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Cooperative metabolic resource allocation in spatially-structured systems J. Math. Biol. (IF 1.939) Pub Date : 2021-01-21 David S. Tourigny
Natural selection has shaped the evolution of cells and multi-cellular organisms such that social cooperation can often be preferred over an individualistic approach to metabolic regulation. This paper extends a framework for dynamic metabolic resource allocation based on the maximum entropy principle to spatiotemporal models of metabolism with cooperation. Much like the maximum entropy principle encapsulates
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Turing conditions for pattern forming systems on evolving manifolds J. Math. Biol. (IF 1.939) Pub Date : 2021-01-20 Robert A. Van Gorder, Václav Klika, Andrew L. Krause
The study of pattern-forming instabilities in reaction–diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental chemistry. Analyzing such instabilities is complicated, as there is a strong dependence of any spatially homogeneous base states on time, and the resulting structure
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Maximizing the total population with logistic growth in a patchy environment J. Math. Biol. (IF 1.939) Pub Date : 2021-01-19 Kentaro Nagahara, Yuan Lou, Eiji Yanagida
This paper is concerned with a nonlinear optimization problem that naturally arises in population biology. We consider the population of a single species with logistic growth residing in a patchy environment and study the effects of dispersal and spatial heterogeneity of patches on the total population at equilibrium. Our objective is to maximize the total population by redistributing the resources
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Destabilization and chaos induced by harvesting: insights from one-dimensional discrete-time models J. Math. Biol. (IF 1.939) Pub Date : 2021-01-19 Víctor Jiménez López, Eduardo Liz
One-dimensional discrete-time population models are often used to investigate the potential effects of increasing harvesting on population dynamics, and it is well known that suitable harvesting rates can stabilize fluctuations of population abundance. However, destabilization is also a possible outcome of increasing harvesting even in simple models. We provide a rigorous approach to study when harvesting
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Unbounded solutions of models for glycolysis J. Math. Biol. (IF 1.939) Pub Date : 2021-01-19 Pia Brechmann, Alan D. Rendall
The Selkov oscillator, a simple description of glycolysis, is a system of two ordinary differential equations with mass action kinetics. In previous work the authors established several properties of the solutions of this system. In the present paper we extend this to prove that this system has solutions which diverge to infinity in an oscillatory manner at late times. This is done with the help of
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Travelling wave solutions in a negative nonlinear diffusion–reaction model J. Math. Biol. (IF 1.939) Pub Date : 2020-11-20 Yifei Li, Peter van Heijster, Robert Marangell, Matthew J. Simpson
We use a geometric approach to prove the existence of smooth travelling wave solutions of a nonlinear diffusion–reaction equation with logistic kinetics and a convex nonlinear diffusivity function which changes sign twice in our domain of interest. We determine the minimum wave speed, \(c^*\), and investigate its relation to the spectral stability of a desingularised linear operator associated with
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Nonlocal and local models for taxis in cell migration: a rigorous limit procedure J. Math. Biol. (IF 1.939) Pub Date : 2020-10-17 Maria Eckardt, Kevin J. Painter, Christina Surulescu, Anna Zhigun
A rigorous limit procedure is presented which links nonlocal models involving adhesion or nonlocal chemotaxis to their local counterparts featuring haptotaxis and classical chemotaxis, respectively. It relies on a novel reformulation of the involved nonlocalities in terms of integral operators applied directly to the gradients of signal-dependent quantities. The proposed approach handles both model
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On the heterozygosity of an admixed population J. Math. Biol. (IF 1.939) Pub Date : 2020-10-09 Simina M. Boca, Lucy Huang, Noah A. Rosenberg
In this study, we consider admixed populations through their expected heterozygosity, a measure of genetic diversity. A population is termed admixed if its members possess recent ancestry from two or more separate sources. As a result of the fusion of source populations with different genetic variants, admixed populations can exhibit high levels of genetic diversity, reflecting contributions of their
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Can a barrier zone stop invasion of a population? J. Math. Biol. (IF 1.939) Pub Date : 2020-10-02 Bingtuan Li, Minghua Zhang, Bradley Coffman
We consider an integro-difference model to study the effect of a stationary barrier zone on invasion of a population with a strong Allee effect. It is assumed that inside the barrier zone a certain proportion of the population is killed. A Laplace dispersal kernel is used in the model. We provide a formula for the critical width \(L^*\) of barrier zone. We show that when a barrier zone is set at the
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Counting phylogenetic networks of level 1 and 2 J. Math. Biol. (IF 1.939) Pub Date : 2020-10-01 Mathilde Bouvel, Philippe Gambette, Marefatollah Mansouri
Phylogenetic networks generalize phylogenetic trees, and have been introduced in order to describe evolution in the case of transfer of genetic material between coexisting species. There are many classes of phylogenetic networks, which can all be modeled as families of graphs with labeled leaves. In this paper, we focus on rooted and unrooted level-k networks and provide enumeration formulas (exact
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Fluctuating-rate model with multiple gene states J. Math. Biol. (IF 1.939) Pub Date : 2020-09-30 Jingwei Li, Hao Ge, Yunxin Zhang
Multiple phenotypic states of single cells often co-exist in the presence of positive feedbacks. Stochastic gene-state switchings and low copy numbers of proteins in single cells cause considerable fluctuations. The chemical master equation (CME) is a powerful tool that describes the dynamics of single cells, but it may be overly complicated. Among many simplified models, a fluctuating-rate (FR) model
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Propagation direction of traveling waves for a class of bistable epidemic models. J. Math. Biol. (IF 1.939) Pub Date : 2020-09-25 Je-Chiang Tsai,Yu-Yu Weng
Traveling waves of a reaction–diffusion (RD) system connecting two spatially uniform stable equilibria are termed as bistable waves. Due to the uniqueness of a bistable wave in RD systems, it is difficult to determine its propagation direction, and there are very few analytical results on this subject. In this study, we propose an approach to give a complete characterization of the propagation direction
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Mathematical models for the effect of anti-vascular endothelial growth factor on visual acuity. J. Math. Biol. (IF 1.939) Pub Date : 2020-09-24 David A Edwards,Brooks Emerick,Anna Georgieva Kondic,Kristian Kiradjiev,Christopher Raymond,Maxim Zyskin
The standard of care treatment for neovascular age-related macular degeneration, delivered as ocular injection, is based on anti-vascular endothelial growth factor (anti-VEGF). The course of treatment may need to be modified quickly for certain patients based on their response. Models that track both the concentration and the response to an anti-VEGF treatment are presented. The specific focus is to
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Cooperativity, absolute interaction, and algebraic optimization. J. Math. Biol. (IF 1.939) Pub Date : 2020-09-23 Nidhi Kaihnsa,Yue Ren,Mohab Safey El Din,Johannes W R Martini
We consider a measure of cooperativity based on the minimal interaction required to generate an observed titration behavior. We describe the corresponding algebraic optimization problem and show how it can be solved using the nonlinear algebra tool SCIP. Moreover, we compute the minimal interactions and minimal molecules for several binding polynomials that describe the oxygen binding of various hemoglobins
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Time-dependent solution of the NIMFA equations around the epidemic threshold. J. Math. Biol. (IF 1.939) Pub Date : 2020-09-22 Bastian Prasse,Piet Van Mieghem
The majority of epidemic models are described by non-linear differential equations which do not have a closed-form solution. Due to the absence of a closed-form solution, the understanding of the precise dynamics of a virus is rather limited. We solve the differential equations of the N-intertwined mean-field approximation of the susceptible-infected-susceptible epidemic process with heterogeneous
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Invasion analysis on a predator-prey system in open advective environments. J. Math. Biol. (IF 1.939) Pub Date : 2020-09-22 Hua Nie,Biao Wang,Jianhua Wu
We investigate a reaction–diffusion–advection system which characterizes the interactions between the predator and prey in advective environments, such as streams or rivers. In contrast with non-advective environments, the dynamics of this system is more complicated. It turns out that there exists a critical mortality rate of the predator and two critical advection rates, which classify the dynamic
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A continuation method for spatially discretized models with nonlocal interactions conserving size and shape of cells and lattices. J. Math. Biol. (IF 1.939) Pub Date : 2020-09-21 Shin-Ichiro Ei,Hiroshi Ishii,Makoto Sato,Yoshitaro Tanaka,Miaoxing Wang,Tetsuo Yasugi
In this paper, we introduce a continuation method for the spatially discretized models, while conserving the size and shape of the cells and lattices. This proposed method is realized using the shift operators and nonlocal operators of convolution types. Through this method and using the shift operator, the nonlinear spatially discretized model on the uniform and nonuniform lattices can be systematically
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Early epidemic spread, percolation and Covid-19. J. Math. Biol. (IF 1.939) Pub Date : 2020-09-18 Gonçalo Oliveira
Human to human transmissible infectious diseases spread in a population using human interactions as its transmission vector. The early stages of such an outbreak can be modeled by a graph whose edges encode these interactions between individuals, the vertices. This article attempts to account for the case when each individual entails in different kinds of interactions which have therefore different
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Structure of the space of taboo-free sequences. J. Math. Biol. (IF 1.939) Pub Date : 2020-09-17 Cassius Manuel,Arndt von Haeseler
Models of sequence evolution typically assume that all sequences are possible. However, restriction enzymes that cut DNA at specific recognition sites provide an example where carrying a recognition site can be lethal. Motivated by this observation, we studied the set of strings over a finite alphabet with taboos, that is, with prohibited substrings. The taboo-set is referred to as \(\mathbb {T}\)
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Influence of a road on a population in an ecological niche facing climate change. J. Math. Biol. (IF 1.939) Pub Date : 2020-09-16 Henri Berestycki,Romain Ducasse,Luca Rossi
We introduce a model designed to account for the influence of a line with fast diffusion–such as a road or another transport network–on the dynamics of a population in an ecological niche.This model consists of a system of coupled reaction-diffusion equations set on domains with different dimensions (line / plane). We first show that, in a stationary climate, the presence of the line is always deleterious
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Caterpillars on three and four leaves are sufficient to reconstruct binary normal networks. J. Math. Biol. (IF 1.939) Pub Date : 2020-09-09 Simone Linz,Charles Semple
While every rooted binary phylogenetic tree is determined by its set of displayed rooted triples, such a result does not hold for an arbitrary rooted binary phylogenetic network. In particular, there exist two non-isomorphic rooted binary temporal normal networks that display the same set of rooted triples. Moreover, without any structural constraint on the rooted phylogenetic networks under consideration
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A modified Ising model of Barabási-Albert network with gene-type spins. J. Math. Biol. (IF 1.939) Pub Date : 2020-09-08 Jeyashree Krishnan,Reza Torabi,Andreas Schuppert,Edoardo Di Napoli
The central question of systems biology is to understand how individual components of a biological system such as genes or proteins cooperate in emerging phenotypes resulting in the evolution of diseases. As living cells are open systems in quasi-steady state type equilibrium in continuous exchange with their environment, computational techniques that have been successfully applied in statistical thermodynamics
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Resident-invader dynamics of similar strategies in fluctuating environments. J. Math. Biol. (IF 1.939) Pub Date : 2020-09-07 Yuhua Cai,Stefan A H Geritz
We study resident-invader dynamics in fluctuating environments when the invader and the resident have close but distinct strategies. First we focus on a class of continuous-time models of unstructured populations of multi-dimensional strategies, which incorporates environmental feedback and environmental stochasticity. Then we generalize our results to a class of structured population models. We classify
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Latent likelihood ratio tests for assessing spatial kernels in epidemic models. J. Math. Biol. (IF 1.939) Pub Date : 2020-09-05 David Thong,George Streftaris,Gavin J Gibson
One of the most important issues in the critical assessment of spatio-temporal stochastic models for epidemics is the selection of the transmission kernel used to represent the relationship between infectious challenge and spatial separation of infected and susceptible hosts. As the design of control strategies is often based on an assessment of the distance over which transmission can realistically
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Correction to: Finite dimensional state representation of physiologically structured populations. J. Math. Biol. (IF 1.939) Pub Date : 2020-09-04 Odo Diekmann,Mats Gyllenberg,Johan A J Metz
In the original publication of the article, the Subsection 2.1.2 was published incorrectly.
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An integrodifference model for vegetation patterns in semi-arid environments with seasonality. J. Math. Biol. (IF 1.939) Pub Date : 2020-09-04 Lukas Eigentler,Jonathan A Sherratt
Vegetation patterns are a characteristic feature of semi-deserts occurring on all continents except Antarctica. In some semi-arid regions, the climate is characterised by seasonality, which yields a synchronisation of seed dispersal with the dry season or the beginning of the wet season. We reformulate the Klausmeier model, a reaction–advection–diffusion system that describes the plant–water dynamics
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Populations in environments with a soft carrying capacity are eventually extinct. J. Math. Biol. (IF 1.939) Pub Date : 2020-08-20 Peter Jagers,Sergei Zuyev
Consider a population whose size changes stepwise by its members reproducing or dying (disappearing), but is otherwise quite general. Denote the initial (non-random) size by \(Z_0\) and the size of the nth change by \(C_n\), \(n= 1, 2, \ldots \). Population sizes hence develop successively as \(Z_1=Z_0+C_1,\ Z_2=Z_1+C_2\) and so on, indefinitely or until there are no further size changes, due to extinction
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Implications of immune-mediated metastatic growth on metastatic dormancy, blow-up, early detection, and treatment. J. Math. Biol. (IF 1.939) Pub Date : 2020-08-13 Adam Rhodes,Thomas Hillen
Metastatic seeding of distant organs can occur in the very early stages of primary tumor development. Once seeded, these micrometastases may enter a dormant phase that can last decades. Curiously, the surgical removal of the primary tumor can stimulate the accelerated growth of distant metastases, a phenomenon known as metastatic blow-up. Recent clinical evidence has shown that the immune response
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Using singular perturbation theory to determine kinetic parameters in a non-standard coupled enzyme assay. J. Math. Biol. (IF 1.939) Pub Date : 2020-08-06 Mohit P Dalwadi,Diego Orol,Frederik Walter,Nigel P Minton,John R King,Katalin Kovács
We investigate how to characterize the kinetic parameters of an aminotransaminase using a non-standard coupled (or auxiliary) enzyme assay, where the peculiarity arises for two reasons. First, one of the products of the auxiliary enzyme is a substrate for the primary enzyme and, second, we explicitly account for the reversibility of the auxiliary enzyme reaction. Using singular perturbation theory
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Target reproduction numbers for reaction-diffusion population models. J. Math. Biol. (IF 1.939) Pub Date : 2020-07-31 Xueying Wang,Xiao-Qiang Zhao
A very important population threshold quantity is the target reproduction number, which is a measure of control effort required for a target prevention, intervention or control. This concept, as a generalization of type reproduction number, was first introduced in Shuai et al. (J Math Biol 67:1067–1082, 2013) for nonnegative matrices with immediate applications to compartmental population models of
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A multiphase model of growth factor-regulated atherosclerotic cap formation. J. Math. Biol. (IF 1.939) Pub Date : 2020-07-29 Michael G Watson,Helen M Byrne,Charlie Macaskill,Mary R Myerscough
Atherosclerosis is characterised by the growth of fatty plaques in the inner artery wall. In mature plaques, vascular smooth muscle cells (SMCs) are recruited from adjacent tissue to deposit a collagenous cap over the fatty plaque core. This cap isolates the thrombogenic plaque content from the bloodstream and prevents the clotting cascade that leads to myocardial infarction or stroke. Despite the
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Boolean analysis of lateral inhibition. J. Math. Biol. (IF 1.939) Pub Date : 2020-07-29 Elisa Tonello,Heike Siebert
We study Boolean networks which are simple spatial models of the highly conserved Delta–Notch system. The models assume the inhibition of Delta in each cell by Notch in the same cell, and the activation of Notch in presence of Delta in surrounding cells. We consider fully asynchronous dynamics over undirected graphs representing the neighbour relation between cells. In this framework, one can show
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Metaheuristics and Pontryagin's minimum principle for optimal therapeutic protocols in cancer immunotherapy: a case study and methods comparison. J. Math. Biol. (IF 1.939) Pub Date : 2020-07-25 Sima Sarv Ahrabi,Alireza Momenzadeh
In this paper, the performance appropriateness of population-based metaheuristics for immunotherapy protocols is investigated on a comparative basis while the goal is to stimulate the immune system to defend against cancer. For this purpose, genetic algorithm and particle swarm optimization are employed and compared with modern method of Pontryagin’s minimum principle (PMP). To this end, a well-known
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The impracticalities of multiplicatively-closed codon models: a retreat to linear alternatives. J. Math. Biol. (IF 1.939) Pub Date : 2020-07-24 Julia A Shore,Jeremy G Sumner,Barbara R Holland
A matrix Lie algebra is a linear space of matrices closed under the operation \( [A, B] = AB-BA \). The “Lie closure” of a set of matrices is the smallest matrix Lie algebra which contains the set. In the context of Markov chain theory, if a set of rate matrices form a Lie algebra, their corresponding Markov matrices are closed under matrix multiplication; this has been found to be a useful property
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Quantitative approximation of the discrete Moran process by a Wright-Fisher diffusion. J. Math. Biol. (IF 1.939) Pub Date : 2020-07-23 Gorgui Gackou,Arnaud Guillin,Arnaud Personne
The Moran discrete process and the Wright–Fisher model are the most popular models in population genetics. The Wright–Fisher diffusion is commonly used as an approximation in order to understand the dynamics of population genetics models. Here, we give a quantitative large-population limit of the error occurring by using the approximating diffusion in the presence of weak selection and weak immigration
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Parameterization of mechanistic models from qualitative data using an efficient optimal scaling approach. J. Math. Biol. (IF 1.939) Pub Date : 2020-07-21 Leonard Schmiester,Daniel Weindl,Jan Hasenauer
Quantitative dynamical models facilitate the understanding of biological processes and the prediction of their dynamics. These models usually comprise unknown parameters, which have to be inferred from experimental data. For quantitative experimental data, there are several methods and software tools available. However, for qualitative data the available approaches are limited and computationally demanding
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Modelling dendritic spines with the finite element method, investigating the impact of geometry on electric and calcic responses. J. Math. Biol. (IF 1.939) Pub Date : 2020-07-21 Frank Boahen,Nicolas Doyon
Understanding the relationship between shape and function of dendritic spines is an elusive topic. Several modelling approaches have been used to investigate the interplay between spine geometry, calcium diffusion and electric signalling. We here use a second order finite element method to solve the Poisson–Nernst–Planck equations and describe electrodiffusion in dendritic spines. With this, we obtain
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On real-valued SDE and nonnegative-valued SDE population models with demographic variability. J. Math. Biol. (IF 1.939) Pub Date : 2020-07-16 E J Allen,L J S Allen,H L Smith
Population dynamics with demographic variability is frequently studied using discrete random variables with continuous-time Markov chain (CTMC) models. An approximation of a CTMC model using continuous random variables can be derived in a straightforward manner by applying standard methods based on the reaction rates in the CTMC model. This leads to a system of Itô stochastic differential equations
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On the effects of carrying capacity and intrinsic growth rate on single and multiple species in spatially heterogeneous environments. J. Math. Biol. (IF 1.939) Pub Date : 2020-07-03 Qian Guo,Xiaoqing He,Wei-Ming Ni
We first consider a diffusive logistic model of a single species in a heterogeneous environment, with two parameters, r(x) for intrinsic growth rate and K(x) for carrying capacity. When r(x) and K(x) are proportional, i.e., \(r=cK\), it is proved by Lou (J Differ Equ 223(2):400–426, 2006) that a population diffusing at any rate will reach a higher total equilibrium biomass than the population in an
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Analysis and optimal control of an HIV model based on CD4 count. J. Math. Biol. (IF 1.939) Pub Date : 2020-06-30 A Ishaku,A M Gazali,S A Abdullahi,N Hussaini
A non-linear mechanistic model for the transmission dynamics of HIV/AIDS is developed and analyzed. The model classified the infected individuals based on their CD4 count level. Furthermore, education campaign, voluntary testing and counseling and treatment are considered as intervention strategies for controlling the disease. The analysis of the model reveals that imperfect public enlightenment campaign
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A two-thresholds policy for a Filippov model in combating influenza. J. Math. Biol. (IF 1.939) Pub Date : 2020-06-25 Can Chen,Pengde Wang,Litao Zhang
This work designs a two-thresholds policy for a Filippov model in combating influenza, so as to estimate when and whether to take control strategies, including the media coverage, antiviral treatment of infected individuals and vaccination of susceptible population. By introducing two tolerance thresholds \(S_{c}\) and \(I_{c}\) of susceptible and infected individuals, the two-thresholds policy is
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Modeling the role of macrophages in HIV persistence during antiretroviral therapy. J. Math. Biol. (IF 1.939) Pub Date : 2020-06-24 Ting Guo,Zhipeng Qiu,Libin Rong
HIV preferentially infects activated CD4+ T cells. Current antiretroviral therapy cannot eradicate the virus. Viral infection of other cells such as macrophages may contribute to viral persistence during antiretroviral therapy. In addition to cell-free virus infection, macrophages can also get infected when engulfing infected CD4+ T cells as innate immune sentinels. How macrophages affect the dynamics
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Mixture distributions in a stochastic gene expression model with delayed feedback: a WKB approximation approach. J. Math. Biol. (IF 1.939) Pub Date : 2020-06-24 Pavol Bokes,Alessandro Borri,Pasquale Palumbo,Abhyudai Singh
Noise in gene expression can be substantively affected by the presence of production delay. Here we consider a mathematical model with bursty production of protein, a one-step production delay (the passage of which activates the protein), and feedback in the frequency of bursts. We specifically focus on examining the steady-state behaviour of the model in the slow-activation (i.e. large-delay) regime
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Population abundance of two-patch competitive systems with asymmetric dispersal. J. Math. Biol. (IF 1.939) Pub Date : 2020-06-22 Yuanshi Wang,Hong Wu,Yiyang He,Zhihui Wang,Kun Hu
This paper considers two-species competitive systems with two patches, in which one of the species can move between the patches. One patch is a source where each species can persist alone, but the other is a sink where the mobile species cannot survive. Based on rigorous analysis on the model, we show global stability of equilibria and bi-stability in the first octant Int\(R_+^3\). Then total population
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Relatedness coefficients in pedigrees with inbred founders. J. Math. Biol. (IF 1.939) Pub Date : 2020-06-08 Magnus Dehli Vigeland
We study an extension of the standard framework for pedigree analysis, in which we allow pedigree founders to be inbred. This solves a number of practical challenges in calculating coefficients of relatedness, including condensed identity coefficients. As a consequence we expand considerably the class of pedigrees for which such coefficients may be efficiently computed. An application of this is the
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Continuous and discrete modeling of HIV-1 decline on therapy. J. Math. Biol. (IF 1.939) Pub Date : 2020-06-02 Elvan Akın,Gülşah Yeni,Alan S Perelson
Mathematical models have shed light on the dynamics of HIV- 1 infection in vivo. In this paper, we generalize continuous mathematical models of drug therapy for HIV-1 by Perelson et al. (Science 271:1582–1586, 1996) and Perelson and Nelson (SIAM Rev 41:3–44, 1999) on time scales, i.e., a nonempty closed subset of real numbers in order to derive new discrete models that predict the total concentration
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Fixation probabilities for the Moran process with three or more strategies: general and coupling results. J. Math. Biol. (IF 1.939) Pub Date : 2020-05-31 Eliza M Ferreira,Armando G M Neves
We study fixation probabilities for the Moran stochastic process for the evolution of a population with three or more types of individuals and frequency-dependent fitnesses. Contrary to the case of populations with two types of individuals, in which fixation probabilities may be calculated by an exact formula, here we must solve a large system of linear equations. We first show that this system always
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Modeling and dynamics of Wolbachia-infected male releases and mating competition on mosquito control. J. Math. Biol. (IF 1.939) Pub Date : 2020-05-26 Xianghong Zhang,Qiyong Liu,Huaiping Zhu
Despite centuries of continuous efforts, mosquito-borne diseases (MBDs) remain enormous health threat of human life worldwide. Lately, the USA government has approved an innovative technology of releasing Wolbachia-infected male mosquitoes to suppress the wild mosquito population. In this paper we first introduce a stage-structured model for natural mosquitos, then we establish a new model considering
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Long-lasting insecticidal nets and the quest for malaria eradication: a mathematical modeling approach. J. Math. Biol. (IF 1.939) Pub Date : 2020-05-23 Iboi Enahoro,Steffen Eikenberry,Abba B Gumel,Silvie Huijben,Krijn Paaijmans
Recent dramatic declines in global malaria burden and mortality can be largely attributed to the large-scale deployment of insecticidal-based measures, namely long-lasting insecticidal nets (LLINs) and indoor residual spraying. However, the sustainability of these gains, and the feasibility of global malaria eradication by 2040, may be affected by increasing insecticide resistance among the Anopheles
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Lotka-Volterra approximations for evolutionary trait-substitution processes. J. Math. Biol. (IF 1.939) Pub Date : 2020-05-21 Hiroshi C Ito,Ulf Dieckmann,Johan A J Metz
A set of axioms is formulated characterizing ecologically plausible community dynamics. Using these axioms, it is proved that the transients following an invasion into a sufficiently stable equilibrium community by a mutant phenotype similar to one of the community's finitely many resident phenotypes can always be approximated by means of an appropriately chosen Lotka-Volterra model. To this end, the
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Dynamic metabolic resource allocation based on the maximum entropy principle. J. Math. Biol. (IF 1.939) Pub Date : 2020-05-18 David S Tourigny
Organisms have evolved a variety of mechanisms to cope with the unpredictability of environmental conditions, and yet mainstream models of metabolic regulation are typically based on strict optimality principles that do not account for uncertainty. This paper introduces a dynamic metabolic modelling framework that is a synthesis of recent ideas on resource allocation and the powerful optimal control
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Global analysis of a predator-prey model with variable predator search rate. J. Math. Biol. (IF 1.939) Pub Date : 2020-05-17 Benjamin D Dalziel,Enrique Thomann,Jan Medlock,Patrick De Leenheer
We consider a modified Holling-type II predator-prey model, based on the premise that the search rate of predators is dependent on the prey density, rather than constant. A complete analysis of the global behavior of the model is presented, and shows that the model exhibits a dichotomy similar to the classical Holling-type II model: either the coexistence steady state is globally stable; or it is unstable
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Interactions between different predator-prey states: a method for the derivation of the functional and numerical response. J. Math. Biol. (IF 1.939) Pub Date : 2020-05-17 Cecilia Berardo,Stefan Geritz,Mats Gyllenberg,Gaël Raoul
In this paper we introduce a formal method for the derivation of a predator's functional response from a system of fast state transitions of the prey or predator on a time scale during which the total prey and predator densities remain constant. Such derivation permits an explicit interpretation of the structure and parameters of the functional response in terms of individual behaviour. The same method
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Optimal open-loop desynchronization of neural oscillator populations. J. Math. Biol. (IF 1.939) Pub Date : 2020-05-16 Dan Wilson
Deep brain stimulation (DBS) is an increasingly used medical treatment for various neurological disorders. While its mechanisms are not fully understood, experimental evidence suggests that through application of periodic electrical stimulation DBS may act to desynchronize pathologically synchronized populations of neurons resulting desirable changes to a larger brain circuit. However, the underlying
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Harvesting and seeding of stochastic populations: analysis and numerical approximation. J. Math. Biol. (IF 1.939) Pub Date : 2020-05-15 Alexandru Hening,Ky Quan Tran
We study an ecosystem of interacting species that are influenced by random environmental fluctuations. At any point in time, we can either harvest or seed (repopulate) species. Harvesting brings an economic gain while seeding incurs a cost. The problem is to find the optimal harvesting-seeding strategy that maximizes the expected total income from harvesting minus the cost one has to pay for the seeding
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A spatial model of honey bee colony collapse due to pesticide contamination of foraging bees. J. Math. Biol. (IF 1.939) Pub Date : 2020-05-15 P Magal,G F Webb,Yixiang Wu
We develop a model of honey bee colony collapse based on contamination of forager bees in pesticide contaminated spatial environments. The model consists of differential and difference equations for the spatial distributions of the uncontaminated and contaminated forager bees. A key feature of the model is incorporation of the return to the hive each day of forager bees. The model quantifies colony
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Asymptotic profiles of the steady states for an SIS epidemic patch model with asymmetric connectivity matrix. J. Math. Biol. (IF 1.939) Pub Date : 2020-05-06 Shanshan Chen,Junping Shi,Zhisheng Shuai,Yixiang Wu
The dynamics of an SIS epidemic patch model with asymmetric connectivity matrix is analyzed. It is shown that the basic reproduction number [Formula: see text] is strictly decreasing with respect to the dispersal rate of the infected individuals. When [Formula: see text], the model admits a unique endemic equilibrium, and its asymptotic profiles are characterized for small dispersal rates. Specifically
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Parameter estimation for a point-source diffusion-decay morphogen model. J. Math. Biol. (IF 1.939) Pub Date : 2020-04-25 Mark B Flegg,Mario A Muñoz,Kate Smith-Miles,Wai Shan Yuen,Jennifer A Flegg,John G Carroll
In this paper we present a novel method for finding unknown parameters for an unknown morphogen. We postulate the existence of an unknown morphogen in a given three-dimensional domain due to the spontaneous arrangement of a downstream species on the domain boundary for which data is known. Assuming a modified Helmholtz model for the morphogen and that it is produced from a single source in the domain
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A cell-cell repulsion model on a hyperbolic Keller-Segel equation. J. Math. Biol. (IF 1.939) Pub Date : 2020-04-24 Xiaoming Fu,Quentin Griette,Pierre Magal
In this work, we discuss a cell-cell repulsion model based on a hyperbolic Keller-Segel equation with two populations, which aims at describing the cell growth and dispersion in the co-culture experiment from the work of Pasquier et al. (Biol Direct 6(1):5, 2011). We introduce the notion of solution integrated along the characteristics, which allows us to prove the existence and uniqueness of solutions
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Distribution of extreme first passage times of diffusion. J. Math. Biol. (IF 1.939) Pub Date : 2020-04-22 Sean D Lawley
Many events in biology are triggered when a diffusing searcher finds a target, which is called a first passage time (FPT). The overwhelming majority of FPT studies have analyzed the time it takes a single searcher to find a target. However, the more relevant timescale in many biological systems is the time it takes the fastest searcher(s) out of many searchers to find a target, which is called an extreme
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