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Mathematical Biosciences

Qihua Huang, Gunog Seo, Chunhua Shan
The study of effects of environmental toxins on ecosystems is of great interest from both environmental and conservation points of view. In this paper, we present a global stability and bifurcation analysis of a toxin-dependent aquatic population model. Our analytical and numerical results show that both the environmental toxin level and the depuration capability of the population significantly affect the population persistence. The model exhibits a multifarious array of dynamics. While low levels of external toxin allow population persistence and high levels of toxin lead to an extirpation, intermediate toxin concentrations can produce very rich dynamics, such as transient oscillations, hysteresis, heteroclinic orbits, and a codimension-two bifurcation...
December 2, 2017: Mathematical Biosciences
Nurun N Nargis, Ralph C Aldredge, Robert D Guy
A major challenge in matrix-metalloproteinase (MMP) target validation and MMP-inhibitor-drug development for anti-cancer clinical trials is to better understand their complex roles (often competing with each other) in tumor progression. While there is extensive research on the growth-promoting effects of MMPs, the growth-inhibiting effects of MMPs has not been investigated thoroughly. So we develop a continuum model of tumor growth and invasion including chemotaxis and haptotaxis in order to examine the complex interaction between the tumor and its host microenvironment and to explore the inhibiting influence of the gradients of soluble fragments of extracellular matrix (ECM) density on tumor growth and morphology...
December 2, 2017: Mathematical Biosciences
Barbara Coluzzi, Alberto M Bersani, Enrico Bersani
We apply to Michaelis-Menten kinetics an alternative approach to the study of Singularly Perturbed Differential Equations, that is based on the Renormalization Group (SPDERG).1 To this aim, we first rebuild the perturbation expansion for Michaelis-Menten kinetics, beyond the standard Quasi-Steady-State Approximation (sQSSA), determining the 2nd order contributions to the inner solutions, that are presented here for the first time to our knowledge. Our main result is that the SPDERG 2nd order uniform approximations reproduce the numerical solutions of the original problem in a better way than the known results of the perturbation expansion, even in the critical matching region...
November 29, 2017: Mathematical Biosciences
Morten Andersen, Jeppe Kari, Kim Borch, Peter Westh
Kinetic studies of homogeneous enzyme reactions where both the substrate and enzyme are soluble have been well described by the Michaelis Menten (MM) equation for more than a century. However, many reactions are taking place at the interface of a solid substrate and enzyme in solution. Such heterogeneous reactions are abundant both in vivo and in industrial application of enzymes but it is not clear whether traditional enzyme kinetic theory developed for homogeneous catalysis can be applied. Since the molar concentration of surface accessible sites (attack-sites) often is unknown for a solid substrate it is difficult to assess whether the requirement of the MM equation is met...
November 29, 2017: Mathematical Biosciences
Guichen Lu, Zhengyi Lu
In this paper, SEIRS epidemiological model with disease caused death and varying total population size is discussed. Based on the geometric approach developed by Li and Muldowney, a new criterion to determine the global asymptotic stability for nonlinear system is proposed. By applying this new criterion, global asymptotic stability of the endemic equilibrium when it is unique is proved. The above global result shows that the basic reproduction number is a sharp threshold for SEIRS model which removes restrictions of rate of loss of immunity and rate of disease caused death in Li and Muldowney's result...
November 29, 2017: Mathematical Biosciences
Evans Otieno Omondi, Titus Okello Orwa, Farai Nyabadza
In this paper, we present a model for onchocerciasis that considers mass administration of ivermectin, contact prevention controls and vector elimination. The model equilibria are computed and stability analysis carried out in terms of the basic reproduction number R0. The model is found to exhibit a backward bifurcation so that for R0 less than unity is not sufficient to eradicate the disease from the population and the need is to lower R0 to below a certain threshold, R0c for effective disease control. The model is fitted to data on individuals with onchocerciasis in Ghana...
November 23, 2017: Mathematical Biosciences
Gabriel Cardona, Arnau Mir, Francesc Rosselló, Lucia Rotger
The cophenetic metrics dφ, p, for p ∈ {0} ∪ [1, ∞), are a recent addition to the kit of available distances for the comparison of phylogenetic trees. Based on a fifty years old idea of Sokal and Rohlf, these metrics compare phylogenetic trees on a same set of taxa by encoding them by means of their vectors of cophenetic values of pairs of taxa and depths of single taxa, and then computing the L(p) norm of the difference of the corresponding vectors. In this paper we compute the expected value of the square of dφ, 2 on the space of fully resolved rooted phylogenetic trees with n leaves, under the Yule and the uniform probability distributions...
November 16, 2017: Mathematical Biosciences
Tom Britton, Désiré Ouédraogo
An SEIRS epidemic with disease fatalities is introduced in a growing population (modelled as a super-critical linear birth and death process). The study of the initial phase of the epidemic is stochastic, while the analysis of the major outbreaks is deterministic. Depending on the values of the parameters, the following scenarios are possible. i) The disease dies out quickly, only infecting few; ii) the epidemic takes off, the number of infected individuals grows exponentially, but the fraction of infected individuals remains negligible; iii) the epidemic takes off, the number of infected grows initially quicker than the population, the disease fatalities diminish the growth rate of the population, but it remains super critical, and the fraction of infected go to an endemic equilibrium; iv) the epidemic takes off, the number of infected individuals grows initially quicker than the population, the diseases fatalities turn the exponential growth of the population to an exponential decay...
November 16, 2017: Mathematical Biosciences
Ranja Sarkar
SUMO (small ubiquitin-like modifier) proteins interact with a large number of target proteins via a key regulatory event called sumoylation that encompasses activation, conjugation and ligation of SUMO proteins through specific E1, E2, and E3-type enzymes respectively. Single-molecule atomic force microscopic (AFM) experiments performed to unravel bound SUMO1 along its NC termini direction reveal that E3-ligases (in the form of small peptides) increase mechanical stability (along the axis) of the flexible protein upon binding...
November 16, 2017: Mathematical Biosciences
B Ambrosio, M A Aziz-Alaoui, R Yafia
Geometrical Singular Perturbation Theory has been successful to investigate a broad range of biological problems with different time scales. The aim of this paper is to apply this theory to a predator-prey model of modified Leslie-Gower type for which we consider that prey reproduces mush faster than predator. This naturally leads to introduce a small parameter ϵ which gives rise to a slow-fast system. This system has a special folded singularity which has not been analyzed in the classical work [15]. We use the blow-up technique to visualize the behavior near this fold point P...
November 13, 2017: Mathematical Biosciences
Philip J G M Voets, Roderick P P W M Maas
Although several methods currently exist to determine that a person is hypovolemic, it often remains very challenging to accurately estimate the effective circulating volume or amount of intravascular volume depletion in a non-controlled setting. This depletion of intravascular volume can have many causes and is frequently accompanied by hypotonic hyponatremia as a result of hypovolemia-induced release of arginine vasopressin (AVP) from the posterior pituitary gland. Here, we derive a novel, comprehensible equation that provides a theoretical insight into the complex interrelationship between the degree of isotonic volume depletion and the resultant change in plasma sodium concentration...
November 10, 2017: Mathematical Biosciences
S Sahmani, M M Aghdam
As a supramolecular construction, lipid protein micro/nano-tubules can be utilized in a variety of sustained biological delivery system. The high slenderness ratio of lipid tubules makes their hierarchical assembly into a desired architecture difficult. Therefore, an accurate prediction of mechanical behavior of lipid tubular is essential. The objective of this study is to capture size dependency in the postbuckling and vibrational response of the postbuckled lipid micro/nano-tubules more comprehensively. To this purpose, the nonlocal strain gradient elasticity theory is incorporated to the third-order shear deformation beam theory to develop an unconventional beam model...
November 8, 2017: Mathematical Biosciences
Fan Bai, Jie Wu, Ren Sun
The receptor-ligand mediated endocytosis of nanoparticles by endothelium cells in a shear flow is investigated theoretically. A set of population balance equations is used to calculate the number of endocytosed nanoparticles of diameters about 100 nm for a given period of time. Hydrodynamic analysis reveals that whether a wash-out procedure is effective to remove incompletely endocytosed nanoparticles depends on the bond formation and rupture rates rather than the shear rate since the rupture rate of bonds linking nanoparticles and endothelium cells does not change with the shear rate appreciably...
November 7, 2017: Mathematical Biosciences
Zachary McCarthy, Ben Smith, Aamir Fazil, Jianhong Wu, Shawn D Ryan, Daniel Munther
Pathogen control during poultry processing critically depends on more enhanced insight into contamination dynamics. In this study we build an individual based model (IBM) of the chilling process. Quantifying the relationships between typical Canadian processing specifications, water chemistry dynamics and pathogen levels both in the chiller water and on individual carcasses, the IBM is shown to provide a useful tool for risk management as it can inform risk assessment models. We apply the IBM to Campylobacter spp...
November 3, 2017: Mathematical Biosciences
Guihong Fan, Rosalind Huff, Jennifer Muir, Zinayida Nektalova, Jane Kruchowsky, Jennifer L Kepler, Haiyan Wang, Pamela A Marshall, Francisco J Solis
Calcium homeostasis is a fundamental cellular process in yeast. The regulation of the cytosolic calcium concentration is required for volume preservation and to regulate many vital calcium dependent processes such as mating and response to stress. The homeostatic mechanism is often studied by applying calcium pulses: sharply changing the calcium concentration in the yeast environment and observing the cellular response. To address these experimental investigations, several mathematical models have been proposed to describe this response...
November 2, 2017: Mathematical Biosciences
Kristinn Gudnason, Sven Sigurdsson, Bergthora S Snorradottir, Mar Masson, Fjola Jonsdottir
Discontinuous boundary conditions arise naturally when describing various physical phenomena and numerically modelling such conditions can prove difficult. In the field of pharmaceutical sciences, two such cases are the partitioning of a compound between different materials and a flux rate membrane controlling mass transfer between materials which both result in a discontinuous jump in concentration across adjacent materials. In this study, we introduce a general one-dimensional finite element drug delivery framework, which along with diffusion, reversible binding and dissolution within material layers, incorporates the partitioning and mass transfer conditions between layers of material...
October 26, 2017: Mathematical Biosciences
David L I Janzén, Mats Jirstrand, Michael J Chappell, Neil D Evans
The concept of structural identifiability for state-space models is expanded to cover mixed-effects state-space models. Two methods applicable for the analytical study of the structural identifiability of mixed-effects models are presented. The two methods are based on previously established techniques for non-mixed-effects models; namely the Taylor series expansion and the input-output form approach. By generating an exhaustive summary, and by assuming an infinite number of subjects, functions of random variables can be derived which in turn determine the distribution of the system's observation function(s)...
October 26, 2017: Mathematical Biosciences
Ali Imanparast, Nasser Fatouraee, Farhad Sharif
BACKGROUND: Understanding the effects of cardiac diseases on the heart's functionality which is the purpose of many biomedical researches, directly affects the diagnostic and therapeutic methods. Myocardial infarction (MI) is a common complication of cardiac ischemia, however, the impact of MI on the left ventricle (LV) flow patterns has not been widely considered by computational fluid dynamics studies thus far. METHODS: In this study, we present an insightful numerical method that creates an artificial MI on an image-based fluid-structure interactional model of normal LV to investigate its influence on the flow in comparison with the normal case...
October 26, 2017: Mathematical Biosciences
Alexander Bratus, Igor Samokhin, Ivan Yegorov, Daniil Yurchenko
In this paper, we study a dynamic optimization problem for a general nonlinear mathematical model for therapy of a lethal form of cancer. The model describes how the populations of cancer and normal cells evolve under the influence of the concentrations of nutrients (oxygen, glucose, etc.) and the applied therapeutic agent (drug). Regulated intensity of the therapy is interpreted as a time-dependent control strategy. The therapy (control) goal is to maximize the viability time, i. e., the duration of staying in a so-called safety region (which specifies safe living conditions of a patient in terms of constraints on the amounts of cancer and normal cells), subject to limited resources of the therapeutic agent...
October 23, 2017: Mathematical Biosciences
T Bastogne, J-L Marchand, S Pinel, P Vallois
This paper deals with the dynamic modeling and simulation of cell damage heterogeneity and associated mutant cell phenotypes in the therapeutic responses of cancer cell populations submitted to a radiotherapy session during in vitro assays. Each cell is described by a finite number of phenotypic states with possible transitions between them. The population dynamics is then given by an age-dependent multi-type branching process. From this representation, we obtain formulas for the average size of the global survival population as well as the one of subpopulations associated with 10 mutation phenotypes...
October 18, 2017: Mathematical Biosciences
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