource for the colony growth and allocates more workers in the risky tasks such as foraging while the larger colony shifts more workers to perform the safer tasks inside the colony.

TL;DR: The application of fuzzy differential equation in the modeling of prey–predator populations with the effect of toxicants is presented and the possibility of the existence of bionomic equilibrium is studied under imprecise biological parameters.

TL;DR: Three different ways of measuring starvation by applying them to starvation-driven diffusion are compared and it is seen that, if species have different starvation measures and different motility functions, both the coexistence and selection are possible.

TL;DR: The role of growth of the domain in the selection of patterns is emphasized, and a comparison between the resulting patterns on the fixed domain and those arising when the domain grows is established.

TL;DR: The results show that maintaining RdCVF above a threshold value allows for coexistence, however, a significant increase above this value threatens the existence of rods as the cones become extremely efficient at uptaking glucose and begin to take most of it for themselves.