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Bulletin of Mathematical Biology

Lawrence Kurowski, Andrew L Krause, Hanako Mizuguchi, Peter Grindrod, Robert A Van Gorder
We extend two-species models of individual aggregation or clustering to two-dimensional spatial domains, allowing for more realistic movement of the populations compared with one spatial dimension. We assume that the domain is bounded and that there is no flux into or out of the domain. The motion of the species is along fitness gradients which allow the species to seek out a resource. In the case of competition, species which exploit the resource alone will disperse while avoiding one another. In the case where one of the species is a predator or generalist predator which exploits the other species, that species will tend to move toward the prey species, while the prey will tend to avoid the predator...
August 18, 2017: Bulletin of Mathematical Biology
Gilles Didier
The time-dependent-asymmetric-linear parsimony is an ancestral state reconstruction method which extends the standard linear parsimony (a.k.a. Wagner parsimony) approach by taking into account both branch lengths and asymmetric evolutionary costs for reconstructing quantitative characters (asymmetric costs amount to assuming an evolutionary trend toward the direction with the lowest cost). A formal study of the influence of the asymmetry parameter shows that the time-dependent-asymmetric-linear parsimony infers states which are all taken among the known states, except for some degenerate cases corresponding to special values of the asymmetry parameter...
August 17, 2017: Bulletin of Mathematical Biology
Roberta Regina Delboni, Hyun Mo Yang
The big challenge for the food industry is the attending to demands for minimally processed foods, avoiding intense heat treatments and reducing the addition of chemical preservatives, but at the same time ensuring microbiological safety of these products. Lactic acid bacteria are traditionally used in the production of fermented foods. They are responsible for the production of antimicrobial compounds, such as organic acids and bacteriocins, which are protein compounds with bactericidal effect against related species and bacteria such as Listeria monocytogenes and Staphylococcus aureus...
August 10, 2017: Bulletin of Mathematical Biology
Frank M Hilker, Marta Paliga, Ezio Venturino
Social predators benefit from cooperation in the form of increased hunting success, but may be at higher risk of disease infection due to living in groups. Here, we use mathematical modeling to investigate the impact of disease transmission on the population dynamics benefits provided by group hunting. We consider a predator-prey model with foraging facilitation that can induce strong Allee effects in the predators. We extend this model by an infectious disease spreading horizontally and vertically in the predator population...
August 9, 2017: Bulletin of Mathematical Biology
Angus McLure, Archie C A Clements, Martyn Kirk, Kathryn Glass
Clostridium difficile infections (CDIs) are some of the most common hospital-associated infections worldwide. Approximately 5% of the general population is colonised with the pathogen, but most are protected from disease by normal intestinal flora or immune responses to toxins. We developed a stochastic compartmental model of CDI in hospitals that captures the condition of the host's gut flora and the role of adaptive immune responses. A novel, derivative-based method for sensitivity analysis of individual-level outcomes was developed and applied to the model...
August 3, 2017: Bulletin of Mathematical Biology
K Minors, J H P Dawes
Motivated by the propagation of thin bacterial films around planar obstacles, this paper considers the dynamics of travelling wave solutions to the Fisher-KPP equation [Formula: see text] in a planar strip [Formula: see text], [Formula: see text]. We examine the propagation of fronts in the presence of a mixed boundary condition (also referred to as a 'partially absorbing' or 'reactive' boundary) [Formula: see text], with [Formula: see text], at [Formula: see text]. The presence of boundary conditions of this kind leads to the development of front solutions that propagate in x but contain transverse structure in y...
August 1, 2017: Bulletin of Mathematical Biology
Ryan M Evans, David A Edwards
Optical biosensors are often used to measure kinetic rate constants associated with chemical reactions. Such instruments operate in the surface-volume configuration, in which ligand molecules are convected through a fluid-filled volume over a surface to which receptors are confined. Currently, scientists are using optical biosensors to measure the kinetic rate constants associated with DNA translesion synthesis-a process critical to DNA damage repair. Biosensor experiments to study this process involve multiple interacting components on the sensor surface...
August 1, 2017: Bulletin of Mathematical Biology
P Gambette, K T Huber, G E Scholz
The need for structures capable of accommodating complex evolutionary signals such as those found in, for example, wheat has fueled research into phylogenetic networks. Such structures generalize the standard model of a phylogenetic tree by also allowing for cycles and have been introduced in rooted and unrooted form. In contrast to phylogenetic trees or their unrooted versions, rooted phylogenetic networks are notoriously difficult to understand. To help alleviate this, recent work on them has also centered on their "uprooted" versions...
July 31, 2017: Bulletin of Mathematical Biology
Angela M Jarrett, N G Cogan, M Y Hussaini
We apply two different sensitivity techniques to a model of bacterial colonization of the anterior nares to better understand the dynamics of Staphylococcus aureus nasal carriage. Specifically, we use partial rank correlation coefficients to investigate sensitivity as a function of time and identify a reduced model with fewer than half of the parameters of the full model. The reduced model is used for the calculation of Sobol' indices to identify interacting parameters by their additional effects indices. Additionally, we found that the model captures an interesting characteristic of the biological phenomenon related to the initial population size of the infection; only two parameters had any significant additional effects, and these parameters have biological evidence suggesting they are connected but not yet completely understood...
July 27, 2017: Bulletin of Mathematical Biology
Chayu Yang, Xueying Wang, Daozhou Gao, Jin Wang
We propose two differential equation-based models to investigate the impact of awareness programs on cholera dynamics. The first model represents the disease transmission rates as decreasing functions of the number of awareness programs, whereas the second model divides the susceptible individuals into two distinct classes depending on their awareness/unawareness of the risk of infection. We study the essential dynamical properties of each model, using both analytical and numerical approaches. We find that the two models, though closely related, exhibit significantly different dynamical behaviors...
July 26, 2017: Bulletin of Mathematical Biology
Maria Gaivão, Francisco Dionisio, Erida Gjini
Humans are often colonized by polymorphic bacteria such as Streptococcus pneumoniae, Bordetella pertussis, Staphylococcus Aureus, and Haemophilus influenzae. Two co-colonizing pathogen clones may interact with each other upon host entry and during within-host dynamics, ranging from competition to facilitation. Here we examine the significance of these exploitation strategies for bacterial spread and persistence in host populations. We model SIS epidemiological dynamics to capture the global behavior of such multi-strain systems, focusing on different parameters of single and dual colonization...
July 24, 2017: Bulletin of Mathematical Biology
Junehyuk Lee, Frederick R Adler, Peter S Kim
Respiratory viral infections are common in the general population and one of the most important causes of asthma aggravation and exacerbation. Despite many studies, it is not well understood how viral infections cause more severe symptoms and exacerbations in asthmatics. We develop a mathematical model of two types of macrophages that play complementary roles in fighting viral infection: classically [Formula: see text]-[Formula: see text] and alternatively activated macrophages [Formula: see text]-[Formula: see text]...
July 24, 2017: Bulletin of Mathematical Biology
P Magal, A Noussair, J Pasquier, P Zongo, F Le Foll
In this paper, we consider a direct protein transfer process between cells in co-culture. Assuming that cells continually encounter each other, and from some hypotheses on cell-to-cell rules of transfer, we derive discrete and continuous Boltzmann-like integro-differential equations. The novelty of this model is to take into account multiple transfer rules. This new transfer model is used to fit the experimental data of cell-to-cell protein transfer in breast cancer.
July 18, 2017: Bulletin of Mathematical Biology
Xiaojing Wang, Yangyang Shi, Zhilan Feng, Jingan Cui
Many mathematical models for the disease transmission dynamics of Ebola have been developed and studied, particularly during and after the 2014 outbreak in West Africa. Most of these models are systems of ordinary differential equations (ODEs). One of the common assumptions made in these ODE models is that the duration of disease stages, such as latent and infectious periods, follows an exponential distribution. Gamma distributions have also been used in some of these models. It has been demonstrated that, when the models are used to evaluate disease control strategies such as quarantine or isolation, the models with exponential and Gamma distribution assumptions may generate contradictory results (Feng et al...
July 18, 2017: Bulletin of Mathematical Biology
Ingemar Nåsell
Moment closure methods are widely used to analyze mathematical models. They are specifically geared toward derivation of approximations of moments of stochastic models, and of similar quantities in other models. The methods possess several weaknesses: Conditions for validity of the approximations are not known, magnitudes of approximation errors are not easily evaluated, spurious solutions can be generated that require large efforts to eliminate, and expressions for the approximations are in many cases too complex to be useful...
July 18, 2017: Bulletin of Mathematical Biology
Matthew H Chan, Kristen Hawkes, Peter S Kim
We present a mathematical simplification for the evolutionary dynamics of a heritable trait within a two-sex population. This trait is assumed to control the timing of sex-specific life-history events, such as the age of sexual maturity and end of female fertility, and each sex has a distinct fitness trade-off associated with the trait. We provide a formula for the fitness landscape of the population and show a natural extension of the result to an arbitrary number of heritable traits. Our method can be viewed as a dynamical systems generalisation of the Price equation to include two sexes, age structure and multiple traits...
July 13, 2017: Bulletin of Mathematical Biology
Cole Zmurchok, Tim Small, Michael J Ward, Leah Edelstein-Keshet
Molecular motors such as kinesin and dynein are responsible for transporting material along microtubule networks in cells. In many contexts, motor dynamics can be modelled by a system of reaction-advection-diffusion partial differential equations (PDEs). Recently, quasi-steady-state (QSS) methods have been applied to models with linear reactions to approximate the behaviour of the full PDE system. Here, we extend this QSS reduction methodology to certain nonlinear reaction models. The QSS method relies on the assumption that the nonlinear binding and unbinding interactions of the cellular motors occur on a faster timescale than the spatial diffusion and advection processes...
July 13, 2017: Bulletin of Mathematical Biology
Milliward Maliyoni, Faraimunashe Chirove, Holly D Gaff, Keshlan S Govinder
We formulate and analyse a stochastic epidemic model for the transmission dynamics of a tick-borne disease in a single population using a continuous-time Markov chain approach. The stochastic model is based on an existing deterministic metapopulation tick-borne disease model. We compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in tick-borne disease dynamics. The probability of disease extinction and that of a major outbreak are computed and approximated using the multitype Galton-Watson branching process and numerical simulations, respectively...
July 13, 2017: Bulletin of Mathematical Biology
Julia Pulwicki, David Hobill
A new model for macroscopic root growth based on a dynamical Riemannian geometry is presented. Assuming that the thickness of the root is much less than its length, the model is restricted to growth in one dimension (1D). We treat 1D tissues as continuous, deformable, growing geometries for sizes larger than 1 mm. The dynamics of the growing root are described by a set of coupled tensor equations for the metric of the tissue and velocity field of material transport in non-Euclidean space. These coupled equations represent a novel feedback mechanism between growth and geometry...
July 7, 2017: Bulletin of Mathematical Biology
Huaming Yan, Anna Konstorum, John S Lowengrub
We develop a three-dimensional multispecies mathematical model to simulate the growth of colon cancer organoids containing stem, progenitor and terminally differentiated cells, as a model of early (prevascular) tumor growth. Stem cells (SCs) secrete short-range self-renewal promoters (e.g., Wnt) and their long-range inhibitors (e.g., Dkk) and proliferate slowly. Committed progenitor (CP) cells proliferate more rapidly and differentiate to produce post-mitotic terminally differentiated cells that release differentiation promoters, forming negative feedback loops on SC and CP self-renewal...
July 5, 2017: Bulletin of Mathematical Biology
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