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Journal of Mathematical Biology

Jason McClelland, David Koslicki
Both the weighted and unweighted UniFrac distances have been very successfully employed to assess if two communities differ, but do not give any information about how two communities differ. We take advantage of recent observations that the UniFrac metric is equivalent to the so-called earth mover's distance (also known as the Kantorovich-Rubinstein metric) to develop an algorithm that not only computes the UniFrac distance in linear time and space, but also simultaneously finds which operational taxonomic units are responsible for the observed differences between samples...
April 25, 2018: Journal of Mathematical Biology
Steffen E Eikenberry, Abba B Gumel
Malaria, one of the greatest historical killers of mankind, continues to claim around half a million lives annually, with almost all deaths occurring in children under the age of five living in tropical Africa. The range of this disease is limited by climate to the warmer regions of the globe, and so anthropogenic global warming (and climate change more broadly) now threatens to alter the geographic area for potential malaria transmission, as both the Plasmodium malaria parasite and Anopheles mosquito vector have highly temperature-dependent lifecycles, while the aquatic immature Anopheles habitats are also strongly dependent upon rainfall and local hydrodynamics...
April 24, 2018: Journal of Mathematical Biology
Oluwole Olobatuyi, Gerda de Vries, Thomas Hillen
In experimental studies, it has been found that certain cell lines are more sensitive to low-dose radiation than would be expected from the classical Linear-Quadratic model (LQ model). In fact, it is frequently observed that cells incur more damage at low dose (say 0.3 Gy) than at higher dose (say 1 Gy). This effect has been termed hyper-radiosensitivity (HRS). The effect depends on the type of cells and on their phase in the cell cycle when radiation is applied. Experiments have shown that the G2-checkpoint plays an important role in the HRS effects...
April 20, 2018: Journal of Mathematical Biology
S Geritz, M Gyllenberg, J Toivonen
We present a model for the coevolution of seed size and germination time within a season when both affect the ability of the seedlings to compete for space. We show that even in the absence of a morphological or physiological constraint between the two traits, a correlation between seed size and germination time is nevertheless likely to evolve. This raises the more general question to what extent a correlation between any two traits should be considered as an a priori constraint or as an evolved means (or "instrument") to actually implement a beneficial combination of traits...
April 20, 2018: Journal of Mathematical Biology
Lida I Michalaki, Dimitris A Goussis
The multi-scale dynamics of a two-compartment with first order absorption Target-Mediated Drug Disposition (TMDD) pharmacokinetics model is analysed, using the Computational Singular Perturbation (CSP) algorithm. It is shown that the process evolves along two Slow Invariant Manifolds (SIMs), on which the most intense components of the model are equilibrated, so that the less intensive are the driving ones. The CSP tools allow for the identification of the components of the TMDD model that (i) constrain the evolution of the process on the SIMs, (ii) drive the system along the SIMs and (iii) generate the fast time scales...
April 19, 2018: Journal of Mathematical Biology
Ellen Baake, Fernando Cordero, Sebastian Hummel
We reconsider the deterministic haploid mutation-selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes ancestral (random) structures inherent in this deterministic model. In a first step, we obtain a representation of the deterministic equation's solution (and, in particular, of its equilibria) in terms of an ancestral process called the killed ancestral selection graph. This representation allows one to understand the bifurcations related to the error threshold phenomenon from a genealogical point of view...
April 19, 2018: Journal of Mathematical Biology
A D Barbour, R McVinish, P K Pollett
We consider the approximation of the equilibrium of a metapopulation model, in which a finite number of patches are randomly distributed over a bounded subset [Formula: see text] of Euclidean space. The approximation is good when a large number of patches contribute to the colonization pressure on any given unoccupied patch, and when the quality of the patches varies little over the length scale determined by the colonization radius. If this is the case, the equilibrium probability of a patch at z being occupied is shown to be close to [Formula: see text], the equilibrium occupation probability in Levins's model, at any point [Formula: see text] not too close to the boundary, if the local colonization pressure and extinction rates appropriate to z are assumed...
April 18, 2018: Journal of Mathematical Biology
Lukas Eigentler, Jonathan A Sherratt
Vegetation patterns are a characteristic feature of semi-arid regions. On hillsides these patterns occur as stripes running parallel to the contours. The Klausmeier model, a coupled reaction-advection-diffusion system, is a deliberately simple model describing the phenomenon. In this paper, we replace the diffusion term describing plant dispersal by a more realistic nonlocal convolution integral to account for the possibility of long-range dispersal of seeds. Our analysis focuses on the rainfall level at which there is a transition between uniform vegetation and pattern formation...
April 17, 2018: Journal of Mathematical Biology
Alan J Aw, Noah A Rosenberg
The homozygosity and the frequency of the most frequent allele at a polymorphic genetic locus have a close mathematical relationship, so that each quantity places a tight constraint on the other. We use the theory of majorization to provide a simplified derivation of the bounds on homozygosity J in terms of the frequency M of the most frequent allele. The method not only enables simpler derivations of known bounds on J in terms of M, it also produces analogous bounds on entropy statistics for genetic diversity and on homozygosity-like statistics that range in their emphasis on the most frequent allele in relation to other alleles...
March 22, 2018: Journal of Mathematical Biology
Lin Zhao, Zhi-Cheng Wang, Shigui Ruan
Host heterogeneity can be modeled by using multi-group structures in the population. In this paper we investigate the existence and nonexistence of traveling waves of a two-group SIR epidemic model with time delay and constant recruitment and show that the existence of traveling waves is determined by the basic reproduction number [Formula: see text] More specifically, we prove that (i) when the basic reproduction number [Formula: see text] there exists a minimal wave speed [Formula: see text] such that for each [Formula: see text] the system admits a nontrivial traveling wave solution with wave speed c and for [Formula: see text] there exists no nontrivial traveling wave satisfying the system; (ii) when [Formula: see text] the system admits no nontrivial traveling waves...
March 21, 2018: Journal of Mathematical Biology
Kara Pham, Emma Turian, Kai Liu, Shuwang Li, John Lowengrub
We consider the nonlinear dynamics of an avascular tumor at the tissue scale using a two-fluid flow Stokes model, where the viscosity of the tumor and host microenvironment may be different. The viscosities reflect the combined properties of cell and extracellular matrix mixtures. We perform a linear morphological stability analysis of the tumors, and we investigate the role of nonlinearity using boundary-integral simulations in two dimensions. The tumor is non-necrotic, although cell death may occur through apoptosis...
March 15, 2018: Journal of Mathematical Biology
Samara Pillay, Helen M Byrne, Philip K Maini
Angiogenesis is the process by which new blood vessels form from existing vessels. During angiogenesis, tip cells migrate via diffusion and chemotaxis, new tip cells are introduced through branching, loops form via tip-to-tip and tip-to-sprout anastomosis, and a vessel network forms as endothelial cells, known as stalk cells, follow the paths of tip cells (a process known as the snail-trail). Using a mean-field approximation, we systematically derive one-dimensional non-linear continuum models from a lattice-based cellular automaton model of angiogenesis in the corneal assay, explicitly accounting for cell volume...
March 6, 2018: Journal of Mathematical Biology
Simon Girel, Fabien Crauste
Unequal partitioning of the molecular content at cell division has been shown to be a source of heterogeneity in a cell population. We propose to model this phenomenon with the help of a scalar, nonlinear impulsive differential equation (IDE). To study the effect of molecular partitioning at cell division on the effector/memory cell-fate decision in a CD8 T-cell lineage, we study an IDE describing the concentration of the protein Tbet in a CD8 T-cell, where impulses are associated to cell division. We discuss how the degree of asymmetry of molecular partitioning can affect the process of cell differentiation and the phenotypical heterogeneity of a cell population...
March 2, 2018: Journal of Mathematical Biology
Qixuan Wang, Hans G Othmer
Recent research has shown that motile cells can adapt their mode of propulsion depending on the environment in which they find themselves. One mode is swimming by blebbing or other shape changes, and in this paper we analyze a class of models for movement of cells by blebbing and of nano-robots in a viscous fluid at low Reynolds number. At the level of individuals, the shape changes comprise volume exchanges between connected spheres that can control their separation, which are simple enough that significant analytical results can be obtained...
March 1, 2018: Journal of Mathematical Biology
J Mushanyu, F Nyabadza, G Muchatibaya, P Mafuta, G Nhawu
Typhoid fever is a systemic infection caused by Salmonella Typhi and occurs predominantly in association with poor sanitation and lack of clean drinking water. Despite recent progress in water and sanitation coverage, the disease remains a substantial public health problem in many developing countries. A mathematical model for the spread of typhoid has been formulated using non linear ordinary differential equations. The model includes a special treatment function to assess the effects of limited treatment resources on the spread of typhoid...
February 27, 2018: Journal of Mathematical Biology
Maria Kleshnina, Jerzy A Filar, Vladimir Ejov, Jody C McKerral
The adaptation process of a species to a new environment is a significant area of study in biology. As part of natural selection, adaptation is a mutation process which improves survival skills and reproductive functions of species. Here, we investigate this process by combining the idea of incompetence with evolutionary game theory. In the sense of evolution, incompetence and training can be interpreted as a special learning process. With focus on the social side of the problem, we analyze the influence of incompetence on behavior of species...
February 26, 2018: Journal of Mathematical Biology
Hao Wu, Marco Avila Ponce de León, Hans G Othmer
Recent research has shown that motile cells can adapt their mode of propulsion to the mechanical properties of the environment in which they find themselves-crawling in some environments while swimming in others. The latter can involve movement by blebbing or other cyclic shape changes, and both highly-simplified and more realistic models of these modes have been studied previously. Herein we study swimming that is driven by membrane tension gradients that arise from flows in the actin cortex underlying the membrane, and does not involve imposed cyclic shape changes...
February 26, 2018: Journal of Mathematical Biology
Magnus Bordewich, Katharina T Huber, Vincent Moulton, Charles Semple
Phylogenetic networks are a type of leaf-labelled, acyclic, directed graph used by biologists to represent the evolutionary history of species whose past includes reticulation events. A phylogenetic network is tree-child if each non-leaf vertex is the parent of a tree vertex or a leaf. Up to a certain equivalence, it has been recently shown that, under two different types of weightings, edge-weighted tree-child networks are determined by their collection of distances between each pair of taxa. However, the size of these collections can be exponential in the size of the taxa set...
February 24, 2018: Journal of Mathematical Biology
Cameron J Browne, Hal L Smith
The host immune response can often efficiently suppress a virus infection, which may lead to selection for immune-resistant viral variants within the host. For example, during HIV infection, an array of CTL immune response populations recognize specific epitopes (viral proteins) presented on the surface of infected cells to effectively mediate their killing. However HIV can rapidly evolve resistance to CTL attack at different epitopes, inducing a dynamic network of interacting viral and immune response variants...
February 23, 2018: Journal of Mathematical Biology
Damian Clancy
For a susceptible-infectious-susceptible infection model in a heterogeneous population, we present simple formulae giving the leading-order asymptotic (large population) behaviour of the mean persistence time, from an endemic state to extinction of infection. Our model may be interpreted as describing an infection spreading through either (1) a population with heterogeneity in individuals' susceptibility and/or infectiousness; or (2) a heterogeneous directed network. Using our asymptotic formulae, we show that such heterogeneity can only reduce (to leading order) the mean persistence time compared to a corresponding homogeneous population, and that the greater the degree of heterogeneity, the more quickly infection will die out...
February 23, 2018: Journal of Mathematical Biology
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