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Bulletin of Mathematical Biology

Qi Zheng
In around 1943, while writing a classic paper with Luria, Delbrück envisioned two kinds of mutation rates: One was expressed as mutations per bacterium per unit time, the other as mutations per bacterium per division cycle. Due to minor mathematical errors, the precise connection between the two concepts remained elusive for Delbrück. As a result, researchers and educators alike are still grappling with the definition of the mutation rate. Within the context of microbial mutation, the current author proposes an idealized model to bring new clarity to the distinction between the two forms of the mutation rate that Delbrück once attempted to define and characterize...
February 17, 2017: Bulletin of Mathematical Biology
Lu Peng, Dumitru Trucu, Ping Lin, Alastair Thompson, Mark A J Chaplain
Known as one of the hallmarks of cancer (Hanahan and Weinberg in Cell 100:57-70, 2000) cancer cell invasion of human body tissue is a complicated spatio-temporal multiscale process which enables a localised solid tumour to transform into a systemic, metastatic and fatal disease. This process explores and takes advantage of the reciprocal relation that solid tumours establish with the extracellular matrix (ECM) components and other multiple distinct cell types from the surrounding microenvironment. Through the secretion of various proteolytic enzymes such as matrix metalloproteinases or the urokinase plasminogen activator (uPA), the cancer cell population alters the configuration of the surrounding ECM composition and overcomes the physical barriers to ultimately achieve local cancer spread into the surrounding tissue...
February 16, 2017: Bulletin of Mathematical Biology
Timmy Ma, Natalia L Komarova
Continuing the discussion of how children can modify and regularize linguistic inputs from adults, we present a new interpretation of existing algorithms to model and investigate the process of a learner learning from an inconsistent source. On the basis of this approach is a (possibly nonlinear) function (the update function) that relates the current state of the learner with an increment that it receives upon processing the source's input, in a sequence of updates. The model can be considered a nonlinear generalization of the classic Bush-Mosteller algorithm...
February 13, 2017: Bulletin of Mathematical Biology
E Penelope Holland, Julie Mugford, Rachelle N Binny, Alex James
If a browse damage index indicates that a tree has been 50% browsed by herbivores, does this mean half the leaves are entirely eaten or are all the leaves half eaten? Were the affected leaves old or young? Large or small? In sunshine or shade? Understanding what effect browsing will have on the photosynthetic capacity and the plant's survival ability clearly requires a greater understanding of browsing strategy across the canopy than can be given by a single index value. We developed stochastic models of leaf production, growth and consumption using data from kamahi (Weinmannia racemosa) trees in New Zealand which have been browsed by possums (Trichosurus vulpecula), to ascertain which of six feasible browsing strategies possums are most likely to be employing...
February 13, 2017: Bulletin of Mathematical Biology
Jeremy G Sumner
We present a method of dimensional reduction for the general Markov model of sequence evolution on a phylogenetic tree. We show that taking certain linear combinations of the associated random variables (site pattern counts) reduces the dimensionality of the model from exponential in the number of extant taxa, to quadratic in the number of taxa, while retaining the ability to statistically identify phylogenetic divergence events. A key feature is the identification of an invariant subspace which depends only bilinearly on the model parameters, in contrast to the usual multi-linear dependence in the full space...
February 10, 2017: Bulletin of Mathematical Biology
Nathaniel J Karst, John B Geddes, Russell T Carr
We show that large microvascular networks with realistic topologies, geometries, boundary conditions, and constitutive laws can exhibit many steady-state flow configurations. This is in direct contrast to most previous studies which have assumed, implicitly or explicitly, that a given network can only possess one equilibrium state. While our techniques are general and can be applied to any network, we focus on two distinct network types that model human tissues: perturbed honeycomb networks and random networks generated from Voronoi diagrams...
February 7, 2017: Bulletin of Mathematical Biology
Li Zhang, Fan Zhang, Shigui Ruan
We study a diffusive predator-prey model describing the interactions of small fishes and their resource base (small invertebrates) in the fluctuating freshwater marsh landscapes of the Florida Everglades. The spatial model is described by a reaction-diffusion system with Beddington-DeAngelis functional response. Uniform bound, local and global asymptotic stability of the steady state of the PDE model under the no-flux boundary conditions are discussed in details. Sufficient conditions on the Turing (diffusion-driven) instability which induces spatial patterns in the model are derived via linear analysis...
January 30, 2017: Bulletin of Mathematical Biology
D L Humphries, J A Grogan, E A Gaffney
Cells contracting in extracellular matrix (ECM) can transmit stress over long distances, communicating their position and orientation to cells many tens of micrometres away. Such phenomena are not observed when cells are seeded on substrates with linear elastic properties, such as polyacrylamide (PA) gel. The ability for fibrous substrates to support far reaching stress and strain fields has implications for many physiological processes, while the mechanical properties of ECM are central to several pathological processes, including tumour invasion and fibrosis...
January 27, 2017: Bulletin of Mathematical Biology
Lakshmi Machineni, Anil Rajapantul, Vandana Nandamuri, Parag D Pawar
The resistance of bacterial biofilms to antibiotic treatment has been attributed to the emergence of structurally heterogeneous microenvironments containing metabolically inactive cell populations. In this study, we use a three-dimensional individual-based cellular automata model to investigate the influence of nutrient availability and quorum sensing on microbial heterogeneity in growing biofilms. Mature biofilms exhibited at least three structurally distinct strata: a high-volume, homogeneous region sandwiched between two compact sections of high heterogeneity...
January 26, 2017: Bulletin of Mathematical Biology
Lin Lin, Hans G Othmer
Fluorescence recovery after photobleaching (FRAP) is used to obtain quantitative information about molecular diffusion and binding kinetics at both cell and tissue levels of organization. FRAP models have been proposed to estimate the diffusion coefficients and binding kinetic parameters of species for a variety of biological systems and experimental settings. However, it is not clear what the connection among the diverse parameter estimates from different models of the same system is, whether the assumptions made in the model are appropriate, and what the qualities of the estimates are...
January 18, 2017: Bulletin of Mathematical Biology
Virginie Ravigné, Valérie Lemesle, Alicia Walter, Ludovic Mailleret, Frédéric M Hamelin
Fungal plant parasites represent a growing concern for biodiversity and food security. Most ascomycete species are capable of producing different types of infectious spores both asexually and sexually. Yet the contributions of both types of spores to epidemiological dynamics have still to been fully researched. Here we studied the effect of mate limitation in parasites which perform both sexual and asexual reproduction in the same host. Since mate limitation implies positive density dependence at low population density, we modeled the dynamics of such species with both density-dependent (sexual) and density-independent (asexual) transmission rates...
January 13, 2017: Bulletin of Mathematical Biology
Philip K Maini, Hans G Othmer, Andreas Deutsch
No abstract text is available yet for this article.
January 4, 2017: Bulletin of Mathematical Biology
C M Saad-Roy, P van den Driessche, Abdul-Aziz Yakubu
A general mathematical model of anthrax (caused by Bacillus anthracis) transmission is formulated that includes live animals, infected carcasses and spores in the environment. The basic reproduction number [Formula: see text] is calculated, and existence of a unique endemic equilibrium is established for [Formula: see text] above the threshold value 1. Using data from the literature, elasticity indices for [Formula: see text] and type reproduction numbers are computed to quantify anthrax control measures. Including only herbivorous animals, anthrax is eradicated if [Formula: see text]...
December 29, 2016: Bulletin of Mathematical Biology
Hayriye Gulbudak, Vincent L Cannataro, Necibe Tuncer, Maia Martcheva
Vector-borne disease transmission is a common dissemination mode used by many pathogens to spread in a host population. Similar to directly transmitted diseases, the within-host interaction of a vector-borne pathogen and a host's immune system influences the pathogen's transmission potential between hosts via vectors. Yet there are few theoretical studies on virulence-transmission trade-offs and evolution in vector-borne pathogen-host systems. Here, we consider an immuno-epidemiological model that links the within-host dynamics to between-host circulation of a vector-borne disease...
December 28, 2016: Bulletin of Mathematical Biology
Richard Kollár, Sebastian Novak
Variation in genotypes may be responsible for differences in dispersal rates, directional biases, and growth rates of individuals. These traits may favor certain genotypes and enhance their spatiotemporal spreading into areas occupied by the less advantageous genotypes. We study how these factors influence the speed of spreading in the case of two competing genotypes under the assumption that spatial variation of the total population is small compared to the spatial variation of the frequencies of the genotypes in the population...
December 22, 2016: Bulletin of Mathematical Biology
Sun-Ho Choi, Yong-Jung Kim
We introduce a mesoscopic scale chemotaxis model for traveling wave phenomena which is induced by food metric. The organisms of this simplified kinetic model have two discrete velocity modes, [Formula: see text] and a constant tumbling rate. The main feature of the model is that the speed of organisms is constant [Formula: see text] with respect to the food metric, not the Euclidean metric. The uniqueness and the existence of the traveling wave solution of the model are obtained. Unlike the classical logarithmic model case there exist traveling waves under super-linear consumption rates and infinite population pulse-type traveling waves are obtained...
December 19, 2016: Bulletin of Mathematical Biology
Matthew Lewis, James Powell
In addition to the memorization, algorithmic skills and vocabulary which are the default focus in many mathematics classrooms, professional mathematicians are expected to creatively apply known techniques, construct new mathematical approaches and communicate with and about mathematics. We propose that students can learn these professional, higher-level skills through Laboratory Experiences in Mathematical Biology which put students in the role of mathematics researcher creating mathematics to describe and understand biological data...
December 19, 2016: Bulletin of Mathematical Biology
Jing Li, Darla V Lindberg, Rachel A Smith, Timothy C Reluga
Public health policies can elicit strong responses from individuals. These responses can promote, reduce, and even reverse the expected benefits of the policies. Therefore, projections of individual responses to policy can be important ingredients in policy design. Yet our foresight of individual responses to public health investment remains limited. This paper formulates a population game describing the prevention of infectious disease transmission when community health depends on the interactions of individual and public investments...
December 6, 2016: Bulletin of Mathematical Biology
Anna Seigal, Portia Mira, Bernd Sturmfels, Miriam Barlow
Nosocomial outbreaks of bacteria are well documented. Based on these incidents, and the heavy usage of antibiotics in hospitals, it has been assumed that antibiotic resistance evolves in hospital environments. To test this assumption, we studied resistance phenotypes of bacteria collected from patient isolates at a community hospital over a 2.5-year period. A graphical model analysis shows no association between resistance and patient information other than time of arrival. This allows us to focus on time-course data...
December 6, 2016: Bulletin of Mathematical Biology
David S Ross, Khamir Mehta, Antonio Cabal
A better understanding of the molecular pathways regulating the bone remodeling process should help in the development of new antiresorptive regulators and anabolic regulators, that is, regulators of bone resorption and of bone formation. Understanding the mechanisms by which parathyroid hormone (PTH) influences bone formation and how it switches from anabolic to catabolic action is important for treating osteoporosis (Poole and Reeve in Curr Opin Pharmacol 5:612-617, 2005). In this paper we describe a mathematical model of bone remodeling that incorporates, extends, and integrates several models of particular aspects of this biochemical system (Cabal et al...
November 30, 2016: Bulletin of Mathematical Biology
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