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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
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...
November 14, 2016: 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...
November 8, 2016: 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...
November 8, 2016: Bulletin of Mathematical Biology
Jason Bintz, Suzanne Lenhart, Cristina Lanzas
We implement an agent-based model for Clostridium difficile transmission in hospitals that accounts for several processes and individual factors including environmental and antibiotic heterogeneity in order to evaluate the efficacy of various control measures aimed at reducing environmental contamination and mitigating the effects of antibiotic use on transmission. In particular, we account for local contamination levels that contribute to the probability of colonization and we account for both the number and type of antibiotic treatments given to patients...
November 8, 2016: Bulletin of Mathematical Biology
Brodie A J Lawson, Graeme J Pettet
The Glazier-Graner-Hogeweg (GGH) model is a cellular automata framework for representing the time evolution of cellular systems, appealing because unlike many other individual-cell-based models it dynamically simulates changes in cell shape and size. Proliferation has seen some implementation into this modelling framework, but without consensus in the literature as to how this behaviour is best represented. Additionally, the majority of published GGH model implementations which feature proliferation do so in order to simulate a certain biological situation where mitosis is important, but without analysis of how these proliferation routines operate on a fundamental level...
November 1, 2016: Bulletin of Mathematical Biology
Eric Numfor, Frank M Hilker, Suzanne Lenhart
Invasive species cause enormous problems in ecosystems around the world. Motivated by introduced feral cats that prey on bird populations and threaten to drive them extinct on remote oceanic islands, we formulate and analyze optimal control problems. Their novelty is that they involve both scalar and time-dependent controls. They represent different forms of control, namely the initial release of infected predators on the one hand and culling as well as trapping, infecting, and returning predators on the other hand...
October 31, 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
J Mushanyu, F Nyabadza, G Muchatibaya, A G R Stewart
The abuse of drugs is now an epidemic globally whose control has been mainly through rehabilitation. The demand for drug abuse rehabilitation has not been matched with the available capacity resulting in limited placement of addicts into rehabilitation. In this paper, we model limited rehabilitation through the Hill function incorporated into a system of nonlinear ordinary differential equations. Not every member of the community is equally likely to embark on drug use, risk structure is included to help differentiate those more likely (high risk) to abuse drugs and those less likely (low risk) to abuse drugs...
October 20, 2016: Bulletin of Mathematical Biology
Vladimir Kozlov, Sergey Vakulenko, Uno Wennergren
This paper considers a model of foodwebs taking into account species extinction and invasion. We show that system stability depends not only on usual parameters (mortality rates, self-limitation coefficients, and resource abundances), but also on an additional parameter ("biodiversity potential"). The main result is as follows. For foodwebs with random parameters, we obtain an estimate of probability that the foodweb exposed to invasion survives. This estimate involves different system parameters, size and its topological properties...
October 19, 2016: Bulletin of Mathematical Biology
Rachelle N Binny, Alex James, Michael J Plank
Collective cell migration and proliferation are integral to tissue repair, embryonic development, the immune response and cancer. Central to collective cell migration and proliferation are interactions among neighbouring cells, such as volume exclusion, contact inhibition and adhesion. These individual-level processes can have important effects on population-level outcomes, such as growth rate and equilibrium density. We develop an individual-based model of cell migration and proliferation that includes these interactions...
October 19, 2016: Bulletin of Mathematical Biology
David Baca-Carrasco, Jorge X Velasco-Hernández
Since the first major outbreak reported on the island Yap in 2007, the Zika virus spread has alerted the scientific community worldwide. Zika is an arbovirus transmitted by Aedes mosquitoes; particularly in Central and South America, the main vector is the same mosquito that transmits dengue and chikungunya, Aedes aegypti. Seeking to understand the dynamics of spread of the Zika, in this paper, three mathematical models are presented, in which vector transmission of the virus, sexual contact transmission and migration are considered...
October 14, 2016: Bulletin of Mathematical Biology
Jimmy Garnier, Mark A Lewis
Range expansion and range shifts are crucial population responses to climate change. Genetic consequences are not well understood but are clearly coupled to ecological dynamics that, in turn, are driven by shifting climate conditions. We model a population with a deterministic reaction-diffusion model coupled to a heterogeneous environment that develops in time due to climate change. We decompose the resulting travelling wave solution into neutral genetic components to analyse the spatio-temporal dynamics of its genetic structure...
October 14, 2016: Bulletin of Mathematical Biology
Xianghong Zhang, Sanyi Tang, Robert A Cheke, Huaiping Zhu
Dengue fever has rapidly become the world's most common vector-borne viral disease. Use of endosymbiotic Wolbachia is an innovative technology to prevent vector mosquitoes from reproducing and so break the cycle of dengue transmission. However, strategies such as population eradication and replacement will only succeed if appropriate augmentations with Wolbachia-infected mosquitoes that take account of a variety of factors are carried out. Here, we describe the spread of Wolbachia in mosquito populations using an impulsive differential system with four state variables, incorporating the effects of cytoplasmic incompatibility and the augmentation of Wolbachia-infected mosquitoes with different sex ratios...
October 12, 2016: Bulletin of Mathematical Biology
Raluca Eftimie, Joseph J Gillard, Doreen A Cantrell
The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take 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...
October 6, 2016: Bulletin of Mathematical Biology
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