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Journal of Mathematical Biology

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https://www.readbyqxmd.com/read/29445854/constrained-minimization-problems-for-the-reproduction-number-in-meta-population-models
#1
Gayane Poghotanyan, Zhilan Feng, John W Glasser, Andrew N Hill
The basic reproduction number ([Formula: see text]) can be considerably higher in an SIR model with heterogeneous mixing compared to that from a corresponding model with homogeneous mixing. For example, in the case of measles, mumps and rubella in San Diego, CA, Glasser et al. (Lancet Infect Dis 16(5):599-605, 2016. https://doi.org/10.1016/S1473-3099(16)00004-9 ), reported an increase of 70% in [Formula: see text] when heterogeneity was accounted for. Meta-population models with simple heterogeneous mixing functions, e...
February 14, 2018: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/29429122/optimal-control-approach-for-establishing-wmelpop-wolbachia-infection-among-wild-aedes-aegypti-populations
#2
Doris E Campo-Duarte, Olga Vasilieva, Daiver Cardona-Salgado, Mikhail Svinin
Wolbachia-based biocontrol has recently emerged as a potential method for prevention and control of dengue and other vector-borne diseases. Major vector species, such as Aedes aegypti females, when deliberately infected with Wolbachia become less capable of getting viral infections and transmitting the virus to human hosts. In this paper, we propose an explicit sex-structured population model that describes an interaction of uninfected (wild) male and female mosquitoes and those deliberately infected with wMelPop strain of Wolbachia in the same locality...
February 10, 2018: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/29429121/on-a-nonlocal-system-for-vegetation-in-drylands
#3
Matthieu Alfaro, Hirofumi Izuhara, Masayasu Mimura
Several mathematical models are proposed to understand spatial patchy vegetation patterns arising in drylands. In this paper, we consider the system with nonlocal dispersal of plants (through a redistribution kernel for seeds) proposed by Pueyo et al. (Oikos 117:1522-1532, 2008) as a model for vegetation in water-limited ecosystems. It consists in two reaction diffusion equations for surface water and soil water, combined with an integro-differential equation for plants. For this system, under suitable assumptions, we prove well-posedness using the Schauder fixed point theorem...
February 10, 2018: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/29397422/periodic-matrix-models-for-seasonal-dynamics-of-structured-populations-with-application-to-a-seabird-population
#4
J M Cushing, Shandelle M Henson
For structured populations with an annual breeding season, life-stage interactions and behavioral tactics may occur on a faster time scale than that of population dynamics. Motivated by recent field studies of the effect of rising sea surface temperature (SST) on within-breeding-season behaviors in colonial seabirds, we formulate and analyze a general class of discrete-time matrix models designed to account for changes in behavioral tactics within the breeding season and their dynamic consequences at the population level across breeding seasons...
February 3, 2018: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/29392399/bayesian-inference-of-agent-based-models-a-tool-for-studying-kidney-branching-morphogenesis
#5
Ben Lambert, Adam L MacLean, Alexander G Fletcher, Alexander N Combes, Melissa H Little, Helen M Byrne
The adult mammalian kidney has a complex, highly-branched collecting duct epithelium that arises as a ureteric bud sidebranch from an epithelial tube known as the nephric duct. Subsequent branching of the ureteric bud to form the collecting duct tree is regulated by subcellular interactions between the epithelium and a population of mesenchymal cells that surround the tips of outgrowing branches. The mesenchymal cells produce glial cell-line derived neurotrophic factor (GDNF), that binds with RET receptors on the surface of the epithelial cells to stimulate several subcellular pathways in the epithelium...
February 1, 2018: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/29387919/extinction-times-in-the-subcritical-stochastic-sis-logistic-epidemic
#6
Graham Brightwell, Thomas House, Malwina Luczak
Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights into the near-critical regime by considering the stochastic SIS logistic epidemic, a well-known birth-and-death chain used to model the spread of an epidemic within a population of a given size N. We study the behaviour of the process as the population size N tends to infinity...
January 31, 2018: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/29368273/modeling-of-the-contrast-enhanced-perfusion-test-in-liver-based-on-the-multi-compartment-flow-in-porous-media
#7
Eduard Rohan, Vladimír Lukeš, Alena Jonášová
The paper deals with modeling the liver perfusion intended to improve quantitative analysis of the tissue scans provided by the contrast-enhanced computed tomography (CT). For this purpose, we developed a model of dynamic transport of the contrast fluid through the hierarchies of the perfusion trees. Conceptually, computed time-space distributions of the so-called tissue density can be compared with the measured data obtained from CT; such a modeling feedback can be used for model parameter identification. The blood flow is characterized at several scales for which different models are used...
January 24, 2018: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/29353313/general-solution-of-the-chemical-master-equation-and-modality-of-marginal-distributions-for-hierarchic-first-order-reaction-networks
#8
Matthias Reis, Justus A Kromer, Edda Klipp
Multimodality is a phenomenon which complicates the analysis of statistical data based exclusively on mean and variance. Here, we present criteria for multimodality in hierarchic first-order reaction networks, consisting of catalytic and splitting reactions. Those networks are characterized by independent and dependent subnetworks. First, we prove the general solvability of the Chemical Master Equation (CME) for this type of reaction network and thereby extend the class of solvable CME's. Our general solution is analytical in the sense that it allows for a detailed analysis of its statistical properties...
January 20, 2018: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/29340755/multiple-invasion-speeds-in-a-two-species-integro-difference-competition-model
#9
Bingtuan Li
We study an integro-difference competition model for the case that two species consecutively invade a habitat. We show that if a species spreads into a traveling wave of its rival, or if two species expand their spatial ranges in both directions, in a direction where open space is available, the species with larger invasion speed can always establish a wave moving into open space with its own speed. We demonstrate that when one species is stronger in competition, under appropriate conditions, the speeds at which the boundaries between two species move can be analytically determined...
January 16, 2018: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/29332298/the-ess-and-replicator-equation-in-matrix-games-under-time-constraints
#10
József Garay, Ross Cressman, Tamás F Móri, Tamás Varga
Recently, we introduced the class of matrix games under time constraints and characterized the concept of (monomorphic) evolutionarily stable strategy (ESS) in them. We are now interested in how the ESS is related to the existence and stability of equilibria for polymorphic populations. We point out that, although the ESS may no longer be a polymorphic equilibrium, there is a connection between them. Specifically, the polymorphic state at which the average strategy of the active individuals in the population is equal to the ESS is an equilibrium of the polymorphic model...
January 13, 2018: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/29332297/integrodifference-equations-in-the-presence-of-climate-change-persistence-criterion-travelling-waves-and-inside-dynamics
#11
Mark A Lewis, Nathan G Marculis, Zhongwei Shen
To understand the effects that the climate change has on the evolution of species as well as the genetic consequences, we analyze an integrodifference equation (IDE) models for a reproducing and dispersing population in a spatio-temporal heterogeneous environment described by a shifting climate envelope. Our analysis on the IDE focuses on the persistence criterion, travelling wave solutions, and the inside dynamics. First, the persistence criterion, characterizing the global dynamics of the IDE, is established in terms of the basic reproduction number...
January 13, 2018: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/29330615/the-parameter-identification-problem-for-sir-epidemic-models-identifying-unreported-cases
#12
Pierre Magal, Glenn Webb
A SIR epidemic model is analyzed with respect to identification of its parameters, based upon reported case data from public health sources. The objective of the analysis is to understand the relation of unreported cases to reported cases. In many epidemic diseases the ratio of unreported to reported cases is very high, and of major importance in implementing measures for controlling the epidemic. This ratio can be estimated by the identification of parameters for the model from reported case data. The analysis is applied to three examples: (1) the Hong Kong seasonal influenza epidemic in New York City in 1968-1969, (2) the bubonic plague epidemic in Bombay, India in 1906, and (3) the seasonal influenza epidemic in Puerto Rico in 2016-2017...
January 13, 2018: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/29307085/sensitivity-of-the-dynamics-of-the-general-rosenzweig-macarthur-model-to-the-mathematical-form-of-the-functional-response-a-bifurcation-theory-approach
#13
Gunog Seo, Gail S K Wolkowicz
The equations in the Rosenzweig-MacArthur predator-prey model have been shown to be sensitive to the mathematical form used to model the predator response function even if the forms used have the same basic shape: zero at zero, monotone increasing, concave down, and saturating. Here, we revisit this model to help explain this sensitivity in the case of three response functions of Holling type II form: Monod, Ivlev, and Hyperbolic tangent. We consider both the local and global dynamics and determine the possible bifurcations with respect to variation of the carrying capacity of the prey, a measure of the enrichment of the environment...
January 6, 2018: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/29305736/a-reaction-diffusion-within-host-hiv-model-with-cell-to-cell-transmission
#14
Xinzhi Ren, Yanni Tian, Lili Liu, Xianning Liu
In this paper, a reaction-diffusion within-host HIV model is proposed. It incorporates cell mobility, spatial heterogeneity and cell-to-cell transmission, which depends on the diffusion ability of the infected cells. In the case of a bounded domain, the basic reproduction number [Formula: see text] is established and shown as a threshold: the virus-free steady state is globally asymptotically stable if [Formula: see text] and the virus is uniformly persistent if [Formula: see text]. The explicit formula for [Formula: see text] and the global asymptotic stability of the constant positive steady state are obtained for the case of homogeneous space...
January 5, 2018: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/29302705/multi-scale-modeling-of-apc-and-formula-see-text-catenin-regulation-in-the-human-colonic-crypt
#15
Brooks Emerick, Gilberto Schleiniger, Bruce M Boman
Stem cell renewal and differentiation in the human colonic crypt are linked to the [Formula: see text]-catenin pathway. The spatial balance of Wnt factors in proliferative cells within the crypt maintain an appropriate level of cellular reproduction needed for normal crypt homeostasis. Mutational events at the gene level are responsible for deregulating the balance of Wnt factors along the crypt, causing an overpopulation of proliferative cells, a loss of structure of the crypt domain, and the initiation of colorectal carcinomas...
January 4, 2018: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/29274002/a-periodic-disease-transmission-model-with-asymptomatic-carriage-and-latency-periods
#16
Isam Al-Darabsah, Yuan Yuan
In this paper, the global dynamics of a periodic disease transmission model with two delays in incubation and asymptomatic carriage periods is investigated. We first derive the model system with a general nonlinear incidence rate function by stage-structure. Then, we identify the basic reproduction ratio [Formula: see text] for the model and present numerical algorithm to calculate it. We obtain the global attractivity of the disease-free state when [Formula: see text] and discuss the disease persistence when [Formula: see text]...
December 22, 2017: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/29260295/expansion-of-gene-clusters-circular-orders-and-the-shortest-hamiltonian-path-problem
#17
Sonja J Prohaska, Sarah J Berkemer, Fabian Gärtner, Thomas Gatter, Nancy Retzlaff, Christian Höner Zu Siederdissen, Peter F Stadler
Clusters of paralogous genes such as the famous HOX cluster of developmental transcription factors tend to evolve by stepwise duplication of its members, often involving unequal crossing over. Gene conversion and possibly other mechanisms of concerted evolution further obfuscate the phylogenetic relationships. As a consequence, it is very difficult or even impossible to disentangle the detailed history of gene duplications in gene clusters. In this contribution we show that the expansion of gene clusters by unequal crossing over as proposed by Walter Gehring leads to distinctive patterns of genetic distances, namely a subclass of circular split systems...
December 19, 2017: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/29248985/on-the-information-content-of-discrete-phylogenetic-characters
#18
Magnus Bordewich, Ina Maria Deutschmann, Mareike Fischer, Elisa Kasbohm, Charles Semple, Mike Steel
Phylogenetic inference aims to reconstruct the evolutionary relationships of different species based on genetic (or other) data. Discrete characters are a particular type of data, which contain information on how the species should be grouped together. However, it has long been known that some characters contain more information than others. For instance, a character that assigns the same state to each species groups all of them together and so provides no insight into the relationships of the species considered...
December 16, 2017: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/29247320/time-dependent-propagators-for-stochastic-models-of-gene-expression-an-analytical-method
#19
Frits Veerman, Carsten Marr, Nikola Popović
The inherent stochasticity of gene expression in the context of regulatory networks profoundly influences the dynamics of the involved species. Mathematically speaking, the propagators which describe the evolution of such networks in time are typically defined as solutions of the corresponding chemical master equation (CME). However, it is not possible in general to obtain exact solutions to the CME in closed form, which is due largely to its high dimensionality. In the present article, we propose an analytical method for the efficient approximation of these propagators...
December 15, 2017: Journal of Mathematical Biology
https://www.readbyqxmd.com/read/29236142/frequency-dependent-growth-in-class-structured-populations-continuous-dynamics-in-the-limit-of-weak-selection
#20
Sabin Lessard, Cíntia Dalila Soares
In this paper we consider class-structured populations in discrete time in the limit of weak selection and with the inverse of the intensity of selection as unit of time. The aim is to establish a continuous model that approximates the discrete model. More precisely, we study frequency-dependent growth in an infinite haploid population structured into a finite number of classes such that individuals in each class contribute to a given subset of classes from one time step to the next. These contributions take the form of generalized fecundity parameters with perturbations of order 1 / N that depends on the class frequencies of each type and the type frequencies...
December 13, 2017: Journal of Mathematical Biology
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