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Journal of Mathematical Biology

Calvin Zhang, Timothy J Lewis
Many neuronal circuits driving coordinated locomotion are composed of chains of half-center oscillators (HCOs) of various lengths. The HCO is a common motif in central pattern generating circuits (CPGs); an HCO consists of two neurons, or two neuronal populations, connected by reciprocal inhibition. To maintain appropriate motor coordination for effective locomotion over a broad range of frequencies, chains of CPGs must produce approximately constant phase-differences in a robust manner. In this article, we study phase-locking in chains of nearest-neighbor coupled HCOs and examine how the circuit architecture can promote phase-constancy, i...
October 13, 2016: Journal of Mathematical Biology
Andrew Hart, Servet Martínez
We present a framework based on information theoretic concepts and the Dirichlet distribution for classifying chromosomes based on the degree to which they use synonymous codons uniformly or preferentially, that is, whether or not codons that code for an amino acid appear with the same relative frequency. At its core is a measure of codon usage bias we call the Kullback-Leibler codon information bias (KL-CIB or CIB for short). Being defined in terms of conditional entropy makes KL-CIB an ideal and natural quantity for expressing a chromosome's degree of departure from uniform synonymous codon usage...
October 12, 2016: Journal of Mathematical Biology
Josep Sardanyés, Regina Martínez, Carles Simó, Ricard Solé
The dynamics of heterogeneous tumor cell populations competing with healthy cells is an important topic in cancer research with deep implications in biomedicine. Multitude of theoretical and computational models have addressed this issue, especially focusing on the nature of the transitions governing tumor clearance as some relevant model parameters are tuned. In this contribution, we analyze a mathematical model of unstable tumor progression using the quasispecies framework. Our aim is to define a minimal model incorporating the dynamics of competition between healthy cells and a heterogeneous population of cancer cell phenotypes involving changes in replication-related genes (i...
October 6, 2016: Journal of Mathematical Biology
Nicolas Bajeux, Frédéric Grognard, Ludovic Mailleret
Intraspecific interactions such as Allee effects are key properties that can guide population management. This contribution considers component Allee effects that are elementary mechanisms leading to declines of fitness at the population scale, i.e. demographic Allee effects. It especially focuses on the consequences of such properties in predator populations, and investigates their repercussions in a biological control context. A modelling framework able to account for reproductive and/or foraging component Allee effects is proposed...
October 6, 2016: Journal of Mathematical Biology
Alexander Pimenov, Thomas C Kelly, Andrei Korobeinikov, Michael J O'Callaghan, Dmitrii Rachinskii
Memory allows organisms to forecast the future on the basis of experience, and thus, in some form, is important for the development of flexible adaptive behavior by animal communities. To model memory, we use the concept of hysteresis, which mathematically is described by the Preisach operator. As a case study, we consider anti-predator adaptation in the classic Lotka-Volterra predator-prey model. Despite its simplicity, the model allows us to naturally incorporate essential features of an adaptive system and memory...
October 4, 2016: Journal of Mathematical Biology
Giuseppe D'Onofrio, Enrica Pirozzi
We consider a stochastic differential equation in a strip, with coefficients suitably chosen to describe the acto-myosin interaction subject to time-varying forces. By simulating trajectories of the stochastic dynamics via an Euler discretization-based algorithm, we fit experimental data and determine the values of involved parameters. The steps of the myosin are represented by the exit events from the strip. Motivated by these results, we propose a specific stochastic model based on the corresponding time-inhomogeneous Gauss-Markov and diffusion process evolving between two absorbing boundaries...
September 26, 2016: Journal of Mathematical Biology
Pavol Bokes, Abhyudai Singh
Inside individual cells, expression of genes is stochastic across organisms ranging from bacterial to human cells. A ubiquitous feature of stochastic expression is burst-like synthesis of gene products, which drives considerable intercellular variability in protein levels across an isogenic cell population. One common mechanism by which cells control such stochasticity is negative feedback regulation, where a protein inhibits its own synthesis. For a single gene that is expressed in bursts, negative feedback can affect the burst frequency or the burst size...
September 24, 2016: Journal of Mathematical Biology
V Yatat, P Couteron, J J Tewa, S Bowong, Y Dumont
Fires and mean annual rainfall are major factors that regulate woody and grassy biomasses in savanna ecosystems. Within the savanna biome, conditions of long-lasting coexistence of trees and grasses have been often studied using continuous-time modelling of tree-grass competition. In these studies, fire is a time-continuous forcing while the relationship between woody plant size and fire-sensitivity is not systematically considered. In this paper, we propose a new mathematical framework to model tree-grass interactions that takes into account both the impulsive nature of fire occurrence and size-dependent fire sensitivity (via two classes of woody plants)...
September 22, 2016: Journal of Mathematical Biology
Li-Ming Cai, Xue-Zhi Li, Bin Fang, Shigui Ruan
Since there exist extrinsic and intrinsic incubation periods of pathogens in the feedback interactions between the vectors and hosts, it is necessary to consider the incubation delays in vector-host disease transmission dynamics. In this paper, we propose vector-host disease models with two time delays, one describing the incubation period in the vector population and another representing the incubation period in the host population. Both distributed and discrete delays are used. By constructing suitable Liapunov functions, we obtain sufficient conditions for the global stability of the endemic equilibria of these models...
September 22, 2016: Journal of Mathematical Biology
Ahmed Abdelrazec, Abba B Gumel
A new stage-structured model for the population dynamics of the mosquito (a major vector for numerous vector-borne diseases), which takes the form of a deterministic system of non-autonomous nonlinear differential equations, is designed and used to study the effect of variability in temperature and rainfall on mosquito abundance in a community. Two functional forms of eggs oviposition rate, namely the Verhulst-Pearl logistic and Maynard-Smith-Slatkin functions, are used. Rigorous analysis of the autonomous version of the model shows that, for any of the oviposition functions considered, the trivial equilibrium of the model is locally- and globally-asymptotically stable if a certain vectorial threshold quantity is less than unity...
September 19, 2016: Journal of Mathematical Biology
Eric Foxall, Nicolas Lanchier
We consider a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in each patch at a rate proportional to the number of pairs of individuals in the patch (sexual reproduction) rather than simply the number of individuals as in the basic contact process. Offspring produced at a given patch either stay in their parents' patch or are sent to a nearby patch with some fixed probabilities...
September 19, 2016: Journal of Mathematical Biology
Mengfeng Sun, Haifeng Zhang, Huiyan Kang, Guanghu Zhu, Xinchu Fu
We introduce three modified SIS models on scale-free networks that take into account variable population size, nonlinear infectivity, adaptive weights, behavior inertia and time delay, so as to better characterize the actual spread of epidemics. We develop new mathematical methods and techniques to study the dynamics of the models, including the basic reproduction number, and the global asymptotic stability of the disease-free and endemic equilibria. We show the disease-free equilibrium cannot undergo a Hopf bifurcation...
September 17, 2016: Journal of Mathematical Biology
Jifa Jiang, Lei Niu
We study the asymptotic behavior of the competitive Leslie/Gower model (map) [Formula: see text]It is shown that T unconditionally admits a globally attracting 1-codimensional invariant hypersurface [Formula: see text], called carrying simplex, such that every nontrivial orbit is asymptotic to one in [Formula: see text]. More general and easily checked conditions to guarantee the existence of carrying simplex for competitive maps are provided. An equivalence relation is defined relative to local stability of fixed points on [Formula: see text] (the boundary of [Formula: see text]) on the space of all three-dimensional Leslie/Gower models...
September 17, 2016: Journal of Mathematical Biology
Lee DeVille, Meghan Galiardi
We consider the Moran process with two populations competing under an iterated Prisoner's Dilemma in the presence of mutation, and concentrate on the case where there are multiple evolutionarily stable strategies. We perform a complete bifurcation analysis of the deterministic system which arises in the infinite population size. We also study the Master equation and obtain asymptotics for the invariant distribution and metastable switching times for the stochastic process in the case of large but finite population...
September 15, 2016: Journal of Mathematical Biology
Michael C Mackey, Marta Tyran-Kamińska, Hans-Otto Walther
Here we analytically examine the response of a limit cycle solution to a simple differential delay equation to a single pulse perturbation of the piecewise linear nonlinearity. We construct the unperturbed limit cycle analytically, and are able to completely characterize the perturbed response to a pulse of positive amplitude and duration with onset at different points in the limit cycle. We determine the perturbed minima and maxima and period of the limit cycle and show how the pulse modifies these from the unperturbed case...
September 9, 2016: Journal of Mathematical Biology
Marta Casanellas, Mike Steel
The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the 'equal input model'...
September 7, 2016: Journal of Mathematical Biology
Tsvetomir Tsachev, Vladimir M Veliov, Andreas Widder
The paper presents an approach for set-membership estimation of the state of a heterogeneous population in which an infectious disease is spreading. The population state may consist of susceptible, infected, recovered, etc. groups, where the individuals are heterogeneous with respect to traits, relevant to the particular disease. Set-membership estimations in this context are reasonable, since only vague information about the distribution of the population along the space of heterogeneity is available in practice...
September 7, 2016: Journal of Mathematical Biology
Abdon Iniguez, Jun Allard
Microtubule (MT) "age" can be interpreted as nucleotide state, lattice defects, or post-translational modification (PTM) such as acetylation and detyrosination. In all three cases, these have been recently shown to have functionally-important effects on the dynamics of MT arrays, and can present spatial and temporal heterogeneity. While mathematical models for MT array densities are well-established, here we present equations describing MT age, defined as the mean time since the MT's building blocks (tubulin) were polymerized from their soluble dimer state...
September 3, 2016: Journal of Mathematical Biology
Diego Avesani, Michael Dumbser, Gabriele Chiogna, Alberto Bellin
Chemotaxis, the microorganisms autonomous motility along or against the concentration gradients of a chemical species, is an important, yet often neglected factor controlling the transport of bacteria through saturated porous media. For example, chemotactic bacteria could enhance bioremediation by directing their own motion to residual contaminants trapped in low hydraulic conductive zones of contaminated aquifers. The aim of the present work is to develop an accurate numerical scheme to model chemotaxis in saturated porous media and other advective dominating flow systems...
August 27, 2016: Journal of Mathematical Biology
Sensen Liu, ShiNung Ching
Burst suppression, a pattern of the electroencephalogram characterized by quasi-periodic alternation of high-voltage activity (burst) and isoelectric silence (suppression), is typically associated with states of unconsciousness, such as in deep general anesthesia and certain etiologies of coma. Recent computational models for burst suppression have attributed the slow (up to tens of seconds) time-scale of burst termination and re-initiation to cycling in supportive physiological process, such as cerebral metabolism...
August 22, 2016: Journal of Mathematical Biology
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