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Bulletin of Mathematical Biology

Luiza Guimarães Fabreti, Diogo Castro, Bruno Gorzoni, Luiz Mario Ramos Janini, Fernando Antoneli
RNA viruses comprise vast populations of closely related, but highly genetically diverse, entities known as quasispecies. Understanding the mechanisms by which this extreme diversity is generated and maintained is fundamental when approaching viral persistence and pathobiology in infected hosts. In this paper, we access quasispecies theory through a mathematical model based on the theory of multitype branching processes, to better understand the roles of mechanisms resulting in viral diversity, persistence and extinction...
December 14, 2018: Bulletin of Mathematical Biology
Mikahl Banwarth-Kuhn, Ali Nematbakhsh, Kevin W Rodriguez, Stephen Snipes, Carolyn G Rasmussen, G Venugopala Reddy, Mark Alber
One of the central problems in animal and plant developmental biology is deciphering how chemical and mechanical signals interact within a tissue to produce organs of defined size, shape, and function. Cell walls in plants impose a unique constraint on cell expansion since cells are under turgor pressure and do not move relative to one another. Cell wall extensibility and constantly changing distribution of stress on the wall are mechanical properties that vary between individual cells and contribute to rates of expansion and orientation of cell division...
December 14, 2018: Bulletin of Mathematical Biology
Andrew M Bate, Frank M Hilker
Preytaxis is the attraction (or repulsion) of predators along prey density gradients and a potentially important mechanism for predator movement. However, the impact preytaxis has on the spatial spread of a predator invasion or of an epidemic within the prey has not been investigated. We investigate the effects preytaxis has on the wavespeed of several different invasion scenarios in an eco-epidemiological system. In general, preytaxis cannot slow down predator or disease invasions and there are scenarios where preytaxis speeds up predator or disease invasions...
December 13, 2018: Bulletin of Mathematical Biology
Aili Wang, Yanni Xiao, Robert Smith
The issue of medical-resource constraints has the potential to dramatically affect disease management, especially in developing countries. We analyze a non-smooth epidemic model with nonlinear incidence rate and resource constraints, which defines a vaccination program with vaccination rate proportional to the number of susceptible individuals when this number is below the threshold level and constant otherwise. To better understand the impact of this non-smooth vaccination policy, we provide a comprehensive qualitative analysis of global dynamics for the whole parameter space...
December 11, 2018: Bulletin of Mathematical Biology
Jicai Huang, Shigui Ruan, Yaqin Shu, Xiao Wu
Human rabies is one of the major public health problems in China with an average of 1977 cases per year. It is estimated that 95% of these human rabies cases are due to dog bites. In recent years, the number of wildlife-associated human rabies cases has increased, particularly in the southeast and northeast regions of mainland China. Chinese ferret badgers (CFBs) are one of the most popular wildlife animals which are distributed mostly in the southeast region of China. Human cases caused by rabid CFB were first recorded in Huzhou, Zhejiang Province, in 1994...
December 10, 2018: Bulletin of Mathematical Biology
Pranas Katauskis, Feliksas Ivanauskas, Aidas Alaburda
Information in the brain is stored in a form of an altered synaptic strength between neurons. The long-term potentiation (LTP), a phenomenon when a short-term increase in neural activity is transformed into a long-lasting increase in strengths of synaptic connectivity, provides an experimental substrate of memory. Using reaction-diffusion equations, we established an LTP model, describing the dynamics of glutamate (Glu), calcium (Ca2+ ) and nitric oxide (NO) in response to the stimulus-a presynaptic action potential...
December 10, 2018: Bulletin of Mathematical Biology
Farzad Peyravi, Alimohammad Latif, Seyed Mohammad Moshtaghioun
The biological function of protein depends mainly on its tertiary structure which is determined by its amino acid sequence via the process of protein folding. Prediction of protein structure from its amino acid sequence is one of the most prominent problems in computational biology. Two basic methodologies on protein structure prediction are combined: ab initio method (3-D space lattice) and fold recognition method (hidden Markov model). The primary structure of proteins and 3-D coordinates of amino acid residues are put together in one hidden Markov model to learn the path of amino acid residues in 3-D space from the first atom to the last atom of each protein of each fold...
December 10, 2018: Bulletin of Mathematical Biology
Cindy Gidoin, Stephan Peischl
Many theoretical studies of range expansions focus on the dynamics of species' ranges or on causes and consequences of biological invasions. The similarities between biological range expansions and the dynamics of tumour growth have recently become more obvious, highlighting that tumours can be viewed as a population of abnormal cells expanding its range in the body of its host. Here, we discuss the potential of recent theoretical developments in the context of range expansions to shed light on intra-tumour heterogeneity, and to develop novel computational and statistical methods for studying the increasingly available genomic and phenotypic data from tumour cells...
December 7, 2018: Bulletin of Mathematical Biology
Irene Balelli, Vuk Milišić, Gilles Wainrib
We analyze the interactions between division, mutation and selection in a simplified evolutionary model, assuming that the population observed can be classified into fitness levels. The construction of our mathematical framework is motivated by the modeling of antibody affinity maturation of B-cells in germinal centers during an immune response. This is a key process in adaptive immunity leading to the production of high-affinity antibodies against a presented antigen. Our aim is to understand how the different biological parameters affect the system's functionality...
December 7, 2018: Bulletin of Mathematical Biology
Fred Brauer
In an epidemic of a serious disease, there is likely to be behavioral response that decreases the epidemic size considerably, and taking this into account may lead to estimates of the final epidemic size that are much smaller and more realistic than estimates that do not take this into account.
December 7, 2018: Bulletin of Mathematical Biology
Marc Manceau, Amaury Lambert
How to define a partition of individuals into species is a long-standing question called the species problem in systematics. Here, we focus on this problem in the thought experiment where individuals reproduce clonally and both the differentiation process and the population genealogies are explicitly known. We specify three desirable properties of species partitions: (A) Heterotypy between species, (B) Homotypy within species and (M) Genealogical monophyly of each species. We then ask: How and when is it possible to delineate species in a way satisfying these properties? We point out that the three desirable properties cannot in general be satisfied simultaneously, but that any two of them can...
December 7, 2018: Bulletin of Mathematical Biology
Camilo Sanabria Malagón, Esteban Vargas Bernal
In this paper, we propose a method to study a general vector-host mathematical model in order to explain how the changes in biodiversity could influence the dynamics of vector-borne diseases. We find that under the assumption of frequency-dependent transmission, i.e., the assumption that the number of contacts is diluted by the total population of hosts, the presence of a competent host is a necessary condition for the existence of an endemic state. In addition, we obtain that in the case of an endemic disease with a unique competent and resilient host, an increase in its density amplifies the disease...
December 7, 2018: Bulletin of Mathematical Biology
P C Bressloff, E Levien
Biochemical reactions are often subject to a complex fluctuating environment, which means that the corresponding reaction rates may themselves be time-varying and stochastic. If the environmental noise is common to a population of downstream processes, then the resulting rate fluctuations will induce statistical correlations between them. In this paper we investigate how such correlations depend on the form of environmental noise by considering a simple birth-death process with dynamical disorder in the birth rate...
December 6, 2018: Bulletin of Mathematical Biology
Andrew L Krause, Meredith A Ellis, Robert A Van Gorder
We study two-species reaction-diffusion systems on growing manifolds, including situations where the growth is anisotropic yet dilational in nature. In contrast to the literature on linear instabilities in such systems, we study how growth and anisotropy impact the qualitative properties of nonlinear patterned states which have formed before growth is initiated. We produce numerical solutions to numerous reaction-diffusion systems with varying reaction kinetics, manner of growth (both isotropic and anisotropic), and timescales of growth on both planar elliptical and curved ellipsoidal domains...
December 3, 2018: Bulletin of Mathematical Biology
Stéphane Honoré, Florence Hubert, Magali Tournus, Diana White
Microtubules (MTs) are protein filaments found in all eukaryotic cells which are crucial for many cellular processes including cell movement, cell differentiation, and cell division. Due to their role in cell division, they are often used as targets for chemotherapy drugs used in cancer treatment. Experimental studies of MT dynamics have played an important role in the development and administration of many novel cancer drugs; however, a complete description of MT dynamics is lacking. Here, we propose a new mathematical model for MT dynamics, that can be used to study the effects of chemotherapy drugs on MT dynamics...
November 27, 2018: Bulletin of Mathematical Biology
Elías Vera-Sigüenza, Nathan Pages, John Rugis, David I Yule, James Sneyd
Salivary gland acinar cells use the calcium ([Formula: see text]) ion as a signalling messenger to regulate a diverse range of intracellular processes, including the secretion of primary saliva. Although the underlying mechanisms responsible for saliva secretion are reasonably well understood, the precise role played by spatially heterogeneous intracellular [Formula: see text] signalling in these cells remains uncertain. In this study, we use a mathematical model, based on new and unpublished experimental data from parotid acinar cells (measured in excised lobules of mouse parotid gland), to investigate how the structure of the cell and the spatio-temporal properties of [Formula: see text] signalling influence the production of primary saliva...
November 27, 2018: Bulletin of Mathematical Biology
Vincent Lemaire, David R Cox
We propose a mathematical model describing the dynamics of osteoblasts and osteoclasts in bone remodeling. The goal of this work is to develop an integrated modeling framework for bone remodeling and bone cell signaling dynamics that could be used to explore qualitatively combination treatments for osteoporosis in humans. The model has been calibrated using 57 checks from the literature. Specific global optimization methods based on qualitative objectives have been developed to perform the model calibration...
November 20, 2018: Bulletin of Mathematical Biology
A Francis, K T Huber, V Moulton
The level-5 example of a network presented in Fig. 4 of Francis et al. (2018) is tree-based even though it states in the caption and in the text that this is not the case.
November 16, 2018: Bulletin of Mathematical Biology
Alexander P Browning, Parvathi Haridas, Matthew J Simpson
We present a novel framework to parameterise a mathematical model of cell invasion that describes how a population of melanoma cells invades into human skin tissue. Using simple experimental data extracted from complex experimental images, we estimate three model parameters: (i) the melanoma cell proliferation rate, [Formula: see text]; (ii) the melanoma cell diffusivity, D; and (iii) [Formula: see text], a constant that determines the rate that melanoma cells degrade the skin tissue. The Bayesian sequential learning framework involves a sequence of increasingly sophisticated experimental data from: (i) a spatially uniform cell proliferation assay; (ii) a two-dimensional circular barrier assay; and (iii) a three-dimensional invasion assay...
November 15, 2018: Bulletin of Mathematical Biology
C D Bayliss, C Fallaize, R Howitt, M V Tretyakov
Temporal evolution of a clonal bacterial population is modelled taking into account reversible mutation and selection mechanisms. For the mutation model, an efficient algorithm is proposed to verify whether experimental data can be explained by this model. The selection-mutation model has unobservable fitness parameters, and, to estimate them, we use an Approximate Bayesian Computation algorithm. The algorithms are illustrated using in vitro data for phase variable genes of Campylobacter jejuni.
November 14, 2018: Bulletin of Mathematical Biology
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