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Mathematical Biosciences

Rabha W Ibrahim, Hemant K Nashine, Norshaliza Kamaruddin
A biological dynamic system carries engineering properties such as control systems and signal processing (or image processing) addicted to molecular biology at the level of bio-molecular communication networks. Dynamical system features and signal reply functions of cellular signaling pathways are some of the main topics in biological dynamic systems (for example the biological segmentation). In the present paper, we introduce new generalized hybrid time-space dynamical systems of growing bacteria. We impose the approximate analytic solution for the system...
July 17, 2017: Mathematical Biosciences
Milad Qomlaqi, Fariba Bahrami, Maryam Ajami, Jamshid Hajati
BACKGROUND: Chemotherapy is usually known as the main modality for cancer treatment. Nevertheless, most of chronic cancers could not be treated with chemotherapy alone. Immunotherapy is a new modality for cancer treatment that is effective for early stages of cancer and it has fewer side effects compared to chemotherapy, specifically for those types of cancer that are resistant to it. METHOD: This work presents an extended mathematical model to depict interactions between cancerous and adaptive immune system in mouse...
July 14, 2017: Mathematical Biosciences
G Moyano, D Marco, D Knopoff, G Torres, C Turner
In the mutualism established between legumes and soil bacteria known as rhizobia, bacteria from soil infect plants roots and reproduce inside root nodules where they fix atmospheric N2 for plant nutrition, receiving carbohydrates in exchange. Host-plant sanctions against non N2 fixing, cheating bacterial symbionts have been proposed to act in the legume-Rhizobium symbiosis, to preserve the mutualistic relationship. Sanctions include decreased rhizobial survival in nodules occupied by cheating rhizobia. Previously, a simple population model experimentally based showed that the coexistence of fixing and cheating rhizobia strains commonly found in field conditions is possible, and that the inclusion of sanctions leads to the extinction of cheating strains in soil...
July 12, 2017: Mathematical Biosciences
Yaghoub Tadi Beni, M Karimi Zeverdejani, Fahimeh Mehralian
Protein microtubules (MTs) are one of the important intercellular components and have a vital role in the stability and strength of the cells. Due to applied external loads, protein microtubules may be involved buckling phenomenon. Due to impact of protein microtubules in cell reactions, it is important to determine their critical buckling load. Considering nature of protein microtubules, various parameters are effective on microtubules buckling. The small size of microtubules and also lack of uniformity of MTs properties in different directions caused the necessity of accuracy in the analysis of these bio-structure...
July 11, 2017: Mathematical Biosciences
Andrew G Smith
Populations often exist, either by choice or by external pressure, in a fragmented way, referred to as a metapopulation. Typically, the dynamics accounted for within metapopulation models are assumed to be static. For example, patch occupancy models often assume that the colonisation and extinction rates do not change, while spatially structured models often assume that the rates of births, deaths and migrations do not depend on time. While some progress has been made when these dynamics are changing deterministically, less is known when the changes are stochastic...
July 11, 2017: Mathematical Biosciences
Michele Caputo, Cesare Cametti
In this note, we present a simple mathematical model of drug delivery through transdermal patches by introducing a memory formalism in the classical Fick diffusion equation based on the fractional derivative. This approach is developed in the case of a medicated adhesive patch placed on the skin to deliver a time released dose of medication through the skin towards the bloodstream.The main resistance to drug transport across the skin resides in the diffusion through its outermost layer (the stratum corneum)...
July 11, 2017: Mathematical Biosciences
T Sari, M J Wade
The complexity of the anaerobic digestion process has motivated the development of complex models, such as the widely used Anaerobic Digestion Model No. 1. However, this complexity makes it intractable to identify the stability profile coupled to the asymptotic behaviour of existing steady-states as a function of conventional chemostat operating parameters (substrate inflow concentration and dilution rate). In a previous study this model was simplified and reduced to its very backbone to describe a three-tiered chlorophenol mineralising food-web, with its stability analysed numerically using consensus values for the various biological parameters of the Monod growth functions...
July 11, 2017: Mathematical Biosciences
Mitchell Eithun, Anne Shiu
Phosphorylation, the enzyme-mediated addition of a phosphate group to a molecule, is a ubiquitous chemical mechanism in biology. Multisite phosphorylation, the addition of phosphate groups to multiple sites of a single molecule, may be distributive or processive. Distributive systems, which require an enzyme and substrate to bind several times in order to add multiple phosphate groups, can be bistable. Processive systems, in contrast, require only one binding to add all phosphate groups, and were recently shown to be globally stable...
June 29, 2017: Mathematical Biosciences
Daniel Figueiredo, Manuel A Martins, Madalena Chaves
Qualitative and quantitative modeling frameworks are widely used for analysis of biological regulatory networks, the former giving a preliminary overview of the system's global dynamics and the latter providing more detailed solutions. Another approach is to model biological regulatory networks as hybrid systems, i.e., systems which can display both continuous and discrete dynamic behaviors. Actually, the development of synthetic biology has shown that this is a suitable way to think about biological systems, which can often be constructed as networks with discrete controllers, and present hybrid behaviors...
June 10, 2017: Mathematical Biosciences
T Eakin
A quantitative measure has been developed for the assessment and skill ordering of target-cued motor control and coordination task performances. It is similar to the classical root mean square error (RMSE) measure but modified with task progress weighting that attenuates with target proximity to its destination and amplifies as data sampling occurrences accumulate prior to task completion. The measure has the same mathematical form whether the task design is of the tracing type or of the tracking type, and thus can be used in cross task type comparisons...
June 9, 2017: Mathematical Biosciences
Ignacio Bajo, Alfonso Ruiz-Herrera
We study a classical model for a population that reproduces and disperses in a landscape of heterogeneous patches. Under symmetrical dispersal, we provide a sufficient condition to ensure the existence of a globally attracting fixed point. This condition is used in order to prove that certain patches with complex dynamics can be stabilized by the combination with stable patches. Specifically, given a patch with complex dynamics, we estimate the necessary number of patches with simple dynamics so that the whole metapopulation has a globally attracting equilibrium...
June 9, 2017: Mathematical Biosciences
Fengying Wei, Lihong Chen
We formulate and investigate the psychological effect of single-species population models in a polluted environment in this paper. For the deterministic single-species population model, the conditions that guarantee the local extinction and persistence in the mean are derived firstly. We then show that, around the pollution-free equilibrium, the stochastic single-species population is weakly persistent in the mean, and is stochastically permanent under some conditions. As a consequence, some numerical simulations demonstrate the efficiency of the main results...
June 2, 2017: Mathematical Biosciences
O Bara, S M Djouadi, J D Day, S Lenhart
Therapeutic strategies to correct an excessive immune response to pathogenic infection is investigated as an optimal control problem. The control problem is formulated around a four dimensional mathematical model describing the inflammatory response to a pathogenic insult with two therapeutic control inputs which have either a direct pro- or anti-inflammatory effect in the given system. We use Pontryagin's maximum principle and discuss necessary optimality conditions. We consider both an L(1) type objective functional as well as an L(2) type objective...
May 31, 2017: Mathematical Biosciences
Z Asghar, N Ali, M Sajid
Bacteria which do not have organelles of motility, such as flagella, adopt gliding as a mode of locomotion. In gliding motility bacterium moves under its own power by secreting a layer of slime on the substrate. The exact mechanism by which a glider achieves motility is yet in controversy but there are evidences which support the wave-like undulation on the surface of the organism, as a possible mechanism of motility. Based on this observation, a model of undulating sheet over a layer of slime is examined as a possible model of the gliding motion of a bacterium...
May 24, 2017: Mathematical Biosciences
Marko Raseta, Jon Pitchford, James Cussens, John Doe
There is an urgent need to refine strategies for testing the safety of chemical compounds. This need arises both from the financial and ethical costs of animal tests, but also from the opportunities presented by new in-vitro and in-silico alternatives. Here we explore the mathematical theory underpinning the formulation of optimal testing strategies in toxicology. We show how the costs and imprecisions of the various tests, and the variability in exposures and responses of individuals, can be assembled rationally to form a Markov Decision Problem...
May 23, 2017: Mathematical Biosciences
Pio Gabrielle B Calderon, Mustafa Habib, Franz Kappel, Aurelio A de Los Reyes
The human cardiovascular system (CVS) and respiratory system (RS) work together in order to supply oxygen (O2) and other substrates needed for metabolism and to remove carbon dioxide (CO2). Global and local control mechanisms act on the CVS in order to adjust blood flow to the different parts of the body. This, in turn, affects the RS since the amount of O2 and CO2 transported, respectively to and away from the tissues depends on the cardiac output and blood flow in both the systemic and pulmonary circuits of the CVS...
May 19, 2017: Mathematical Biosciences
Xuebing Zhang, Hongyong Zhao
This paper deals with a delayed reaction-diffusion predator-prey model with non-continuous threshold harvesting. Sufficient conditions for the local stability of the regular equilibrium, the existence of Hopf bifurcation and Turing bifurcation are obtained by analyzing the associated characteristic equation. By utilizing upper-lower solution method and Lyapunov functions the globally asymptotically stability of a unique regular equilibrium and asymptotically stability of a unique pseudoequilibrium are studied respectively...
May 19, 2017: Mathematical Biosciences
Raluca Eftimie, Matthieu Perez, Pietro-Luciano Buono
The growth and invasion of cancer cells are very complex processes, which can be regulated by the cross-talk between various signalling pathways, or by single signalling pathways that can control multiple aspects of cell behaviour. TGF-β is one of the most investigated signalling pathways in oncology, since it can regulate multiple aspects of cell behaviour: cell proliferation and apoptosis, cell-cell adhesion and epithelial-to-mesenchimal transition via loss of cell adhesion. In this study, we use a mathematical modelling approach to investigate the complex roles of TGF-β signalling pathways on the inhibition and growth of tumours, as well as on the epithelial-to-mesenchimal transition involved in the metastasis of tumour cells...
May 13, 2017: Mathematical Biosciences
Abbas Rammal, Eric Perrin, Valeriu Vrabie, Rabih Assaf, Hassan Fenniri
Infrared spectroscopy provides useful information on the molecular compositions of biological systems related to molecular vibrations, overtones, and combinations of fundamental vibrations. Mid-infrared (MIR) spectroscopy is sensitive to organic and mineral components and has attracted growing interest in the development of biomarkers related to intrinsic characteristics of lignocellulose biomass. However, not all spectral information is valuable for biomarker construction or for applying analysis methods such as classification...
May 13, 2017: Mathematical Biosciences
Tom Britton, Ali Traoré
We consider a stochastic model describing the spread of a vector borne disease in a community where individuals (hosts and vectors) die and new individuals (hosts and vectors) are born. The time to extinction of the disease, TQ, starting in quasi-stationary (conditional on non extinction) is studied. Properties of the limiting distribution are used to obtain an approximate expression for E(TQ), the mean-parameter in the exponential distribution of the time to extinction, for a finite population. It is then investigated numerically and by means of simulations how E(TQ) and its approximations depend on the different model parameters...
May 13, 2017: Mathematical Biosciences
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