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Mathematical Biosciences

Jonas Bühler, Gregor Huber, Eric von Lieres
Compartmental models can be used for inverse modeling of long distance tracer transport experiments in plants. Such transport models describe axial convection and diffusion as well as exchange between compartments, and are defined by partial differential equations (PDEs). Since for inverse modelling, the forward simulation needs to be evaluated frequently, a fast PDE solver is required. Here, we compare several different finite volumes schemes up to fifth order for spatial discretization with respect to accuracy, computation time and numerical oscillations...
February 16, 2017: Mathematical Biosciences
M U Bogdańska, M Bodnar, J Belmonte-Beitia, M Murek, P Schucht, J Beck, V M Pérez-García
Low grade gliomas (LGGs) are infiltrative and incurable primary brain tumours with typically slow evolution. These tumours usually occur in young and otherwise healthy patients, bringing controversies in treatment planning since aggressive treatment may lead to undesirable side effects. Thus, for management decisions it would be valuable to obtain early estimates of LGG growth potential. Here we propose a simple mathematical model of LGG growth and its response to chemotherapy which allows the growth of LGGs to be described in real patients...
February 15, 2017: Mathematical Biosciences
Shun Kurokawa
One key potential explanation for the evolution of cooperation is conditional cooperation. This allows cooperation to evolve for cooperators who switch their behavior on the basis of information about the opponent's behavior or reputation. However, information about the opponent's behavior or reputation is sometimes unavailable, and previous studies have assumed that a player cooperates with some default probability when no information about the opponent's previous behavior or reputation is available. This default probability has been interpreted as the player's "optimism"...
February 14, 2017: Mathematical Biosciences
Radhouane Fekih-Salem, Claude Lobry, Tewfik Sari
This paper deals with a two-microbial species model in competition for a single-resource in the chemostat including general intra- and interspecific density-dependent growth rates with distinct removal rates for each species. In order to understand the effects of intra- and interspecific interference, this general model is first studied by determining the conditions of existence and local stability of steady states. With the same removal rate, the model can be reduced to a planar system and then the global stability results for each steady state are derived...
February 14, 2017: Mathematical Biosciences
Gabrielle K Van Scoy, Estee L George, Flora Opoku Asantewaa, Lucy Kerns, Marnie M Saunders, Alicia Prieto-Langarica
Bone remodeling is an elegantly orchestrated process by which osteocytes, osteoblasts and osteoclasts function as a syncytium to maintain or modify bone. On the microscopic level, bone consists of cells that create, destroy and monitor the bone matrix. These cells interact in a coordinated manner to maintain a tightly regulated homeostasis. It is this regulation that is responsible for the observed increase in bone gain in the dominant arm of a tennis player and the observed increase in bone loss associated with spaceflight and osteoporosis...
February 9, 2017: Mathematical Biosciences
Shigui Ruan
Human rabies was first recorded in ancient China in about 556 BC and is still one of the major public-health problems in China. From 1950 to 2015, 130,494 human rabies cases were reported in Mainland China with an average of 1,977 cases per year. It is estimated that 95% of these human rabies cases are due to dog bites. The purpose of this article is to provide a review about the models, results, and simulations that we have obtained recently on studying the transmission of rabies in China. We first construct a basic susceptible, exposed, infectious, and recovered (SEIR) type model for the spread of rabies virus among dogs and from dogs to humans and use the model to simulate the human rabies data in China from 1996 to 2010...
February 7, 2017: Mathematical Biosciences
Abir Alharbi, F Tchier
The computer-aided diagnosis has become one of the major research topics in medical diagnostics. In this research paper, we focus on designing an automated computer diagnosis by combining two major methodologies, namely the fuzzy base systems and the evolutionary genetic algorithms and applying them to the Saudi Arabian breast cancer diagnosis database, to be employed for assisting physicians in the early detection of breast cancers, and hence obtaining an early-computerized diagnosis complementary to that by physicians...
February 6, 2017: Mathematical Biosciences
Bapan Ghosh, Debprasad Pal, T K Kar, Jose C Valverde
This article addresses how depleted stock can be restored by creation of marine reserve and species mobility when alternative stable states persist in a marine ecosystem. To understand the role of a marine protected area, we develop a two-patch version of an originally single-patch model. In the two-patch model, we prove that some of the locally stable equilibria are not stable equilibria from an ecological viewpoint. Similarly, some unstable equilibria determined classically from the mathematical model are no longer equilibria...
February 3, 2017: Mathematical Biosciences
G O Agaba, Y N Kyrychko, K B Blyuss
This paper analyses an SIRS-type model for infectious diseases with account for behavioural changes associated with the simultaneous spread of awareness in the population. Two types of awareness are included into the model: private awareness associated with direct contacts between unaware and aware populations, and public information campaign. Stability analysis of different steady states in the model provides information about potential spread of disease in a population, and well as about how the disease dynamics is affected by the two types of awareness...
February 2, 2017: Mathematical Biosciences
Vincent Jacquemet
The extracellular domain of the heart is anisotropic, which affects volume conduction and therefore body surface potentials. This paper tests the hypothesis that when wall thickness is sufficiently small (such as in the atria), the effect of extracellular anisotropy can be estimated by modifying local dipole current sources. A formula based on the Gabor-Nelson equivalent dipole and on the reciprocity theorem is derived to compute a linear transformation of the dipole sources that approximates in an isotropic volume conductor the far-field of the actual sources in an anisotropic volume conductor...
January 31, 2017: Mathematical Biosciences
Hyun Mo Yang
The anthropophilic and peridomestic female mosquito Aedes aegypti bites humans to suck blood to maturate fertilized eggs, during which dengue virus can be spread between mosquito and human populations. Besides this route of transmission, there is a possibility of dengue virus being passed directly to offspring through transovarial (or vertical) transmission. The effects of both horizontal and transovarial transmission routes on the dengue virus transmission are assessed by mathematical modeling. From the model, the reproduction number is obtained and the contribution of transovarial transmission is evaluated for different levels of horizontal transmission...
January 25, 2017: Mathematical Biosciences
Marcin Majka, Giacomo Gadda, Angelo Taibi, Mirosław Gałązka, Piotr Zieliński
An anatomically detailed model consisting of a network of electric transmission lines is developed to simulate propagation of the pulse waves in humans. The simulations show that the real arterial tree geometry, together with the elastic and rheological parameters of particular segments, ensure an efficient protection of vital organs against pulse waves generated at peripheral locations. Because locomotive movements are the most obvious source of such disturbances, additional cyclic perturbations are applied to the model femoral arteries...
January 25, 2017: Mathematical Biosciences
Shaun M Davidson, Paul D Docherty, Rua Murray
Parameter identification is an important and widely used process across the field of biomedical engineering. However, it is susceptible to a number of potential difficulties, such as parameter trade-off, causing premature convergence at non-optimal parameter values. The proposed Dimensional Reduction Method (DRM) addresses this issue by iteratively reducing the dimension of hyperplanes where trade off occurs, and running subsequent identification processes within these hyperplanes. The DRM was validated using clinical data to optimize 4 parameters of the widely used Bergman Minimal Model of glucose and insulin kinetics, as well as in-silico data to optimize 5 parameters of the Pulmonary Recruitment (PR) Model...
January 18, 2017: Mathematical Biosciences
Richard Bertram, Eberhard O Voit
No abstract text is available yet for this article.
January 4, 2017: Mathematical Biosciences
Avan Al-Saffar, Eun-Jin Kim
Information theory provides a useful tool to understand the evolution of complex nonlinear systems and their sustainability. In particular, Fisher information has been evoked as a useful measure of sustainability and the variability of dynamical systems including self-organising systems. By utilising Fisher information, we investigate the sustainability of the logistic model for different perturbations in the positive and/or negative feedback. Specifically, we consider different oscillatory modulations in the parameters for positive and negative feedback and investigate their effect on the evolution of the system and Probability Density Functions (PDFs)...
January 2, 2017: Mathematical Biosciences
Seyedvahid Khodaei, Nasser Fatouraee, Malikeh Nabaei
Heart failure is one of the most important issues that has been investigated in recent research studies. Variations that occur in apparatus of mitral valve, such as chordae tendineaea rupture, can affect the valve function during ventricular contraction and lead to regurgitation from the left ventricle into the left atrium. One method for understanding mitral valve function in such conditions is computational analysis. In this paper, we develop a finite element model of mitral valve prolapse, considering the direct effect of left ventricular motion on blood flow interacting with the mitral valve...
December 28, 2016: Mathematical Biosciences
Eva Santermans, Kim Van Kerckhove, Amin Azmon, W John Edmunds, Philippe Beutels, Christel Faes, Niel Hens
Most infectious disease data is obtained from disease surveillance which is based on observations of symptomatic cases only. However, many infectious diseases are transmitted before the onset of symptoms or without developing symptoms at all throughout the entire disease course, referred to as asymptomatic transmission. Fraser and colleagues [1] showed that this type of transmission plays a key role in assessing the feasibility of intervention measures in controlling an epidemic outbreak. To account for asymptomatic transmission in epidemic models, methods often rely on assumptions that cannot be verified given the data at hand...
December 24, 2016: Mathematical Biosciences
Linglong Yuan
Kingman's model of selection and mutation studies the limit type value distribution in an asexual population of discrete generations and infinite size undergoing selection and mutation. This paper generalizes the model to analyze the long-term evolution of Escherichia. coli in Lenski experiment. Weak assumptions for fitness functions are proposed and the mutation mechanism is the same as in Kingman's model. General macroscopic epistasis are designable through fitness functions. Convergence to the unique limit type distribution is obtained...
December 23, 2016: Mathematical Biosciences
Lei Zhao, Huayong Zhang, Wang Tian, Ran Li, Xiang Xu
Species loss is becoming a major threat to ecosystems. An urgent task in ecology is to predict the consequence of species loss which requires an extending of our traditional study of the topology of network structure to the population dynamic analyses in complex food webs. Here, via numerical simulations of the model combining structural networks with nonlinear bioenergetic models of population dynamics, we analyzed the secondary effects of species removal on biomass distribution and population stability, as well as the factors influencing these effects...
December 23, 2016: Mathematical Biosciences
Michel Iskin da S Costa, Pedro V Esteves, Lucas Del Bianco Faria, Lucas Dos Anjos
In this paper, by means of mathematical dynamical models we investigate the impacts of predator culling on a prey population structured in two stage classes, juveniles and adults, assuming stage specific predation by two generalist predators with functional responses types 2 and 3 in all possible combinations. According to the chosen set of parameter values, these impacts can manifest through possible demographic Allee effects, sustained population oscillations, alternative stable states (e.g., predator-pit-like behavior) and Hydra effect, which are all discussed, in turn, in terms of species conservation, harvest yield and pest biological control...
December 21, 2016: Mathematical Biosciences
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