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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 17, 2017: Mathematical Biosciences
Paul J Harris
Chemotaxis is the process by which cells and clusters of cells follow chemical signals in order to combine and form larger clusters. The spreading of the chemical signal from any given cell can be modelled using the linear diffusion equation, and the standard equations of motion can be used to determine how a cell, or cluster of cells, moves in response to the chemical signal. The resulting differential equations for the cell locations are integrated through time using the fourth-order Runge-Kutta method. The effect which changing the initial concentration magnitude, diffusion constant and velocity damping parameter has on the shape of the final clusters of cells is investigated and discussed...
October 14, 2017: Mathematical Biosciences
Hyoeun Kim, Roktaek Lim, Young-Il Seo, Dongwoo Sheen
Fish growth models are widely used in fisheries as well in aquacultures and ecology. Water temperature is one of the most important factors determining the growth of fish. In the present study, we propose a growth model that includes the effect of water temperature on the growth in the von Bertalanffy growth model. Our model was applied to fit the growth data of bullhead (Cottus gobio), brown trout (Salmo trutta L.), juvenile salmon (Salmo salar), and Araucanian herring (Strangomera bentincki). The model reproduces the growth patterns of each species and fits a set of appropriate parameter values for each species...
October 12, 2017: Mathematical Biosciences
Anna Shcherbacheva, Heikki Haario, Gerry Killeen
The efficiency of spatial repellents and long-lasting insecticide-treated nets (LLINs) is a key research topic in malaria control. Insecticidal nets reduce the mosquito-human contact rate and simultaneously decrease mosquito populations. However, LLINs demonstrate dissimilar efficiency against different species of malaria mosquitoes. Various factors have been proposed as an explanation, including differences in insecticide-induced mortality, flight characteristics, or persistence of attack. Here we present a discrete agent-based approach that enables the efficiency of LLINs, baited traps and Insecticide Residual Sprays (IRS) to be examined...
October 11, 2017: Mathematical Biosciences
Matthias Chung, Justin Krueger, Mihai Pop
The compositions of in-host microbial communities (microbiota) play a significant role in host health, and a better understanding of the microbiota's role in a host's transition from health to disease or vice versa could lead to novel medical treatments. One of the first steps toward this understanding is modeling interaction dynamics of the microbiota, which can be exceedingly challenging given the complexity of the dynamics and difficulties in collecting sufficient data. Methods such as principal differential analysis, dynamic flux estimation, and others have been developed to overcome these challenges...
October 10, 2017: Mathematical Biosciences
Hossein Hassani, Emmanuel Sirimal Silva, Zara Ghodsi
Signal extraction and analysis is of great importance, not only in fields such as economics and meteorology, but also in genetics and even biomedicine. There exists a range of parametric and nonparametric techniques which can perform signal extractions. However, the aim of this paper is to define a new approach for optimising signal extraction from bicoid gene expression profile. Having studied both parametric and nonparametric signal extraction techniques, we identified the lack of specific criteria enabling users to select the optimal signal extraction parameters...
October 10, 2017: Mathematical Biosciences
Ping Xie
XPD (Xeroderma pigmentosum complementation group D) is a prototypical 5' - 3' translocating DNA helicase that exhibits frequent backward steps during DNA unwinding. Here, we propose a model of DNA unwinding by XPD. With the model we explain why XPD exhibits frequent backsteps while other helicases show rare backsteps. We explain quantitatively the single-molecule data on probability of -1-bp step and mean dwell time of one step versus ATP concentration for XPD at fixed large external force applied to the ends of the DNA hairpin to unzip the hairpin...
October 10, 2017: Mathematical Biosciences
Matthew D Johnston
Recent work of M.D. Johnston et al. has produced sufficient conditions on the structure of a chemical reaction network which guarantee that the corresponding discrete state space system exhibits an extinction event. The conditions consist of a series of systems of equalities and inequalities on the edges of a modified reaction network called a domination-expanded reaction network. In this paper, we present a computational implementation of these conditions written in Python and apply the program on examples drawn from the biochemical literature...
October 9, 2017: Mathematical Biosciences
Kevin J Anderson, Adelaide de Guillebon, Andrew Hughes, Weiwei Wang, Michael R King
Selectin-mediated adhesion of circulating tumor cells (CTCs) to the endothelium is a critical step in cancer metastasis, which is a major factor contributing to the mortality of cancer. The formation of tethers between tumor cells and endothelial selectins initiates cell rolling, which leads to firm adhesion, extravasation and the formation of secondary metastases. Tumor cells can travel through the bloodstream as single cells, or as aggregates known as circulating tumor microemboli (CTM). CTM have increased survivability and metastatic potential relative to CTCs, and the presence of CTM is associated with worse patient prognosis...
October 9, 2017: Mathematical Biosciences
Elena Fimmel, Christian J Michel, Lutz Strüngmann
The graph approach of circular codes recently developed (Fimmel et al.,2016) allows here a detailed study of diletter circular codes over finite alphabets. A new class of circular codes is identified, strong comma-free codes. New theorems are proved with the diletter circular codes of maximal length in relation to (i) a characterisation of their graphs as acyclic tournaments; (ii) their explicit description; and (iii) the non-existence of other maximal diletter circular codes. The maximal lengths of paths in the graphs of the comma-free and strong comma-free codes are determined...
October 9, 2017: Mathematical Biosciences
G O Agaba, Y N Kyrychko, K B Blyuss
This paper investigates the effects of vaccination on the dynamics of infectious disease, which is spreading in a population concurrently with awareness. The model considers contributions to the overall awareness from a global information campaign, direct contacts between unaware and aware individuals, and reported cases of infection. It is assumed that there is some time delay between individuals becoming aware and modifying their behaviour. Vaccination is administered to newborns, as well as to aware individuals, and it is further assumed that vaccine-induced immunity may wane with time...
September 28, 2017: Mathematical Biosciences
Hildegard Uecker, Sebastian Bonhoeffer
In order to manage bacterial infections in hospitals in the face of antibiotic resistance, the two treatment protocols "mixing" and "cycling" have received considerable attention both from modelers and clinicians. However, the terms are not used in exactly the same way by both groups. This comes because the standard modeling approach disregards the perspective of individual patients. In this article, we investigate a model that comes closer to clinical practice and compare the predictions to the standard model...
September 26, 2017: Mathematical Biosciences
Sandra B Maier, Xiao Huang, Eduardo Massad, Marcos Amaku, Marcelo N Burattini, David Greenhalgh
In this paper we study a mathematical model to analyse the optimal vaccination age against Dengue in Brazil. Data from Brazil are used to estimate the basic reproduction numbers for each of the four Dengue serotypes and then the optimal vaccination age is calculated using a method due to Hethcote [1]. The vaccine has different efficacies against each serotype. Vaccination that is too early is ineffective as individuals are protected by maternal antibodies but leaving vaccination until later may allow the disease to spread...
September 19, 2017: Mathematical Biosciences
Alireza Zehi Mofrad, Shohreh Mashayekhan, Dariush Bastani
This study proposes a mathematical model to evaluate the impact of oxygen carriers and scaffold geometry on oxygen distribution and cell growth in a 3D cardiac construct using computational fluid dynamics (CFD). Flow equations, oxygen balance equation and cell balance equation were solved using special initial and boundary conditions. The modeling results revealed that 55% increase in cardiac cell density occurred by using 6.4% perfluorocarbon oxygen carrier (PFC) compared to pure culture medium without PFC supplementation...
September 14, 2017: Mathematical Biosciences
A Farhat, D Jiang, D Cui, E T Keller, T L Jackson
Despite advanced efforts in early diagnosis, aggressive surgical treatment, and use of targeted chemotherapies, the prognosis for many cancers is still dismal. This emphasizes the necessity to develop new strategies for understanding tumor growth and metastasis. Here we use a systems approach that combines mathematical modeling and numerical simulation to develop a predictive computational model for prostate cancer and its subversion of the bone microenvironment. This model simulates metastatic prostate cancer evolution, progressing from normal bone and hormone levels to quantifiable diseased states...
September 14, 2017: Mathematical Biosciences
Siddhartha Kundu
Informative phylogenetic analysis is dependent on the presence of curated and annotated sequences. This may be complemented by the simultaneous availability of empirical data pertaining to their in vivo function. Confounding sequences, with their similarity to more than one functional cluster, can therefore, render any categorization ambiguous, subjective, and imprecise. Here, I analyze and discuss the development of a mathematical expression that can characterize a potential confounding protein sequence. Specifically, statistical descriptors of combinatorially arranged profile HMM scores are computed and evaluated...
September 13, 2017: Mathematical Biosciences
Lourdes Esteva, Cristobal Vargas, Cruz Vargas de León
Leishmaniasis is a parasite disease transmitted by the bites of sandflies. Cutaneous leishmaniasis is the most common form of the disease and it is endemic in the Americas. Around 70 animal species, including humans, have been found as natural reservoir hosts of leishmania parasites. Among the reservoirs, dogs are the most important ones due to their proximity to the human habitat. Infection by leishmaniasis does not invariably cause illness in the host, and it also can remain asymptomatic for a long period, specially in dogs...
August 31, 2017: Mathematical Biosciences
Attila Dénes, László Székely
Motivated by studies warning about a possible re-emergence of poliomyelitis in Europe, we analyse a compartmental model for the transmission of polio describing the possible effect of unvaccinated people arriving to a region with low vaccination coverage. We calculate the basic reproduction number, and determine the global dynamics of the system: we show that, depending on the parameters, one of the two equilibria is globally asymptotically stable. The main tools applied are Lyapunov functions and persistence theory...
August 30, 2017: Mathematical Biosciences
Dinesh Kumar, P Kumar, K N Rai
This paper deals with numerical modeling and simulation of heat transfer in skin tissues using non-linear dual-phase-lag (DPL) bioheat transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL bioheat transfer model in order to predict more accurate results. A numerical method of line which is based on finite difference and Runge-Kutta (4,5) schemes, is used to solve the present non-linear problem. Under specific case, the exact solution has been obtained and compared with the present numerical scheme, and we found that those are in good agreement...
August 30, 2017: Mathematical Biosciences
Irina Bashkirtseva, Lev Ryashko, Tatyana Ryazanova
Motivated by important ecological applications we study how noise can reduce a number of trophic levels in hierarchically related multidimensional population systems. A nonlinear model with three trophic levels under the influence of external stochastic forcing is considered as a basic conceptual example. We analyze a probabilistic mechanism of noise-induced extinction of separate populations in this "prey-predator-top predator" system. We propose a new general mathematical approach for the estimation of the proximity of equilibrium regimes of this stochastic model to hazardous borders where abrupt changes in dynamics of ecological systems can occur...
August 26, 2017: Mathematical Biosciences
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