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Bulletin of Mathematical Biology

H T Banks, Kidist Bekele-Maxwell, R A Everett, Lyric Stephenson, Sijing Shao, Jon Morgenstern
We use dynamical systems modeling to help understand how selected intra-personal factors interact to form mechanisms of behavior change in problem drinkers. Our modeling effort illustrates the iterative process of modeling using an individual's clinical data. Due to the lack of previous work in modeling behavior change in individual patients, we build our preliminary model relying on our understandings of the psychological relationships among the variables. This model is refined and the psychological understanding is then enhanced through the iterative modeling process...
April 20, 2017: Bulletin of Mathematical Biology
Chiara Giverso, Alessandro Arduino, Luigi Preziosi
In order to move in a three-dimensional extracellular matrix, the nucleus of a cell must squeeze through the narrow spacing among the fibers and, by adhering to them, the cell needs to exert sufficiently strong traction forces. If the nucleus is too stiff, the spacing too narrow, or traction forces too weak, the cell is not able to penetrate the network. In this article, we formulate a mathematical model based on an energetic approach, for cells entering cylindrical channels composed of extracellular matrix fibers...
April 13, 2017: Bulletin of Mathematical Biology
Alexandra B Hogan, Mary R Myerscough
Tradescantia fluminensis is an invasive weed and a serious threat to native forests in eastern Australia and New Zealand. Current methods of eradication are often ineffective, so understanding the growth mechanisms of Tradescantia is important in formulating better control strategies. We present a partial differential equation (PDE) model for Tradescantia growth and spatial proliferation that accounts for Tradescantia's particular creeping and branching morphology, and the impact of self-shading on plant growth...
April 12, 2017: Bulletin of Mathematical Biology
Vardayani Ratti, Peter G Kevan, Hermann J Eberl
We incorporate a mathematical model of Varroa destructor and the Acute Bee Paralysis Virus with an existing model for a honeybee colony, in which the bee population is divided into hive bees and forager bees based on tasks performed in the colony. The model is a system of five ordinary differential equations with dependent variables: uninfected hive bees, uninfected forager bees, infected hive bees, virus-free mites and virus-carrying mites. The interplay between forager loss and disease infestation is studied...
April 11, 2017: Bulletin of Mathematical Biology
Xiunan Wang, Xiao-Qiang Zhao
Malaria is an infectious disease caused by Plasmodium parasites and is transmitted among humans by female Anopheles mosquitoes. Climate factors have significant impact on both mosquito life cycle and parasite development. To consider the temperature sensitivity of the extrinsic incubation period (EIP) of malaria parasites, we formulate a delay differential equations model with a periodic time delay. We derive the basic reproduction ratio [Formula: see text] and establish a threshold type result on the global dynamics in terms of [Formula: see text], that is, the unique disease-free periodic solution is globally asymptotically stable if [Formula: see text]; and the model system admits a unique positive periodic solution which is globally asymptotically stable if [Formula: see text]...
April 7, 2017: Bulletin of Mathematical Biology
Leo van Iersel, Vincent Moulton, Eveline de Swart, Taoyang Wu
Phylogenetic networks are a generalization of evolutionary trees that are used by biologists to represent the evolution of organisms which have undergone reticulate evolution. Essentially, a phylogenetic network is a directed acyclic graph having a unique root in which the leaves are labelled by a given set of species. Recently, some approaches have been developed to construct phylogenetic networks from collections of networks on 2- and 3-leaved networks, which are known as binets and trinets, respectively...
April 6, 2017: Bulletin of Mathematical Biology
Bashar Ibrahim
Proliferating cells properly divide into their daughter cells through a process that is mediated by kinetochores, protein-complexes that assemble at the centromere of each sister chromatid. Each kinetochore has to establish a tight bipolar attachment to the spindle apparatus before sister chromatid separation is initiated. The spindle assembly checkpoint (SAC) links the biophysical attachment status of the kinetochores to mitotic progression and ensures that even a single misaligned kinetochore keeps the checkpoint active...
April 6, 2017: Bulletin of Mathematical Biology
Anne Talkington, Claudia Dantoin, Rick Durrett
Modified T cells that have been engineered to recognize the CD19 surface marker have recently been shown to be very successful at treating acute lymphocytic leukemias. Here, we explore four previous approaches that have used ordinary differential equations to model this type of therapy, compare their properties, and modify the models to address their deficiencies. Although the four models treat the workings of the immune system in slightly different ways, they all predict that adoptive immunotherapy can be successful to move a patient from the large tumor fixed point to an equilibrium with little or no tumor...
April 5, 2017: Bulletin of Mathematical Biology
Avner Friedman, Wenrui Hao
Exosomes are nanovesicles shed by cells as a means of communication with other cells. Exosomes contain mRNAs, microRNAs (miRs) and functional proteins. In the present paper, we develop a mathematical model of tumor-immune interaction by means of exosomes shed by pancreatic cancer cells and dendritic cells. Cancer cells' exosomes contain miRs that promote their proliferation and that inhibit immune response by dendritic cells, and by CD4+ and CD8+ T cells. Dendritic cells release exosomes with proteins that induce apoptosis of cancer cells and that block regulatory T cells...
April 5, 2017: Bulletin of Mathematical Biology
Annwesha Dutta, Debashish Chowdhury
The sequence of amino acid monomers in the primary structure of a protein is decided by the corresponding sequence of codons (triplets of nucleic acid monomers) on the template messenger RNA (mRNA). The polymerization of a protein, by incorporation of the successive amino acid monomers, is carried out by a molecular machine called ribosome. We develop a stochastic kinetic model that captures the possibilities of mis-reading of mRNA codon and prior mis-charging of a tRNA. By a combination of analytical and numerical methods, we obtain the distribution of the times taken for incorporation of the successive amino acids in the growing protein in this mathematical model...
April 3, 2017: Bulletin of Mathematical Biology
Fabio Della Rossa, Fabio Dercole, Cristina Vicini
We show that when selection is extreme-the fittest strategy always reproduces or is imitated-the unequivalence between the possible evolutionary game scenarios in finite and infinite populations resolves, in the sense that the three generic outcomes-dominance, coexistence, and mutual exclusion-emerge in well-mixed populations of any size. We consider the simplest setting of a 2-player-2-strategy symmetric game and the two most common microscopic definitions of strategy spreading-the frequency-dependent Moran process and the imitation process by pairwise comparison-both in the case allowing any intensity of selection...
March 31, 2017: Bulletin of Mathematical Biology
Martin Golubitsky, Wenrui Hao, King-Yeung Lam, Yuan Lou
Geritz, Gyllenberg, Jacobs, and Parvinen show that two similar species can coexist only if their strategies are in a sector of parameter space near a nondegenerate evolutionarily singular strategy. We show that the dimorphism region can be more general by using the unfolding theory of Wang and Golubitsky near a degenerate evolutionarily singular strategy. Specifically, we use a PDE model of river species as an example of this approach. Our finding shows that the dimorphism region can exhibit various different forms that are strikingly different from previously known results in adaptive dynamics...
March 29, 2017: Bulletin of Mathematical Biology
Indrajit Ghosh, Tridip Sardar, Joydev Chattopadhyay
In this manuscript, we propose and analyze a compartmental model of visceral leishmaniasis (VL). We model the human population with six compartments including asymptomatic, symptomatic and PKDL-infected, animal population as second host and sandfly population as the vector. Furthermore, the non-adult stage of the sandfly population is introduced in the system, which was not considered before in the literature. We show that the increase in the number of host of sandfly population generates a backward bifurcation...
March 29, 2017: Bulletin of Mathematical Biology
Daniel A Korytowski, Hal Smith
We focus on the long-term dynamics of "killing the winner" Lotka-Volterra models of marine communities consisting of bacteria, virus, and zooplankton. Under suitable conditions, it is shown that there is a unique equilibrium with all populations present which is stable, the system is permanent, and the limiting behavior of its solutions is strongly constrained.
March 27, 2017: Bulletin of Mathematical Biology
Wang Jin, Esha T Shah, Catherine J Penington, Scott W McCue, Philip K Maini, Matthew J Simpson
Scratch assays are used to study how a population of cells re-colonises a vacant region on a two-dimensional substrate after a cell monolayer is scratched. These experiments are used in many applications including drug design for the treatment of cancer and chronic wounds. To provide insights into the mechanisms that drive scratch assays, solutions of continuum reaction-diffusion models have been calibrated to data from scratch assays. These models typically include a logistic source term to describe carrying capacity-limited proliferation; however, the choice of using a logistic source term is often made without examining whether it is valid...
March 23, 2017: 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
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