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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
Nikolaos Sfakianakis, Niklas Kolbe, Nadja Hellmann, Mária Lukáčová-Medvid'ová
We propose a multiscale model for the invasion of the extracellular matrix by two types of cancer cells, the differentiated cancer cells and the cancer stem cells. We investigate the epithelial mesenchymal-like transition between them being driven primarily by the epidermal growth factors. We moreover take into account the transdifferentiation program of the cancer stem cells towards the cancer-associated fibroblast cells as well as the fibroblast-driven remodelling of the extracellular matrix. The proposed haptotaxis model combines the macroscopic phenomenon of the invasion of the extracellular matrix by both types of cancer cells with the microscopic dynamics of the epidermal growth factors...
November 30, 2016: Bulletin of Mathematical Biology
K Storey, M D Ryser, K Leder, J Foo
In this work we explore the temporal dynamics of spatial heterogeneity during the process of tumorigenesis from healthy tissue. We utilize a spatial stochastic model of mutation accumulation and clonal expansion in a structured tissue to describe this process. Under a two-step tumorigenesis model, we first derive estimates of a non-spatial measure of diversity: Simpson's Index, which is the probability that two individuals sampled at random from the population are identical, in the premalignant population. We next analyze two new measures of spatial population heterogeneity...
November 30, 2016: Bulletin of Mathematical Biology
Tom Britton, David Juher, Joan Saldaña
This paper is concerned with stochastic SIR and SEIR epidemic models on random networks in which individuals may rewire away from infected neighbors at some rate [Formula: see text] (and reconnect to non-infectious individuals with probability [Formula: see text] or else simply drop the edge if [Formula: see text]), so-called preventive rewiring. The models are denoted SIR-[Formula: see text] and SEIR-[Formula: see text], and we focus attention on the early stages of an outbreak, where we derive the expressions for the basic reproduction number [Formula: see text] and the expected degree of the infectious nodes [Formula: see text] using two different approximation approaches...
October 31, 2016: Bulletin of Mathematical Biology
Alan Hastings, Reinhard Laubenbacher
No abstract text is available yet for this article.
October 27, 2016: Bulletin of Mathematical Biology
Rodrick Wallace
Chemical exposures, pre- and neonatal infections, psychosocial stress, and the cross-generational cultural and epigenetic impacts of these and other toxicants become an integrated, sometimes synergistic, signal that can overwhelm essential neurodevelopmental regulation. We characterize that dynamic through statistical models based on the asymptotic limit theorems of control and information theories. Schizophrenia and autism emerge as two different 'phases' of pathological neurodevelopmental 'condensations' that impair the dynamic, shifting global workspace of normal mental function...
October 26, 2016: Bulletin of Mathematical Biology
Samuel Bernard
No abstract text is available yet for this article.
October 26, 2016: Bulletin of Mathematical Biology
Qiang-Hui Guo, Lisa Hui Sun, Jian Wang
A protein fold can be viewed as a self-avoiding walk in certain lattice model, and its contact map is a graph that represents the patterns of contacts in the fold. Goldman, Istrail, and Papadimitriou showed that a contact map in the 2D square lattice can be decomposed into at most two stacks and one queue. In the terminology of combinatorics, stacks and queues are noncrossing and nonnesting partitions, respectively. In this paper, we are concerned with 2-regular and 3-regular simple queues, for which the degree of each vertex is at most one and the arc lengths are at least 2 and 3, respectively...
January 2017: Bulletin of Mathematical Biology
G An, B G Fitzpatrick, S Christley, P Federico, A Kanarek, R Miller Neilan, M Oremland, R Salinas, R Laubenbacher, S Lenhart
Agent-based models (ABMs) have become an increasingly important mode of inquiry for the life sciences. They are particularly valuable for systems that are not understood well enough to build an equation-based model. These advantages, however, are counterbalanced by the difficulty of analyzing and using ABMs, due to the lack of the type of mathematical tools available for more traditional models, which leaves simulation as the primary approach. As models become large, simulation becomes challenging. This paper proposes a novel approach to two mathematical aspects of ABMs, optimization and control, and it presents a few first steps outlining how one might carry out this approach...
January 2017: Bulletin of Mathematical Biology
Camilla Fiorini
In order to describe the velocity and the anaerobic energy of two runners competing against each other for middle-distance races, we present a mathematical model relying on an optimal control problem for a system of ordinary differential equations. The model is based on energy conservation and on Newton's second law: resistive forces, propulsive forces and variations in the maximal oxygen uptake are taken into account. The interaction between the runners provides a minimum for staying 1 m behind one's competitor...
January 2017: Bulletin of Mathematical Biology
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