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Modeling LSD1-Mediated Tumor Stagnation Bull. Math. Biol. (IF 1.812) Pub Date : 2021-01-12 Jesse Milzman, Wanqiang Sheng, Doron Levy
LSD1 (KDMA1) has gained attention in the last decade as a cancer biomarker and drug target. In particular, recent work suggests that LSD1 inhibition alone reduces tumor growth, increases T cell tumor infiltration, and complements PD1/PDL1 checkpoint inhibitor therapy. In order to elucidate the immunogenic effects of LSD1 inhibition, we develop a mathematical model of tumor growth under the influence
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Modeling Rabies Transmission in Spatially Heterogeneous Environments via $$\theta $$ θ -diffusion Bull. Math. Biol. (IF 1.812) Pub Date : 2021-01-12 Xiunan Wang, Hao Wang, Michael Y. Li
Rabies among dogs remains a considerable risk to humans and constitutes a serious public health concern in many parts of the world. Conventional mathematical models for rabies typically assume homogeneous environments, with a standard diffusion term for the population of rabid animals. It has recently been recognized, however, that spatial heterogeneity plays an important role in determining spatial
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A Geometrical Framework for f -Statistics Bull. Math. Biol. (IF 1.812) Pub Date : 2021-01-08 Gonzalo Oteo-García, José-Angel Oteo
A detailed derivation of the f-statistics formalism is made from a geometrical framework. It is shown that the f-statistics appear when a genetic distance matrix is constrained to describe a four population phylogenetic tree. The choice of genetic metric is crucial and plays an outstanding role as regards the tree-like-ness criterion. The case of lack of treeness is interpreted in the formalism as
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Correction to: Mathematical Model of Chronic Dermal Wounds in Diabetes and Obesity Bull. Math. Biol. (IF 1.812) Pub Date : 2021-01-07 Avner Friedman, Nourridine Siewe
We apologize for the error in the figure.
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On the Mathematical Modelling of Competitive Invasive Weed Dynamics Bull. Math. Biol. (IF 1.812) Pub Date : 2021-01-07 Tedi Ramaj
We explore the dynamics of invasive weeds by partial differential equation (PDE) modelling and applying dynamical system and phase portrait techniques. We begin by applying the method of characteristics to a preexisting PDE model of the spreading of T. fluminensis, an invasive weed which has been responsible for native forest depletion. We explore the system both at particular points in space and over
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Motor Protein Transport Along Inhomogeneous Microtubules Bull. Math. Biol. (IF 1.812) Pub Date : 2021-01-07 S. D. Ryan, Z. McCarthy, M. Potomkin
Many cellular processes rely on the cell’s ability to transport material to and from the nucleus. Networks consisting of many microtubules and actin filaments are key to this transport. Recently, the inhibition of intracellular transport has been implicated in neurodegenerative diseases such as Alzheimer’s disease and Amyotrophic Lateral Sclerosis. Furthermore, microtubules may contain so-called defective
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Thermodynamic Inhibition in a Biofilm Reactor with Suspended Bacteria Bull. Math. Biol. (IF 1.812) Pub Date : 2021-01-07 Harry J. Gaebler, Jack M. Hughes, Hermann J. Eberl
We formulate a biofilm reactor model with suspended bacteria that accounts for thermodynamic growth inhibition. The reactor model is a chemostat style model consisting of a single replenished growth promoting substrate, a single reaction product, suspended bacteria, and wall attached bacteria in the form of a bacterial biofilm. We present stability conditions for the washout equilibrium using standard
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A Two-Step Model of Human Entrainment: A Quantitative Study of Circadian Period and Phase of Entrainment Bull. Math. Biol. (IF 1.812) Pub Date : 2021-01-07 Zheming An, Nathaniel J. Merrill, Kwangwon Lee, Rémi Robin, Amaury Hayat, Olivia Zapfe, Benedetto Piccoli
One of the essential characteristics of an authentic circadian clock is that the free-running period sustains an approximately 24-hour cycle. When organisms are exposed to an external stimulus, the endogenous oscillators synchronize to the cycling environment signal in a process known as entrainment. These environmental cues perform an important role in resetting the phase and period of the circadian
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Optimal Control of Mitigation Strategies for Dengue Virus Transmission Bull. Math. Biol. (IF 1.812) Pub Date : 2021-01-06 Ling Xue, Xue Ren, Felicia Magpantay, Wei Sun, Huaiping Zhu
Dengue virus is transmitted by Aedes mosquitoes, posing threat to people’s health and leading to great economic cost in many tropical and subtropical regions. We develop an ordinary differential equation model taking into account multiple strains of dengue virus. Using the model, we assess the effectiveness of human vaccination considering its waning and failure. We derive the lower bound and upper
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A Mathematical Modeling Study: Assessing Impact of Mismatch Between Influenza Vaccine Strains and Circulating Strains in Hajj Bull. Math. Biol. (IF 1.812) Pub Date : 2021-01-02 Mohammed H. Alharbi, Christopher M. Kribs
The influenza virus causes severe respiratory illnesses and deaths worldwide every year. It spreads quickly in an overcrowded area like the annual Hajj pilgrimage in Saudi Arabia. Vaccination is the primary strategy for protection against influenza. Due to the occurrence of antigenic shift and drift of the influenza virus, a mismatch between vaccine strains and circulating strains of influenza may
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Competitive Exclusion in a General Multi-species Chemostat Model with Stochastic Perturbations Bull. Math. Biol. (IF 1.812) Pub Date : 2021-01-02 Chaoqun Xu, Sanling Yuan, Tonghua Zhang
Based on the fact that the continuous culture of microorganisms in a chemostat is subject to environmental noises, we present and analyze a stochastic competition chemostat model with general monotonic response functions and differential removal rates. The existence and boundedness of the unique positive solution are first obtained. By defining a stochastic break-even concentration for every species
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Antibody Dynamics for Plasmodium vivax Malaria: A Mathematical Model Bull. Math. Biol. (IF 1.812) Pub Date : 2021-01-02 Somya Mehra, James M. McCaw, Mark B. Flegg, Peter G. Taylor, Jennifer A. Flegg
Malaria is a mosquito-borne disease that, despite intensive control and mitigation initiatives, continues to pose an enormous public health burden. Plasmodium vivax is one of the principal causes of malaria in humans. Antibodies, which play a fundamental role in the host response to P. vivax, are acquired through exposure to the parasite. Here, we introduce a stochastic, within-host model of antibody
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A Dynamic Model to Assess Human Papillomavirus Vaccination Strategies in a Heterosexual Population Combined with Men Who have Sex with Men Bull. Math. Biol. (IF 1.812) Pub Date : 2021-01-02 Shasha Gao, Maia Martcheva, Hongyu Miao, Libin Rong
Vaccination is effective in preventing human papillomavirus (HPV) infection. It is imperative to investigate who should be vaccinated and what the best vaccine distribution strategy is. In this paper, we use a dynamic model to assess HPV vaccination strategies in a heterosexual population combined with gay, bisexual, and other men who have sex with men (MSM). The basic reproduction numbers for heterosexual
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Statistics of Nascent and Mature RNA Fluctuations in a Stochastic Model of Transcriptional Initiation, Elongation, Pausing, and Termination Bull. Math. Biol. (IF 1.812) Pub Date : 2020-12-22 Tatiana Filatova, Nikola Popovic, Ramon Grima
Recent advances in fluorescence microscopy have made it possible to measure the fluctuations of nascent (actively transcribed) RNA. These closely reflect transcription kinetics, as opposed to conventional measurements of mature (cellular) RNA, whose kinetics is affected by additional processes downstream of transcription. Here, we formulate a stochastic model which describes promoter switching, initiation
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Propagation of Epidemics Along Lines with Fast Diffusion Bull. Math. Biol. (IF 1.812) Pub Date : 2020-12-14 Henri Berestycki, Jean-Michel Roquejoffre, Luca Rossi
It has long been known that epidemics can travel along communication lines, such as roads. In the current COVID-19 epidemic, it has been observed that major roads have enhanced its propagation in Italy. We propose a new simple model of propagation of epidemics which exhibits this effect and allows for a quantitative analysis. The model consists of a classical SIR model with diffusion, to which an additional
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Sequential Data Assimilation of the Stochastic SEIR Epidemic Model for Regional COVID-19 Dynamics Bull. Math. Biol. (IF 1.812) Pub Date : 2020-12-08 Ralf Engbert, Maximilian M. Rabe, Reinhold Kliegl, Sebastian Reich
Newly emerging pandemics like COVID-19 call for predictive models to implement precisely tuned responses to limit their deep impact on society. Standard epidemic models provide a theoretically well-founded dynamical description of disease incidence. For COVID-19 with infectiousness peaking before and at symptom onset, the SEIR model explains the hidden build-up of exposed individuals which creates
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Modeling the Mechanisms by Which Coexisting Biomolecular RNA–Protein Condensates Form Bull. Math. Biol. (IF 1.812) Pub Date : 2020-11-24 K. Gasior, M. G. Forest, A. S. Gladfelter, J. M. Newby
Liquid–liquid phase separation is an emerging mechanism for intracellular organization. This work presents a mathematical model to examine molecular mechanisms that yield phase-separated droplets composed of different RNA–protein complexes. Using a Cahn–Hilliard diffuse interface model with a Flory–Huggins free energy scheme, we explore how multiple (here two, for simplicity) protein–RNA complexes
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Disease Emergence in Multi-Patch Stochastic Epidemic Models with Demographic and Seasonal Variability Bull. Math. Biol. (IF 1.812) Pub Date : 2020-11-24 Kaniz Fatema Nipa, Linda J. S. Allen
Factors such as seasonality and spatial connectivity affect the spread of an infectious disease. Accounting for these factors in infectious disease models provides useful information on the times and locations of greatest risk for disease outbreaks. In this investigation, stochastic multi-patch epidemic models are formulated with seasonal and demographic variability. The stochastic models are used
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Phylosymmetric Algebras: Mathematical Properties of a New Tool in Phylogenetics Bull. Math. Biol. (IF 1.812) Pub Date : 2020-11-21 Michael Hendriksen, Julia A. Shore
In phylogenetics, it is of interest for rate matrix sets to satisfy closure under matrix multiplication as this makes finding the set of corresponding transition matrices possible without having to compute matrix exponentials. It is also advantageous to have a small number of free parameters as this, in applications, will result in a reduction in computation time. We explore a method of building a
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Stationary Distribution of Telomere Lengths in Cells with Telomere Length Maintenance and its Parametric Inference Bull. Math. Biol. (IF 1.812) Pub Date : 2020-11-20 Kyung Hyun Lee, Marek Kimmel
Telomeres are nucleotide caps located at the ends of each eukaryotic chromosome. Under normal physiological conditions as well as in culture, they shorten during each DNA replication round. Short telomeres initiate a proliferative arrest of cells termed ‘replicative senescence’. However, cancer cells possessing limitless replication potential can avoid senescence by the telomere maintenance mechanism
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Electro-physiology Models of Cells with Spherical Geometry with Non-conducting Center Bull. Math. Biol. (IF 1.812) Pub Date : 2020-11-19 Jiamu Jiang, Paul Smith, Mark C. W. van Rossum
We study the flow of electrical currents in spherical cells with a non-conducting core, so that current flow is restricted to a thin shell below the cell’s membrane. Examples of such cells are fat storing cells (adipocytes). We derive the relation between current and voltage in the passive regime and examine the conditions under which the cell is electro-tonically compact. We compare our results to
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Directionality of Macrophages Movement in Tumour Invasion: A Multiscale Moving-Boundary Approach Bull. Math. Biol. (IF 1.812) Pub Date : 2020-11-19 Szabolcs Suveges, Raluca Eftimie, Dumitru Trucu
Invasion of the surrounding tissue is one of the recognised hallmarks of cancer (Hanahan and Weinberg in Cell 100: 57–70, 2000. https://doi.org/10.1016/S0092-8674(00)81683-9), which is accomplished through a complex heterotypic multiscale dynamics involving tissue-scale random and directed movement of the population of both cancer cells and other accompanying cells (including here, the family of tumour-associated
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Spatial Dynamics and Spread of Ecosystem Engineers: Two Patch Analysis Bull. Math. Biol. (IF 1.812) Pub Date : 2020-11-19 Jorge Arroyo-Esquivel, Alan Hastings
Ecosystem engineers are organisms characterized by interacting with other organisms thorough physical modifications or modifying their habitat. Examples of ecosystem engineers include Spartina alterniflora cordgrass or the zebra mussel Dreissena polymorpha. For both of these, the effect of modifying the environment can be nonlocal, affecting other regions farther away from the region populated by the
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A Nonparametric Model for Analysis of Flowering Patterns of Herbaceous Multi-flowered Monocarpic Shoots Bull. Math. Biol. (IF 1.812) Pub Date : 2020-11-17 Eduard Fomin, Tatyana Fomina
One of the approaches to plant development description involves phenological curves, which represent the time variations of certain traits. Most models applied to various plant taxa and life forms describe their phenology, including flowering, at the population level, and insufficient attention is paid to the modeling at the individual one. Individual modeling is more complicated than populational
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Stochastic Turing Pattern Formation in a Model with Active and Passive Transport Bull. Math. Biol. (IF 1.812) Pub Date : 2020-11-07 Hyunjoong Kim, Paul C. Bressloff
We investigate Turing pattern formation in a stochastic and spatially discretized version of a reaction–diffusion–advection (RDA) equation, which was previously introduced to model synaptogenesis in C. elegans. The model describes the interactions between a passively diffusing molecular species and an advecting species that switches between anterograde and retrograde motor-driven transport (bidirectional
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A Mechanistic Investigation into Ischemia-Driven Distal Recurrence of Glioblastoma Bull. Math. Biol. (IF 1.812) Pub Date : 2020-11-07 Lee Curtin, Andrea Hawkins-Daarud, Alyx B. Porter, Kristoffer G. van der Zee, Markus R. Owen, Kristin R. Swanson
Glioblastoma (GBM) is the most aggressive primary brain tumor with a short median survival. Tumor recurrence is a clinical expectation of this disease and usually occurs along the resection cavity wall. However, previous clinical observations have suggested that in cases of ischemia following surgery, tumors are more likely to recur distally. Through the use of a previously established mechanistic
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A Time Scales Approach for Modeling Intermittent Hormone Therapy for Prostate Cancer Bull. Math. Biol. (IF 1.812) Pub Date : 2020-11-07 Raegan Higgins, Casey J. Mills, Angela Peace
Prostate cancer is a common cancer among males in the USA and is often treated by intermittent androgen deprivation therapy. This therapy requires a patient to alternate between periods of androgen suppression treatment and no treatment. Prostate-specific antigen levels are used to track relative changes in tumor volume of prostate cancer patients undergoing intermittent androgen deprivation therapy
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Predicting N -Strain Coexistence from Co-colonization Interactions: Epidemiology Meets Ecology and the Replicator Equation Bull. Math. Biol. (IF 1.812) Pub Date : 2020-10-29 Sten Madec, Erida Gjini
Multi-type infection processes are ubiquitous in ecology, epidemiology and social systems, but remain hard to analyze and to understand on a fundamental level. Here, we study a multi-strain susceptible-infected-susceptible model with coinfection. A host already colonized by one strain can become more or less vulnerable to co-colonization by a second strain, as a result of facilitating or competitive
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Dynamics of Vesicles Driven Into Closed Constrictions by Molecular Motors Bull. Math. Biol. (IF 1.812) Pub Date : 2020-10-23 Youngmin Park, Thomas G. Fai
We study the dynamics of a model of membrane vesicle transport into dendritic spines, which are bulbous intracellular compartments in neurons driven by molecular motors. We reduce the lubrication model proposed in Fai et al. (Phys Rev Fluids 2:113601, 2017) to a fast–slow system, yielding an analytically and numerically tractable equation equivalent to the original model in the overdamped limit. The
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Local Immunodeficiency: Role of Neutral Viruses Bull. Math. Biol. (IF 1.812) Pub Date : 2020-10-23 Leonid Bunimovich, Longmei Shu
This paper analyzes the role of neutral viruses in the phenomenon of local immunodeficiency. We show that, even in the absence of altruistic viruses, neutral viruses can support the existence of persistent viruses and thus local immunodeficiency. However, in all such cases neutral viruses can maintain only bounded (relatively small) concentration of persistent viruses. Moreover, in all such cases the
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Optimal Management of Public Perceptions During A Flu Outbreak: A Game-Theoretic Perspective Bull. Math. Biol. (IF 1.812) Pub Date : 2020-10-16 Aniruddha Deka, Buddhi Pantha, Samit Bhattacharyya
Public perceptions and sentiments play a crucial role in the success of vaccine uptake in the community. While vaccines have proven to be the best preventive method to combat the flu, the attitude and knowledge about vaccines are a major hindrance to higher uptake in most of the countries. The yearly coverage, especially in the vulnerable groups in the population, often remains below the herd immunity
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Mathematical Model of Chronic Dermal Wounds in Diabetes and Obesity Bull. Math. Biol. (IF 1.812) Pub Date : 2020-10-15 Avner Friedman, Nourridine Siewe
Chronic dermal-wound patients frequently suffer from diabetes type 2 and obesity; without treatment or early intervention, these patients are at risk of amputation. In this paper, we identified four factors that impair wound healing in these populations: excessive production of glycation, excessive production of leukotrient, decreased production of stromal derived factor (SDF-1), and insulin resistance
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Pushing the Boundaries: Models for the Spatial Spread of Ecosystem Engineers Bull. Math. Biol. (IF 1.812) Pub Date : 2020-10-15 Frithjof Lutscher, Justus Fink, Yingjie Zhu
Ecosystems engineers are species that can substantially alter their abiotic environment and thereby enhance their population growth. The net growth rate of obligate engineers is even negative unless they modify the environment. We derive and analyze a model for the spread and invasion of such species. Prior to engineering, the landscape consists of unsuitable habitat; after engineering, the habitat
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Turing Patterning in Stratified Domains Bull. Math. Biol. (IF 1.812) Pub Date : 2020-10-15 Andrew L. Krause, Václav Klika, Jacob Halatek, Paul K. Grant, Thomas E. Woolley, Neil Dalchau, Eamonn A. Gaffney
Reaction–diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal–mesenchymal coupling in development, and symmetry-breaking in cell polarization. We develop a modeling framework for bilayer reaction–diffusion systems and relate it to a range of existing models. We derive conditions for diffusion-driven instability of
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Cholesterol Regulation in Age-Related Macular Degeneration: A Framework for Mathematical Modelling of Drusen Biogenesis Bull. Math. Biol. (IF 1.812) Pub Date : 2020-10-12 Ronél Scheepers, Graeme J. Pettet, Peter van Heijster, Robyn P. Araujo
In age-related macular degeneration (AMD), there is, in common with many other age-related diseases, the need to distinguish between changes in the ageing eye that lead to disease and those changes that are considered part of a healthy, ageing eye. Various studies investigating the multitude of mechanisms involved in the aetiology of AMD exist within the field of ophthalmology and related medical fields
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Modeling Progressive Damage Accumulation in Bone Remodeling Explains the Thermodynamic Basis of Bone Resorption by Overloading Bull. Math. Biol. (IF 1.812) Pub Date : 2020-10-10 T. J. Sego, Yung-Ting Hsu, Tien-Min Chu, Andres Tovar
Computational modeling of skeletal tissue seeks to predict the structural adaptation of bone in response to mechanical loading. The theory of continuum damage–repair, a mathematical description of structural adaptation based on principles of damage mechanics, continues to be developed and utilized for the prediction of long-term peri-implant outcomes. Despite its technical soundness, CDR does not account
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On the Problem of Reconstructing a Mixture of rna Structures Bull. Math. Biol. (IF 1.812) Pub Date : 2020-10-07 Torin Greenwood, Christine E. Heitsch
A growing number of rna sequences are now known to exist in some distribution with two or more different stable structures. Recent algorithms attempt to reconstruct such mixtures using the list of nucleotides in a sequence in conjunction with auxiliary experimental footprinting data. In this paper, we demonstrate some challenges which remain in addressing this problem; in particular we consider the
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Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models Bull. Math. Biol. (IF 1.812) Pub Date : 2020-10-06 Sonja Mathias, Adrien Coulier, Anass Bouchnita, Andreas Hellander
Centre-based or cell-centre models are a framework for the computational study of multicellular systems with widespread use in cancer modelling and computational developmental biology. At the core of these models are the numerical method used to update cell positions and the force functions that encode the pairwise mechanical interactions of cells. For the latter, there are multiple choices that could
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Are Two-Patch Models Sufficient? The Evolution of Dispersal and Topology of River Network Modules Bull. Math. Biol. (IF 1.812) Pub Date : 2020-10-06 Hongyan Jiang, King-Yeung Lam, Yuan Lou
We study the dynamics of two competing species in three-patch models and illustrate how the topology of directed river network modules may affect the evolution of dispersal. Each model assumes that patch 1 is at the upstream end, patch 3 is at the downstream end, but patch 2 could be upstream, or middle stream, or downstream, depending on the specific topology of the modules. We posit that individuals
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Mechanical Cell Competition in Heterogeneous Epithelial Tissues. Bull. Math. Biol. (IF 1.812) Pub Date : 2020-09-26 Ryan J Murphy,Pascal R Buenzli,Ruth E Baker,Matthew J Simpson
Mechanical cell competition is important during tissue development, cancer invasion, and tissue ageing. Heterogeneity plays a key role in practical applications since cancer cells can have different cell stiffness and different proliferation rates than normal cells. To study this phenomenon, we propose a one-dimensional mechanical model of heterogeneous epithelial tissue dynamics that includes cell-length-dependent
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Large-Scale Dynamics of Self-propelled Particles Moving Through Obstacles: Model Derivation and Pattern Formation Bull. Math. Biol. (IF 1.812) Pub Date : 2020-09-25 P. Aceves-Sanchez, P. Degond, E. E. Keaveny, A. Manhart, S. Merino-Aceituno, D. Peurichard
We model and study the patterns created through the interaction of collectively moving self-propelled particles (SPPs) and elastically tethered obstacles. Simulations of an individual-based model reveal at least three distinct large-scale patterns: travelling bands, trails and moving clusters. This motivates the derivation of a macroscopic partial differential equations model for the interactions between
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Electrical Propagation of Vasodilatory Signals in Capillary Networks. Bull. Math. Biol. (IF 1.812) Pub Date : 2020-09-23 Pilhwa Lee
We have developed a computational model to study electrical propagation of vasodilatory signals and arteriolar regulation of blood flow depending on the oxygen tension and agonist distribution in the capillary network. The involving key parameters of endothelial cell-to-cell electrical conductivity and plasma membrane area per unit volume were calibrated with the experimental data on an isolated endothelial
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Changing the Nature of Quantitative Biology Education: Data Science as a Driver. Bull. Math. Biol. (IF 1.812) Pub Date : 2020-09-19 Raina S Robeva,John R Jungck,Louis J Gross
We live in a data-rich world with rapidly growing databases with zettabytes of data. Innovation, computation, and technological advances have now tremendously accelerated the pace of discovery, providing driverless cars, robotic devices, expert healthcare systems, precision medicine, and automated discovery to mention a few. Even though the definition of the term data science continues to evolve, the
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Renewal Reward Perspective on Linear Switching Diffusion Systems in Models of Intracellular Transport. Bull. Math. Biol. (IF 1.812) Pub Date : 2020-09-16 Maria-Veronica Ciocanel,John Fricks,Peter R Kramer,Scott A McKinley
In many biological systems, the movement of individual agents is characterized having multiple qualitatively distinct behaviors that arise from a variety of biophysical states. For example, in cells the movement of vesicles, organelles, and other intracellular cargo is affected by their binding to and unbinding from cytoskeletal filaments such as microtubules through molecular motor proteins. A typical
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Why Males Compete Rather Than Care, with an Application to Supplying Collective Goods. Bull. Math. Biol. (IF 1.812) Pub Date : 2020-09-16 Sara L Loo,Danya Rose,Michael Weight,Kristen Hawkes,Peter S Kim
The question of why males invest more into competition than offspring care is an age-old problem in evolutionary biology. On the one hand, paternal care could increase the fraction of offspring surviving to maturity. On the other hand, competition could increase the likelihood of more paternities and thus the relative number of offspring produced. While drivers of these behaviours are often intertwined
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Modeling the Effect of Memory in the Adaptive Immune Response. Bull. Math. Biol. (IF 1.812) Pub Date : 2020-09-14 Asia Wyatt,Doron Levy
It is well understood that there are key differences between a primary immune response and subsequent responses. Specifically, memory T cells that remain after a primary response drive the clearance of antigen in later encounters. While the existence of memory T cells is widely accepted, the specific mechanisms that govern their function are generally debated. In this paper, we develop a mathematical
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Impossibility of Consistent Distance Estimation from Sequence Lengths Under the TKF91 Model. Bull. Math. Biol. (IF 1.812) Pub Date : 2020-09-13 Wai-Tong Louis Fan,Brandon Legried,Sebastien Roch
We consider the problem of distance estimation under the TKF91 model of sequence evolution by insertions, deletions and substitutions on a phylogeny. In an asymptotic regime where the expected sequence lengths tend to infinity, we show that no consistent distance estimation is possible from sequence lengths alone. More formally, we establish that the distributions of pairs of sequence lengths at different
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Traveling Waves and Estimation of Minimal Wave Speed for a Diffusive Influenza Model with Multiple Strains. Bull. Math. Biol. (IF 1.812) Pub Date : 2020-09-13 Guoting Chen,Xinchu Fu,Mengfeng Sun
Antiviral treatment remains one of the key pharmacological interventions against influenza pandemic. However, widespread use of antiviral drugs brings with it the danger of drug resistance evolution. To assess the risk of the emergence and diffusion of resistance, in this paper, we develop a diffusive influenza model where influenza infection involves both drug-sensitive and drug-resistant strains
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Epidemic Dynamics and Adaptive Vaccination Strategy: Renewal Equation Approach. Bull. Math. Biol. (IF 1.812) Pub Date : 2020-09-13 Aubain Nzokem,Neal Madras
We use analytical methods to investigate a continuous vaccination strategy’s effects on the infectious disease dynamics in a closed population and a demographically open population. The methodology and key assumptions are based on Breda et al. (J Biol Dyn 6(Sup2):103–117, 2012). We show that the cumulative force of infection for the closed population and the endemic force of infection in the demographically
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Mathematical Biology: Expand, Expose, and Educate! Bull. Math. Biol. (IF 1.812) Pub Date : 2020-09-10 Shernita Lee,LaShania Clinedinst
Mathematical biology has made significant contributions and advancements in the biological sciences. Recruitment efforts focus on encouraging students, especially those who are underrepresented and underserved, to pursue the field of mathematical biology, regardless of their undergraduate institution type, and raise awareness about the countless professional and academic possibilities provided by this
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Learning Equations from Biological Data with Limited Time Samples. Bull. Math. Biol. (IF 1.812) Pub Date : 2020-09-09 John T Nardini,John H Lagergren,Andrea Hawkins-Daarud,Lee Curtin,Bethan Morris,Erica M Rutter,Kristin R Swanson,Kevin B Flores
Equation learning methods present a promising tool to aid scientists in the modeling process for biological data. Previous equation learning studies have demonstrated that these methods can infer models from rich datasets; however, the performance of these methods in the presence of common challenges from biological data has not been thoroughly explored. We present an equation learning methodology
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Optimal Control of the COVID-19 Pandemic with Non-pharmaceutical Interventions. Bull. Math. Biol. (IF 1.812) Pub Date : 2020-09-04 T Alex Perkins,Guido España
The COVID-19 pandemic has forced societies across the world to resort to social distancing to slow the spread of the SARS-CoV-2 virus. Due to the economic impacts of social distancing, there is growing desire to relax these measures. To characterize a range of possible strategies for control and to understand their consequences, we performed an optimal control analysis of a mathematical model of SARS-CoV-2
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Detailed Balance [Formula: see text] Complex Balance [Formula: see text] Cycle Balance: A Graph-Theoretic Proof for Reaction Networks and Markov Chains. Bull. Math. Biol. (IF 1.812) Pub Date : 2020-09-03 Stefan Müller,Badal Joshi
We further clarify the relation between detailed-balanced and complex-balanced equilibria of reversible chemical reaction networks. Our results hold for arbitrary kinetics and also for boundary equilibria. Detailed balance, complex balance, “formal balance,” and the new notion of “cycle balance” are all defined in terms of the underlying graph. This fact allows elementary graph-theoretic (non-algebraic)
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Mathematical Biology Education: Changes, Communities, Connections, and Challenges. Bull. Math. Biol. (IF 1.812) Pub Date : 2020-09-04 John R Jungck,Raina Robeva,Louis J Gross
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The Case for Algebraic Biology: from Research to Education. Bull. Math. Biol. (IF 1.812) Pub Date : 2020-08-20 Matthew Macauley,Nora Youngs
Though it goes without saying that linear algebra is fundamental to mathematical biology, polynomial algebra is less visible. In this article, we will give a brief tour of four diverse biological problems where multivariate polynomials play a central role—a subfield that is sometimes called algebraic biology. Namely, these topics include biochemical reaction networks, Boolean models of gene regulatory
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Effects of Latency on Estimates of the COVID-19 Replication Number. Bull. Math. Biol. (IF 1.812) Pub Date : 2020-08-20 Lorenzo Sadun
There is continued uncertainty in how long it takes a person infected by the COVID-19 virus to become infectious. In this paper, we quantify how this uncertainty affects estimates of the basic replication number \(R_0\), and thus estimates of the fraction of the population that would become infected in the absence of effective interventions. The analysis is general, and applies to all SEIR-based models
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A Non-local Cross-Diffusion Model of Population Dynamics II: Exact, Approximate, and Numerical Traveling Waves in Single- and Multi-species Populations. Bull. Math. Biol. (IF 1.812) Pub Date : 2020-08-11 Andrew L Krause,Robert A Van Gorder
We study traveling waves in a non-local cross-diffusion-type model, where organisms move along gradients in population densities. Such models are valuable for understanding waves of migration and invasion and how directed motion can impact such scenarios. In this paper, we demonstrate the emergence of traveling wave solutions, studying properties of both planar and radial wave fronts in one- and two-species
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A Non-local Cross-Diffusion Model of Population Dynamics I: Emergent Spatial and Spatiotemporal Patterns. Bull. Math. Biol. (IF 1.812) Pub Date : 2020-08-11 Nick P Taylor,Hyunyeon Kim,Andrew L Krause,Robert A Van Gorder
We extend a spatially non-local cross-diffusion model of aggregation between multiple species with directed motion toward resource gradients to include many species and more general kinds of dispersal. We first consider diffusive instabilities, determining that for directed motion along fecundity gradients, the model permits the Turing instability leading to colony formation and persistence provided
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Basic Reproduction Numbers for a Class of Reaction-Diffusion Epidemic Models. Bull. Math. Biol. (IF 1.812) Pub Date : 2020-08-09 Chayu Yang,Jin Wang
We study the basic reproduction numbers for a class of reaction-diffusion epidemic models that are developed from autonomous ODE systems. We present a general numerical framework to compute such basic reproduction numbers; meanwhile, the numerical formulation provides useful insight into their characterizations. Using matrix analysis, we show that the basic reproduction numbers are the same for these
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On Nonlinear Pest/Vector Control via the Sterile Insect Technique: Impact of Residual Fertility. Bull. Math. Biol. (IF 1.812) Pub Date : 2020-08-09 M Soledad Aronna,Yves Dumont
We consider a minimalist model for the Sterile Insect Technique (SIT), assuming that residual fertility can occur in the sterile male population. Taking into account that we are able to get regular measurements from the biological system along the control duration, such as the size of the wild insect population, we study different control strategies that involve either continuous or periodic impulsive
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