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Journal of Mathematical Biology

Mojtaba Tefagh, Stephen P Boyd
Flux coupling analysis (FCA) aims to describe the functional dependencies among reactions in a metabolic network. Currently studied coupling relations are qualitative in the sense that they identify pairs of reactions for which the activity of one reaction necessitates the activity of the other one, but without giving any numerical bounds relating the possible activity rates. The potential applications of FCA are heavily investigated, however apart from some trivial cases there is no clue of what bottleneck in the metabolic network causes each dependency...
December 10, 2018: Journal of Mathematical Biology
J V Morais, A L Custódio, G M Marques
Dynamic Energy Budget (DEB) theory aims to capture the quantitative aspects of metabolism at the individual level, for all species. The parametrization of a DEB model is based on information obtained through the observation of natural populations and experimental research. Currently the DEB toolbox estimates these parameters using the Nelder-Mead Simplex method, a derivative-free direct-search method. However, this procedure presents some limitations regarding convergence and how to address constraints. Framed in the calibration of parameters in DEB theory, this work presents a numerical comparison between the Nelder-Mead Simplex method and the SID-PSM algorithm, a Directional Direct-Search method for which convergence can be established both for unconstrained and constrained problems...
December 7, 2018: Journal of Mathematical Biology
Balázs Bárány, Gregory Moses, Todd Young
We show that when cell-cell feedback is added to a model of the cell cycle for a large population of cells, then instability of the steady state solution occurs in many cases. We show this in the context of a generic agent-based ODE model. If the feedback is positive, then instability of the steady state solution is proved for all parameter values except for a small set on the boundary of parameter space. For negative feedback we prove instability for half the parameter space. We also show by example that instability in the other half may be proved on a case by case basis...
December 6, 2018: Journal of Mathematical Biology
Getachew K Befekadu, Quanyan Zhu
In this paper, we consider the problem of controlling a diffusion process pertaining to an opioid epidemic dynamical model with random perturbation so as to prevent it from leaving a given bounded open domain. In particular, we assume that the random perturbation enters only through the dynamics of the susceptible group in the compartmental model of the opioid epidemic dynamics and, as a result of this, the corresponding diffusion is degenerate, for which we further assume that the associated diffusion operator is hypoelliptic, i...
December 4, 2018: Journal of Mathematical Biology
Rachel Jennings, Yang Kuang, Horst R Thieme, Jianhong Wu, Xiaotian Wu
Ixodid ticks are acknowledged as one of the most important hematophagous arthropods because of their ability in transmitting a variety of tick-borne diseases. Mathematical models have been developed, based on emerging knowledge about tick ecology, pathogen epidemiology and their interface, to understand tick population dynamics and tick-borne diseases spread patterns. However, no serious effort has been made to model and assess the impact of host immunity triggered by tick feeding on the distribution of the tick population according to tick stages and on tick population extinction and persistence...
November 26, 2018: Journal of Mathematical Biology
E Moraki, R Grima, K J Painter
Various biological studies suggest that the corneal epithelium is maintained by active stem cells located in the limbus, the so-called limbal epithelial stem cell hypothesis. While numerous mathematical models have been developed to describe corneal epithelium wound healing, only a few have explored the process of corneal epithelium homeostasis. In this paper we present a purposefully simple stochastic mathematical model based on a chemical master equation approach, with the aim of clarifying the main factors involved in the maintenance process...
November 26, 2018: Journal of Mathematical Biology
Beibei Li, Steven M Roper, Lei Wang, Xiaoyu Luo, N A Hill
We develop a mathematical model for a small axisymmetric tear in a residually stressed and axially pre-stretched cylindrical tube. The residual stress is modelled by an opening angle when the load-free tube is sliced along a generator. This has application to the study of an aortic dissection, in which a tear develops in the wall of the artery. The artery is idealised as a single-layer thick-walled axisymmetric hyperelastic tube with collagen fibres using a Holzapfel-Gasser-Ogden strain-energy function, and the tear is treated as an incremental deformation of this tube...
November 19, 2018: Journal of Mathematical Biology
Eva Stadler
Plasmids are autonomously replicating genetic elements in bacteria. At cell division, plasmids are distributed among the two daughter cells. This gene transfer from one generation to the next is called vertical gene transfer. We study the dynamics of a bacterial population carrying plasmids and are in particular interested in the long-time distribution of plasmids. Starting with a model for a bacterial population structured by the discrete number of plasmids, we proceed to the continuum limit in order to derive a continuous model...
November 19, 2018: Journal of Mathematical Biology
Benjamin Allen, Alex McAvoy
We define a general class of models representing natural selection between two alleles. The population size and spatial structure are arbitrary, but fixed. Genetics can be haploid, diploid, or otherwise; reproduction can be asexual or sexual. Biological events (e.g. births, deaths, mating, dispersal) depend in arbitrary fashion on the current population state. Our formalism is based on the idea of genetic sites. Each genetic site resides at a particular locus and houses a single allele. Each individual contains a number of sites equal to its ploidy (one for haploids, two for diploids, etc...
November 14, 2018: Journal of Mathematical Biology
Conrad J Burden, Robert C Griffiths
The stationary distribution of a sample taken from a Wright-Fisher diffusion with general small mutation rates is found using a coalescent approach. The approximation is equivalent to having at most one mutation in the coalescent tree to the first order in the rates. The sample probabilities characterize an approximation for the stationary distribution from the Wright-Fisher diffusion. The approach is different from Burden and Tang (Theor Popul Biol 112:22-32, 2016; Theor Popul Biol 113:23-33, 2017) who use a probability flux argument to obtain the same results from a forward diffusion generator equation...
November 13, 2018: Journal of Mathematical Biology
U A Rozikov, M V Velasco
Recently, continuous-time dynamical systems of mosquito populations have been studied. In this paper, we consider a discrete-time dynamical system, generated by an evolution quadratic operator of a mosquito population, and show that this system has two fixed points, which become saddle points under some conditions on the parameters of the system. We construct an evolution algebra, taking its matrix of structural constants equal to the Jacobian of the quadratic operator at a fixed point. Idempotent and absolute nilpotent elements, simplicity properties, and some limit points of the evolution operator corresponding to the evolution algebra are studied...
November 13, 2018: Journal of Mathematical Biology
Magalí Giaroli, Frédéric Bihan, Alicia Dickenstein
We consider cascades of enzymatic Goldbeter-Koshland loops (Goldbeter and Koshland in Proc Natl Acad Sci 78(11):6840-6844, 1981) with any number n of layers, for which there exist two layers involving the same phosphatase. Even if the number of variables and the number of conservation laws grow linearly with n, we find explicit regions in reaction rate constant and total conservation constant space for which the associated mass-action kinetics dynamical system is multistationary. Our computations are based on the theoretical results of our companion paper (Bihan, Dickenstein and Giaroli 2018, preprint: arXiv:1807...
November 10, 2018: Journal of Mathematical Biology
Robert Stephen Cantrell, Chris Cosner, Mark A Lewis, Yuan Lou
We study the evolutionary stability of dispersal strategies, including but not limited to those that can produce ideal free population distributions (that is, distributions where all individuals have equal fitness and there is no net movement of individuals at equilibrium). The environment is assumed to be variable in space but constant in time. We assume that there is a separation of times scales, so that dispersal occurs on a fast timescale, evolution occurs on a slow timescale, and population dynamics and interactions occur on an intermediate timescale...
November 3, 2018: Journal of Mathematical Biology
Bruno Buonomo, Piero Manfredi, Alberto d'Onofrio
In order to seek the optimal time-profiles of public health systems (PHS) Intervention to favor vaccine propensity, we apply optimal control (OC) to a SIR model with voluntary vaccination and PHS intervention. We focus on short-term horizons, and on both continuous control strategies resulting from the forward-backward sweep deterministic algorithm, and piecewise-constant strategies (which are closer to the PHS way of working) investigated by the simulated annealing (SA) stochastic algorithm. For childhood diseases, where disease costs are much larger than vaccination costs, the OC solution sets at its maximum for most of the policy horizon, meaning that the PHS cannot further improve perceptions about the net benefit of immunization...
November 2, 2018: Journal of Mathematical Biology
Evandro P de Souza, Eliza M Ferreira, Armando G M Neves
This paper is based on the complete classification of evolutionary scenarios for the Moran process with two strategies given by Taylor et al. (Bull Math Biol 66(6):1621-1644, 2004. ). Their classification is based on whether each strategy is a Nash equilibrium and whether the fixation probability for a single individual of each strategy is larger or smaller than its value for neutral evolution. We improve on this analysis by showing that each evolutionary scenario is characterized by a definite graph shape for the fixation probability function...
October 24, 2018: Journal of Mathematical Biology
Ivan Yegorov, Francis Mairet, Hidde de Jong, Jean-Luc Gouzé
Microorganisms have evolved complex strategies for controlling the distribution of available resources over cellular functions. Biotechnology aims at interfering with these strategies, so as to optimize the production of metabolites and other compounds of interest, by (re)engineering the underlying regulatory networks of the cell. The resulting reallocation of resources can be described by simple so-called self-replicator models and the maximization of the synthesis of a product of interest formulated as a dynamic optimal control problem...
October 17, 2018: Journal of Mathematical Biology
Térence Bayen, Pedro Gajardo
In this paper, we study the optimization problem of maximizing biogas production at steady state in a two-stage anaerobic digestion model, which was initially proposed in Bernard et al. (Biotechnol Bioeng 75(4):424-438, 2001). Nominal operating points, consisting of steady states where the involved microorganisms coexist, are usually referred to as desired operational conditions, in particular for maximizing biogas production. Nevertheless, we prove that under some conditions related to input substrate concentrations and microorganism biology, characterized by their growth functions, the optimal steady state can be the extinction of one of the two species...
October 17, 2018: Journal of Mathematical Biology
Paulo Amorim, Thierry Goudon, Fernando Peruani
We analyze an ant navigation model based on Weber's law, where the ants move across a pheromone landscape sensing the area using two antennae. The key parameter of the model is the angle [Formula: see text] representing the span of the ant's sensing area. We show that when [Formula: see text] ants are able to follow (straight) pheromone trails proving that for initial conditions close to the trail, there exists a Lyapunov function that ensures ant trajectories converge on and follow the pheromone trail, with these solutions being locally asymptotically stable...
October 9, 2018: Journal of Mathematical Biology
Catheryn W Gray, Adelle C F Coster
Akt/PKB is an important crosstalk node at the junction between a number of major signalling pathways in the mammalian cell. As a significant nutrient sensor, Akt plays a central role in many cellular processes, including cell growth, cell survival and glucose metabolism. The dysregulation of Akt signalling is implicated in the development of many diseases, from diabetes to cancer. The translocation of Akt from cytosol to plasma membrane is a crucial step in Akt activation. Akt is initially synthesized on the endoplasmic reticulum, but translocates to the plasma membrane (PM) in response to insulin stimulation, where it may be activated...
October 9, 2018: Journal of Mathematical Biology
Li Ge, Jiaguo Liu, Yusen Zhang, Matthias Dehmer
We generalize chaos game representation (CGR) to higher dimensional spaces while maintaining its bijection, keeping such method sufficiently representative and mathematically rigorous compare to previous attempts. We first state and prove the asymptotic property of CGR and our generalized chaos game representation (GCGR) method. The prediction follows that the dissimilarity of sequences which possess identical subsequences but distinct positions would be lowered exponentially by the length of the identical subsequence; this effect was taking place unbeknownst to researchers...
October 5, 2018: Journal of Mathematical Biology
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