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Mathematical Biosciences

Komi Afassinou, Faraimunashe Chirove, Keshlan S Govinder
We introduce a model for HIV/AIDS which can be utilized to assess the impact of combining pre-exposure prophylaxis (PrEP) and antiretroviral drugs (ARVs) use interventions (incorporating drug resistance). Mathematical and numerical analyses are carried out to investigate the effects of the combined controls in the presence of PrEP drug resistance. Our results predict a significant decrease in the number of new HIV infections when PrEP and ARVs are concurrently implemented at high levels. The results also reveal that PrEP drug resistance has the potential to slow down or reverse the effects of PrEP, especially at low efficacy levels...
January 14, 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
Ozgur Aydogmus, Wen Zhou, Yun Kang
Nonlocal interactions such as spatial interaction are ubiquitous in nature and may alter the equilibrium in evolutionary dynamics. Models including nonlocal spatial interactions can provide a further understanding on the preservation and emergence of cooperation in evolutionary dynamics. In this paper, we consider a variety of two-strategy evolutionary spatial games with nonlocal interactions based on an integro-differential replicator equation. By defining the invasion speed and minimal traveling wave speed for the derived model, we study the effects of the payoffs, the selection pressure and the spatial parameter on the preservation of cooperation...
December 13, 2016: Mathematical Biosciences
Michael J Chappell, Jennifer Dickson, Nicole Radde, J Geoffrey Chase
No abstract text is available yet for this article.
December 12, 2016: Mathematical Biosciences
Marek Bodnar, Natalia Okińczyc, M Vela-Pérez
Several models have been proposed to describe the behavior of ants when moving from nest to food sources. Most of these studies where based on numerical simulations with no mathematical justification. In this paper, we propose a mechanism for the formation of paths of minimal length between two points by a collection of individuals undergoing reinforced random walks taking into account not only the lengths of the paths but also the angles (connected to the preference of ants to move along straight lines). Our model involves reinforcement (pheromone accumulation), persistence (tendency to preferably follow straight directions in absence of any external effect) and takes into account the bifurcation angles of each edge (represented by a probability of willingness of choosing the path with the smallest angle)...
December 12, 2016: Mathematical Biosciences
M Leguèbe, M G Notarangelo, M Twarogowska, R Natalini, C Poignard
We propose a mathematical model for the transport of DNA plasmids from the extracellular matrix up to the cell nucleus. The model couples two phenomena: the electroporation process, describing the cell membrane permeabilization to plasmids and the intracellular transport enhanced by the presence of microtubules. Numerical simulations of cells with arbitrary geometry, in 2D and 3D, and a network of microtubules show numerically the importance of the microtubules and the electroporation on the effectiveness of the DNA transfection, as observed by previous biological data...
November 30, 2016: Mathematical Biosciences
N Chatzistefani, M J Chappell, C Hutchinson, S Kletzenbauer, N D Evans
The purpose of this study is to acquire mechanistic knowledge of the gastrocnemius muscle-Achilles tendon complex behaviour during specific movements in humans through mathematical modelling. Analysis of this muscle-tendon complex was performed to see if already existing muscle-tendon models of other parts of the body could be applied to the leg muscles, especially the gastrocnemius muscle-Achilles tendon complex, and whether they could adequately characterise its behaviour. Five healthy volunteers were asked to take part in experiments where dorsiflexion and plantar flexion of the foot were studied...
November 8, 2016: Mathematical Biosciences
Logan Ward, Mical Paul, Steen Andreassen
The aim of this paper is to apply machine learning as a method to refine a manually constructed CPN for the assessment of the severity of the systemic inflammatory response syndrome (SIRS).The goal of tuning the CPN is to create a scoring system that uses only objective data, compares favourably with other severity-scoring systems and differentiates between sepsis and non-infectious SIRS. The resulting model, the Learned-Age (LA) -Sepsis CPN has good discriminatory ability for the prediction of 30-day mortality with an area under the ROC curve of 0...
November 8, 2016: Mathematical Biosciences
Elisabeth O Bangsgaard, Johnny T Ottesen
A novel model of the hypothalamic-pituitary-adrenal axis is presented. The axis is an endocrine system responsible for coping with stress and it is likely to be involved in depression. The dynamics of the system is studied and existence, uniqueness and positivity of the solution and the existence of an attracting trapping region are proved. The model is calibrated and compared to data for healthy and depressed subjects. A sensitivity analysis resulting in a set of identifiable physiological parameters is provided...
November 2, 2016: Mathematical Biosciences
Subekshya Bidari, Xinying Chen, Daniel Peters, Dylanger Pittman, Péter L Simon
Final epidemic size relations play a central role in mathematical epidemiology. These can be written in the form of an implicit equation which is not analytically solvable in most of the cases. While final size relations were derived for several complex models, including multiple infective stages and models in which the durations of stages are arbitrarily distributed, the solvability of those implicit equations have been less studied. In this paper the SIR homogeneous mean-field and pairwise models and the heterogeneous mean-field model are studied...
October 29, 2016: Mathematical Biosciences
Juliette Hell, Alan D Rendall
The MAP kinase cascade is a network of enzymatic reactions arranged in layers. In each layer occurs a multiple futile cycle of phosphorylations. The fully phosphorylated substrate then serves as an enzyme for the layer below. This paper focusses on the existence of parameters for which Hopf bifurcations occur and generate periodic orbits. Furthermore it is explained how geometric singular perturbation theory allows to generalize results from simple models to more complex ones.
October 29, 2016: Mathematical Biosciences
Valeria Mamouridis, Nadja Klein, Thomas Kneib, Carmen Cadarso Suarez, Francesc Maynou
We analysed the landings per unit effort (LPUE) from the Barcelona trawl fleet targeting the red shrimp (Aristeus antennatus) using novel Bayesian structured additive distributional regression to gain a better understanding of the dynamics and determinants of variation in LPUE. The data set, covering a time span of 17 years, includes fleet-dependent variables (e.g. the number of trips performed by vessels), temporal variables (inter- and intra-annual variability) and environmental variables (the North Atlantic Oscillation index)...
January 2017: Mathematical Biosciences
Dharmendra Tripathi, Ashu Yadav, O Anwar Bég
Analytical solutions are developed for the electro-kinetic flow of a viscoelastic biological liquid in a finite length cylindrical capillary geometry under peristaltic waves. The Jefferys' non-Newtonian constitutive model is employed to characterize rheological properties of the fluid. The unsteady conservation equations for mass and momentum with electro-kinetic and Darcian porous medium drag force terms are reduced to a system of steady linearized conservation equations in an axisymmetric coordinate system...
January 2017: Mathematical Biosciences
Sanhong Liu, Shigui Ruan, Xinan Zhang
Avian influenza is a zoonotic disease caused by the transmission of the avian influenza A virus, such as H5N1 and H7N9, from birds to humans. The avian influenza A H5N1 virus has caused more than 500 human infections worldwide with nearly a 60% death rate since it was first reported in Hong Kong in 1997. The four outbreaks of the avian influenza A H7N9 in China from March 2013 to June 2016 have resulted in 580 human cases including 202 deaths with a death rate of nearly 35%. In this paper, we construct two avian influenza bird-to-human transmission models with different growth laws of the avian population, one with logistic growth and the other with Allee effect, and analyze their dynamical behavior...
January 2017: Mathematical Biosciences
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