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Bulletin of Mathematical Biology

Stefan Forcey, Logan Keefe, William Sands
Understanding the face structure of the balanced minimal evolution (BME) polytope, especially its top-dimensional facets, is a fundamental problem in phylogenetic theory. We show that BME polytope has a sublattice of its poset of faces which is isomorphic to a quotient of the well-studied permutoassociahedron. This sublattice corresponds to compatible sets of splits displayed by phylogenetic trees and extends the lattice of faces of the BME polytope found by Hodge, Haws and Yoshida. Each of the maximal elements in our new poset of faces corresponds to a single split of the leaves...
March 22, 2017: Bulletin of Mathematical Biology
Joe Collis, Anthony J Connor, Marcin Paczkowski, Pavitra Kannan, Joe Pitt-Francis, Helen M Byrne, Matthew E Hubbard
In this work, we present a pedagogical tumour growth example, in which we apply calibration and validation techniques to an uncertain, Gompertzian model of tumour spheroid growth. The key contribution of this article is the discussion and application of these methods (that are not commonly employed in the field of cancer modelling) in the context of a simple model, whose deterministic analogue is widely known within the community. In the course of the example, we calibrate the model against experimental data that are subject to measurement errors, and then validate the resulting uncertain model predictions...
March 13, 2017: Bulletin of Mathematical Biology
Nathan G Marculis, Roger Lui, Mark A Lewis
We investigate the inside dynamics of solutions to integrodifference equations to understand the genetic consequences of a population with nonoverlapping generations undergoing range expansion. To obtain the inside dynamics, we decompose the solution into neutral genetic components. The inside dynamics are given by the spatiotemporal evolution of the neutral genetic components. We consider thin-tailed dispersal kernels and a variety of per capita growth rate functions to classify the traveling wave solutions as either pushed or pulled fronts...
March 13, 2017: Bulletin of Mathematical Biology
Jia Zhao, Qi Wang
We develop a multiphasic hydrodynamic theory for biofilms taking into account interactions among various bacterial phenotypes, extracellular polymeric substance (EPS), quorum sensing (QS) molecules, solvent, and antibiotics. In the model, bacteria are classified into down-regulated QS, up-regulated QS, and non-QS cells based on their QS ability. The model is first benchmarked against an experiment yielding an excellent fit to experimental measurements on the concentration of QS molecules and the cell density during biofilm development...
March 13, 2017: Bulletin of Mathematical Biology
Noble J Malunguza, Senelani D Hove-Musekwa, Zindoga Mukandavire
HIV susceptibility linked to hormonal contraception (HC) has been studied before, but with mixed results. Reports from some of the recent findings have prompted the World Health Organisation to encourage women who use HC to concurrently use condoms in order to prevent HIV infection in the light of possible increased HIV risk of infection associated with hormone-based contraceptives. A two-sex HIV model classifying women into three risk groups consisting of individuals who use condoms, natural methods, and hormone-based contraceptives is formulated and analysed to assess the possible effects of various birth control strategies on the transmission dynamics of the disease...
March 3, 2017: Bulletin of Mathematical Biology
Julien Baste, Christophe Paul, Ignasi Sau, Celine Scornavacca
In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species X; these relationships are often depicted via a phylogenetic tree-a tree having its leaves labeled bijectively by elements of X and without degree-2 nodes-called the "species tree." One common approach for reconstructing a species tree consists in first constructing several phylogenetic trees from primary data (e.g., DNA sequences originating from some species in X), and then constructing a single phylogenetic tree maximizing the "concordance" with the input trees...
February 28, 2017: Bulletin of Mathematical Biology
Daljit Singh J Dhillon, Michel C Milinkovitch, Matthias Zwicker
In this paper, we present computational techniques to investigate the effect of surface geometry on biological pattern formation. In particular, we study two-component, nonlinear reaction-diffusion (RD) systems on arbitrary surfaces. We build on standard techniques for linear and nonlinear analysis of RD systems and extend them to operate on large-scale meshes for arbitrary surfaces. In particular, we use spectral techniques for a linear stability analysis to characterise and directly compose patterns emerging from homogeneities...
February 28, 2017: Bulletin of Mathematical Biology
Kenneth Y Wertheim, Tiina Roose
The lymphatic system of a vertebrate is important in health and diseases. We propose a novel mathematical model to elucidate the lymphangiogenic processes in zebrafish embryos. Specifically, we are interested in the period when lymphatic endothelial cells (LECs) exit the posterior cardinal vein and migrate to the horizontal myoseptum of a zebrafish embryo. We wonder whether vascular endothelial growth factor C (VEGFC) is a morphogen and a chemotactic factor for these LECs. The model considers the interstitial flow driving convection, the reactive transport of VEGFC, and the changing dynamics of the extracellular matrix in the embryo...
February 23, 2017: Bulletin of Mathematical Biology
José Martins, Alberto Pinto
We use the reinfection SIRI epidemiological model to analyze the impact of education programs and vaccine scares on individuals decisions to vaccinate or not. The presence of the reinfection provokes the novelty of the existence of three Nash equilibria for the same level of the morbidity relative risk instead of a single Nash equilibrium as occurs in the SIR model studied by Bauch and Earn (PNAS 101:13391-13394, 2004). The existence of three Nash equilibria, with two of them being evolutionary stable, introduces two scenarios with relevant and opposite features for the same level of the morbidity relative risk: the low-vaccination scenario corresponding to the evolutionary stable vaccination strategy, where individuals will vaccinate with a low probability; and the high-vaccination scenario corresponding to the evolutionary stable vaccination strategy, where individuals will vaccinate with a high probability...
February 23, 2017: 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
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
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
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