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Mathematical Biosciences and Engineering: MBE

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https://www.readbyqxmd.com/read/28608710/a-surface-model-of-nonlinear-non-steady-state-phloem-transport
#1
Youcef Mammeri, Damien Sellier
Phloem transport is the process by which carbohydrates produced by photosynthesis in the leaves get distributed in a plant. According to Münch, the osmotically generated hydrostatic phloem pressure is the force driving the long-distance transport of photoassimilates. Following Thompson and Holbrook[35]'s approach, we develop a mathematical model of coupled water-carbohydrate transport. It is first proven that the model presented here preserves the positivity. The model is then applied to simulate the flow of phloem sap for an organic tree shape, on a 3D surface and in a channel with orthotropic hydraulic properties...
August 1, 2017: Mathematical Biosciences and Engineering: MBE
https://www.readbyqxmd.com/read/28608709/the-spatial-dynamics-of-a-zebrafish-model-with-cross-diffusions
#2
Hongyong Zhao, Qianjin Zhang, Linhe Zhu
This paper investigates the spatial dynamics of a zebrafish model with cross-diffusions. Sufficient conditions for Hopf bifurcation and Turing bifurcation are obtained by analyzing the associated characteristic equation. In addition, we deduce amplitude equations based on multiple-scale analysis, and further by analyzing amplitude equations five categories of Turing patterns are gained. Finally, numerical simulation results are presented to validate the theoretical analysis. Furthermore, some examples demonstrate that cross-diffusions have an effect on the selection of patterns, which explains the diversity of zebrafish pattern very well...
August 1, 2017: Mathematical Biosciences and Engineering: MBE
https://www.readbyqxmd.com/read/28608708/global-stability-of-infectious-disease-models-with-contact-rate-as-a-function-of-prevalence-index
#3
Cruz Vargas-De-Leon, Alberto d'Onofrio
In this paper, we consider a SEIR epidemiological model with information--related changes in contact patterns. One of the main features of the model is that it includes an information variable, a negative feedback on the behavior of susceptible subjects, and a function that describes the role played by the infectious size in the information dynamics. Here we focus in the case of delayed information. By using suitable assumptions, we analyze the global stability of the endemic equilibrium point and disease--free equilibrium point...
August 1, 2017: Mathematical Biosciences and Engineering: MBE
https://www.readbyqxmd.com/read/28608707/modeling-environmental-transmission-of-map-infection-in-dairy-cows
#4
Kokum R De Silva, Shigetoshi Eda, Suzanne Lenhart
Johne's disease is caused by Mycobacterium avium subspecies paratuberculosis(MAP). It is a chronic, progressive, and inflammatory disease which has a long incubation period. One main problem with the disease is the reduction of milk production in infected dairy cows. In our study we develop a system of ordinary differential equations to describe the dynamics of MAP infection in a dairy farm. This model includes the progression of the disease and the age structure of the cows. To investigate the effect of persistence of this bacteria on the farm on transmission in our model, we include environmental compartments, representing the pathogen input in an explicit way...
August 1, 2017: Mathematical Biosciences and Engineering: MBE
https://www.readbyqxmd.com/read/28608706/stability-analysis-on-an-economic-epidemiological-model-with-vaccination-pages-and
#5
Wisdom S Avusuglo, Kenzu Abdella, Wenying Feng
In this paper, an economic epidemiological model with vaccination is studied. The stability of the endemic steady-state is analyzed and some bifurcation properties of the system are investigated. It is established that the system exhibits saddle-point and period-doubling bifurcations when adult susceptible individuals are vaccinated. Furthermore, it is shown that susceptible individuals also have the tendency of opting for more number of contacts even if the vaccine is inefficacious and thus causes the disease endemic to increase in the long run...
August 1, 2017: Mathematical Biosciences and Engineering: MBE
https://www.readbyqxmd.com/read/28608705/a-tridiagonal-patch-model-of-bacteria-inhabiting-a-nanofabricated-landscape
#6
Robert Stephen Cantrell, Brian Coomes, Yifan Sha
In this paper we employ a discrete-diffusion modeling framework to examine a system inspired by the nano-ecology experiments on the bacterium Escherichia coli reported upon in Keymer et al. (2006). In these experiments, the bacteria inhabit a linear array of 85 ``microhabitat patches (MHP's)", linked by comparatively thinner corridors through which bacteria may pass between adjacent MHP's. Each MHP is connected to its own source of nutrient substrate, which flows into the MHP at a rate that can be controlled in the experiment...
August 1, 2017: Mathematical Biosciences and Engineering: MBE
https://www.readbyqxmd.com/read/28608704/a-numerical-framework-for-computing-steady-states-of-structured-population-models-and-their-stability
#7
Inom Mirzaev, David M Bortz
Structured population models are a class of general evolution equations which are widely used in the study of biological systems. Many theoretical methods are available for establishing existence and stability of steady states of general evolution equations. However, except for very special cases, finding an analytical form of stationary solutions for evolution equations is a challenging task. In the present paper, we develop a numerical framework for computing approximations to stationary solutions of general evolution equations, which can also be used to produce approximate existence and stability regions for steady states...
August 1, 2017: Mathematical Biosciences and Engineering: MBE
https://www.readbyqxmd.com/read/28608703/a-numerical-framework-for-computing-steady-states-of-structured-population-models-and-their-stability
#8
Inom Mirzaev, David M Bortz
Structured population models are a class of general evolution equations which are widely used in the study of biological systems. Many theoretical methods are available for establishing existence and stability of steady states of general evolution equations. However, except for very special cases, finding an analytical form of stationary solutions for evolution equations is a challenging task. In the present paper, we develop a numerical framework for computing approximations to stationary solutions of general evolution equations, which can also be used to produce approximate existence and stability regions for steady states...
August 1, 2017: Mathematical Biosciences and Engineering: MBE
https://www.readbyqxmd.com/read/28608702/a-proton-therapy-model-using-discrete-difference-equations-with-an-example-of-treating-hepatocellular-carcinoma
#9
Erin N Bodine, K Lars Monia
Proton therapy is a type of radiation therapy used to treat cancer. It provides more localized particle exposure than other types of radiotherapy (e.g., x-ray and electron) thus reducing damage to tissue surrounding a tumor and reducing unwanted side effects. We have developed a novel discrete difference equation model of the spatial and temporal dynamics of cancer and healthy cells before, during, and after the application of a proton therapy treatment course. Specifically, the model simulates the growth and diffusion of the cancer and healthy cells in and surrounding a tumor over one spatial dimension (tissue depth) and the treatment of the tumor with discrete bursts of proton radiation...
August 1, 2017: Mathematical Biosciences and Engineering: MBE
https://www.readbyqxmd.com/read/28608701/a-two-patch-prey-predator-model-with-predator-dispersal-driven-by-the-predation-strength
#10
Yun Kang, Sourav Kumar Sasmal, Komi Messan
Foraging movements of predator play an important role in population dynamics of prey-predator systems, which have been considered as mechanisms that contribute to spatial self-organization of prey and predator. In nature, there are many examples of prey-predator interactions where prey is immobile while predator disperses between patches non-randomly through different factors such as stimuli following the encounter of a prey. In this work, we formulate a Rosenzweig-MacArthur prey-predator two patch model with mobility only in predator and the assumption that predators move towards patches with more concentrated prey-predator interactions...
August 1, 2017: Mathematical Biosciences and Engineering: MBE
https://www.readbyqxmd.com/read/28608700/a-chaotic-bursting-spiking-transition-in-a-pancreatic-beta-cells-system-observation-of-an-interior-glucose-induced-crisis
#11
Jorge Duarte, Cristina Januario, Nuno Martins
Nonlinear systems are commonly able to display abrupt qualitative changes (or transitions) in the dynamics. A particular type of these transitions occurs when the size of a chaotic attractor suddenly changes. In this article, we present such a transition through the observation of a chaotic interior crisis in the Deng bursting-spiking model for the glucose-induced electrical activity of pancreatic β-cells. To this chaos-chaos transition corresponds precisely the change between the bursting and spiking dynamics, which are central and key dynamical regimes that the Deng model is able to perform...
August 1, 2017: Mathematical Biosciences and Engineering: MBE
https://www.readbyqxmd.com/read/28092964/a-note-on-the-global-properties-of-an-age-structured-viral-dynamic-model-with-multiple-target-cell-populations
#12
Shaoli Wang, Jianhong Wu, Libin Rong
Some viruses can infect different classes of cells. The age of infection can affect the dynamics of infected cells and viral production. Here we develop a viral dynamic model with the age of infection and multiple target cell populations. Using the methods of semigroup and Lyapunov function, we study the global asymptotic property of the steady states of the model. The results show that when the basic reproductive number falls below 1, the infection is predicted to die out. When the basic reproductive number exceeds 1, there exists a unique infected steady state which is globally asymptotically stable...
June 1, 2017: Mathematical Biosciences and Engineering: MBE
https://www.readbyqxmd.com/read/28092963/mathematical-modeling-of-continuous-and-intermittent-androgen-suppression-for-the-treatment-of-advanced-prostate-cancer
#13
Alacia M Voth, John G Alford, Edward W Swim
Prostate cancer is one of the most prevalent types of cancer among men. It is stimulated by the androgens, or male sexual hormones, which circulate in the blood and diffuse into the tissue where they stimulate the prostate tumor to grow. One of the most important treatments for advanced prostate cancer has become androgen deprivation therapy (ADT). In this paper we present three different models of ADT for prostate cancer: continuous androgen suppression (CAS), intermittent androgen suppression (IAS), and periodic androgen suppression...
June 1, 2017: Mathematical Biosciences and Engineering: MBE
https://www.readbyqxmd.com/read/28092962/effects-of-selection-and-mutation-on-epidemiology-of-x-linked-genetic-diseases
#14
Francesca Verrilli, Hamed Kebriaei, Luigi Glielmo, Martin Corless, Carmen Del Vecchio
The epidemiology of X-linked recessive diseases, a class of genetic disorders, is modeled with a discrete-time, structured, non linear mathematical system. The model accounts for both de novo mutations (i.e., affected sibling born to unaffected parents) and selection (i.e., distinct fitness rates depending on individual's health conditions). Assuming that the population is constant over generations and relying on Lyapunov theory we found the domain of attraction of model's equilibrium point and studied the convergence properties of the degenerate equilibrium where only affected individuals survive...
June 1, 2017: Mathematical Biosciences and Engineering: MBE
https://www.readbyqxmd.com/read/28092961/effect-of-the-epidemiological-heterogeneity-on-the-outbreak-outcomes
#15
Alina Macacu, Dominique J Bicout
Multi-host pathogens infect and are transmitted by different kinds of hosts and, therefore, the host heterogeneity may have a great impact on the outbreak outcome of the system. This paper deals with the following problem: consider the system of interacting and mixed populations of hosts epidemiologically different, what would be the outbreak outcome for each host population composing the system as a result of mixing in comparison to the situation with zero mixing? To address this issue we have characterized the epidemic response function for a single-host population and defined a heterogeneity index measuring how host systems are epidemiologically different in terms of generation time, basic reproduction number R0 and, therefore, epidemic response function...
June 1, 2017: Mathematical Biosciences and Engineering: MBE
https://www.readbyqxmd.com/read/28092960/mathematical-analysis-and-dynamic-active-subspaces-for-a-long-term-model-of-hiv
#16
Tyson Loudon, Stephen Pankavich
a long-term model of HIV infection dynamics [8] was developed to describe the entire time course of the disease. It consists of a large system of ODEs with many parameters, and is expensive to simulate. In the current paper, this model is analyzed by determining all infection-free steady states and studying the local stability properties of the unique biologically-relevant equilibrium. Active subspace methods are then used to perform a global sensitivity analysis and study the dependence of an infected individual's T-cell count on the parameter space...
June 1, 2017: Mathematical Biosciences and Engineering: MBE
https://www.readbyqxmd.com/read/28092959/mixed-vaccination-strategy-for-the-control-of-tuberculosis-a-case-study-in-china
#17
Siyu Liu, Yong Li, Yingjie Bi, Qingdao Huang
This study first presents a mathematical model of TB transmission considering BCG vaccination compartment to investigate the transmission dynamics nowadays. Based on data reported by the National Bureau of Statistics of China, the basic reproduction number is estimated approximately as R0=1.1892. To reach the new End TB goal raised by WHO in 2015, considering the health system in China, we design a mixed vaccination strategy. Theoretical analysis indicates that the infectious population asymptotically tends to zero with the new vaccination strategy which is the combination of constant vaccination and pulse vaccination...
June 1, 2017: Mathematical Biosciences and Engineering: MBE
https://www.readbyqxmd.com/read/28092958/moments-of-von-mises-and-fisher-distributions-and-applications
#18
Thomas Hillen, Kevin J Painter, Amanda C Swan, Albert D Murtha
The von Mises and Fisher distributions are spherical analogues to the Normal distribution on the unit circle and unit sphere, respectively. The computation of their moments, and in particular the second moment, usually involves solving tedious trigonometric integrals. Here we present a new method to compute the moments of spherical distributions, based on the divergence theorem. This method allows a clear derivation of the second moments and can be easily generalized to higher dimensions. In particular we note that, to our knowledge, the variance-covariance matrix of the three dimensional Fisher distribution has not previously been explicitly computed...
June 1, 2017: Mathematical Biosciences and Engineering: MBE
https://www.readbyqxmd.com/read/28092957/germinal-center-dynamics-during-acute-and-chronic-infection
#19
Samantha Erwin, Stanca M Ciupe
The ability of the immune system to clear pathogens is limited during chronic virus infections where potent long-lived plasma and memory B-cells are produced only after germinal center B-cells undergo many rounds of somatic hypermutations. In this paper, we investigate the mechanisms of germinal center B-cell formation by developing mathematical models for the dynamics of B-cell somatic hypermutations. We use the models to determine how B-cell selection and competition for T follicular helper cells and antigen influences the size and composition of germinal centers in acute and chronic infections...
June 1, 2017: Mathematical Biosciences and Engineering: MBE
https://www.readbyqxmd.com/read/28092956/mathematical-analysis-of-a-quorum-sensing-induced-biofilm-dispersal-model-and-numerical-simulation-of-hollowing-effects
#20
Blessing O Emerenini, Stefanie Sonner, Hermann J Eberl
We analyze a mathematical model of quorum sensing induced biofilm dispersal. It is formulated as a system of non-linear, density-dependent, diffusion-reaction equations. The governing equation for the sessile biomass comprises two non-linear diffusion effects, a degeneracy as in the porous medium equation and fast diffusion. This equation is coupled with three semi-linear diffusion-reaction equations for the concentrations of growth limiting nutrients, autoinducers, and dispersed cells. We prove the existence and uniqueness of bounded non-negative solutions of this system and study the behavior of the model in numerical simulations, where we focus on hollowing effects in established biofilms...
June 1, 2017: Mathematical Biosciences and Engineering: MBE
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