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Applied Mathematics

Virginia Commonwealth University

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Full-Text Articles in Physical Sciences and Mathematics

A Game-Theoretic Model Of Monkeypox To Assess Vaccination Strategies, Sri Vibhaav Bankuru, Samuel Kossol, William Hou, Parsa Mahmoudi, Jan Rychtář, Dewey Taylor Jan 2020

A Game-Theoretic Model Of Monkeypox To Assess Vaccination Strategies, Sri Vibhaav Bankuru, Samuel Kossol, William Hou, Parsa Mahmoudi, Jan Rychtář, Dewey Taylor

Mathematics and Applied Mathematics Publications

Monkeypox (MPX) is a zoonotic disease similar to smallpox. Its fatality rate is about 11% and it is endemic to the Central and West African countries. In this paper, we analyze a compartmental model of MPX dynamics. Our goal is to see whether MPX can be controlled and eradicated by voluntary vaccinations. We show that there are three equilibria—disease free, fully endemic and previously neglected semi-endemic (with disease existing only among humans). The existence of semi-endemic equilibrium has severe implications should the MPX virus mutate to increased viral fitness in humans. We find that MPX is controllable and can be …

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Identifying Important Parameters In The Inflammatory Process With A Mathematical Model Of Immune Cell Influx And Macrophage Polarization, Marcella Torres, Jing Wang, Paul J. Yannie, Shobha Ghosh, Rebecca A. Segal, Angela M. Reynolds Jan 2019

Identifying Important Parameters In The Inflammatory Process With A Mathematical Model Of Immune Cell Influx And Macrophage Polarization, Marcella Torres, Jing Wang, Paul J. Yannie, Shobha Ghosh, Rebecca A. Segal, Angela M. Reynolds

Mathematics and Applied Mathematics Publications

In an inflammatory setting, macrophages can be polarized to an inflammatory M1 phenotype or to an anti-inflammatory M2 phenotype, as well as existing on a spectrum between these two extremes. Dysfunction of this phenotypic switch can result in a population imbalance that leads to chronic wounds or disease due to unresolved inflammation. Therapeutic interventions that target macrophages have therefore been proposed and implemented in diseases that feature chronic inflammation such as diabetes mellitus and atherosclerosis. We have developed a model for the sequential influx of immune cells in the peritoneal cavity in response to a bacterial stimulus that includes macrophage …

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Classification Of Symmetry Lie Algebras Of The Canonical Geodesic Equations Of Five-Dimensional Solvable Lie Algebras, Hassan Almusawa, Ryad Ghanam, Gerard Thompson Jan 2019

Classification Of Symmetry Lie Algebras Of The Canonical Geodesic Equations Of Five-Dimensional Solvable Lie Algebras, Hassan Almusawa, Ryad Ghanam, Gerard Thompson

Mathematics and Applied Mathematics Publications

In this investigation, we present symmetry algebras of the canonical geodesic equations of the indecomposable solvable Lie groups of dimension five, confined to algebras A_{5,7}^{abc} to A_{18}^a. For each algebra, the related system of geodesics is provided. Moreover, a basis for the associated Lie algebra of the symmetry vector fields, as well as the corresponding nonzero brackets, are constructed and categorized.

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Theoretical Open-Loop Model Of Respiratory Mechanics In The Extremely Preterm Infant, Laura Ellwein Fix, Joseph Khoury, Russell R. Moores Jr., Lauren Linkous, Matthew Brandes, Henry J. Rozycki Jan 2018

Theoretical Open-Loop Model Of Respiratory Mechanics In The Extremely Preterm Infant, Laura Ellwein Fix, Joseph Khoury, Russell R. Moores Jr., Lauren Linkous, Matthew Brandes, Henry J. Rozycki

Mathematics and Applied Mathematics Publications

Non-invasive ventilation is increasingly used for respiratory support in preterm infants, and is associated with a lower risk of chronic lung disease. However, this mode is often not successful in the extremely preterm infant in part due to their markedly increased chest wall compliance that does not provide enough structure against which the forces of inhalation can generate sufficient pressure. To address the continued challenge of studying treatments in this fragile population, we developed a nonlinear lumped-parameter respiratory system mechanics model of the extremely preterm infant that incorporates nonlinear lung and chest wall compliances and lung volume parameters tuned to …

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Code For "Noise-Enhanced Coding In Phasic Neuron Spike Trains", Cheng Ly, Brent D. Doiron Jan 2017

Code For "Noise-Enhanced Coding In Phasic Neuron Spike Trains", Cheng Ly, Brent D. Doiron

Statistical Sciences and Operations Research Data

This zip file contains Matlab scripts and ode (XPP) files to calculate the statistics of the models in "Noise-Enhanced Coding in Phasic Neuron Spike Trains". This article is published in PLoS ONE.

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A Two-Species Stage-Structured Model For West Nile Virus Transmission, Taylor A. Beebe, Suzanne L. Robertson Jan 2017

A Two-Species Stage-Structured Model For West Nile Virus Transmission, Taylor A. Beebe, Suzanne L. Robertson

Mathematics and Applied Mathematics Publications

We develop a host–vector model of West Nile virus (WNV) transmission that incorporates multiple avian host species as well as host stage-structure (juvenile and adult stages), allowing for both species-specific and stage-specific biting rates of vectors on hosts. We use this ordinary differential equation model to explore WNV transmission dynamics that occur between vectors and multiple structured host populations as a result of heterogeneous biting rates on species and/or life stages. Our analysis shows that increased exposure of juvenile hosts generally results in larger outbreaks of WNV infectious vectors when compared to differential host species exposure. We also find that …

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A Theoretical Framework For Analyzing Coupled Neuronal Networks: Application To The Olfactory System, Andrea K. Barreiro, Shree Hari Gautam, Woodrow L. Shew, Cheng Ly Jan 2017

A Theoretical Framework For Analyzing Coupled Neuronal Networks: Application To The Olfactory System, Andrea K. Barreiro, Shree Hari Gautam, Woodrow L. Shew, Cheng Ly

Mathematics and Applied Mathematics Publications

Determining how synaptic coupling within and between regions is modulated during sensory processing is an important topic in neuroscience. Electrophysiological recordings provide detailed information about neural spiking but have traditionally been confined to a particular region or layer of cortex. Here we develop new theoretical methods to study interactions between and within two brain regions, based on experimental measurements of spiking activity simultaneously recorded from the two regions. By systematically comparing experimentally-obtained spiking statistics to (efficiently computed) model spike rate statistics, we identify regions in model parameter space that are consistent with the experimental data. We apply our new technique …

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A Mathematical System For Human Implantable Wound Model Studies, Salomonsky Paul-Michael, Rebecca Segal Jan 2017

A Mathematical System For Human Implantable Wound Model Studies, Salomonsky Paul-Michael, Rebecca Segal

Mathematics and Applied Mathematics Publications

In this work, we present a mathematical model, which accounts for two fundamental processes involved in the repair of an acute dermal wound. These processes include the inflammatory response and fibroplasia. Our system describes each of these events through the time evolution of four primary species or variables. These include the density of initial damage, inflammatory cells, fibroblasts and deposition of new collagen matrix. Since it is difficult to populate the equations of our model with coefficients that have been empirically derived, we fit these constants by carrying out a large number of simulations until there is reasonable agreement between …

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Management Of Invasive Allee Species, David Chan, C. M. Kent, D. M. Johnson Jan 2017

Management Of Invasive Allee Species, David Chan, C. M. Kent, D. M. Johnson

Mathematics and Applied Mathematics Publications

In this study, we use a discrete, two-patch population model of an Allee species to examine different methods in managing invasions. We first analytically examine the model to show the presence of the strong Allee effect, and then we numerically explore the model to test the effectiveness of different management strategies. As expected invasion is facilitated by lower Allee thresholds, greater carrying capacities and greater proportions of dispersers. These effects are interacting, however, and moderated by population growth rate. Using the gypsy moth as an example species, we demonstrate that the effectiveness of different invasion management strategies is context-dependent, combining …

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Dynamics Of Planar Systems That Model Stage-Structured Populations, N. Lazaryan, Hassan Sedaghat Jan 2015

Dynamics Of Planar Systems That Model Stage-Structured Populations, N. Lazaryan, Hassan Sedaghat

Mathematics and Applied Mathematics Publications

We study a general discrete planar system for modeling stage-structured populations. Our results include conditions for the global convergence of orbits to zero (extinction) when the parameters (vital rates) are time and density dependent. When the parameters are periodic we obtain weaker conditions for extinction. We also study a rational special case of the system for Beverton-Holt type interactions and show that the persistence equilibrium (in the positive quadrant) may be globally attracting even in the presence of interstage competition. However, we determine that with a sufficiently high level of competition, the persistence equilibrium becomes unstable (a saddle point) and …

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Firing Rate Dynamics In Recurrent Spiking Neural Networks With Intrinsic And Network Heterogeneity, Cheng Ly Jan 2015

Firing Rate Dynamics In Recurrent Spiking Neural Networks With Intrinsic And Network Heterogeneity, Cheng Ly

Statistical Sciences and Operations Research Publications

Heterogeneity of neural attributes has recently gained a lot of attention and is increasing recognized as a crucial feature in neural processing. Despite its importance, this physiological feature has traditionally been neglected in theoretical studies of cortical neural networks. Thus, there is still a lot unknown about the consequences of cellular and circuit heterogeneity in spiking neural networks. In particular, combining network or synaptic heterogeneity and intrinsic heterogeneity has yet to be considered systematically despite the fact that both are known to exist and likely have significant roles in neural network dynamics. In a canonical recurrent spiking neural network model, …

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Periodic And Chaotic Orbits Of A Discrete Rational System, N. Lazaryan, Hassan Sedaghat Jan 2015

Periodic And Chaotic Orbits Of A Discrete Rational System, N. Lazaryan, Hassan Sedaghat

Mathematics and Applied Mathematics Publications

We study a rational planar system consisting of one linear-affine and one linear-fractional difference equation. If all of the system’s parameters are positive (so that the positive quadrant is invariant and the system is continuous), then we show that the unique fixed point of the system in the positive quadrant cannot be repelling and the system does not have a snap-back repeller. By folding the system into a second-order equation, we find special cases of the system with some negative parameter values that do exhibit chaos in the sense of Li and Yorke within the positive quadrant of the plane.

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Random Processes With Convex Coordinates On Triangular Graphs, J. N. Boyd, P. N. Raychowdhury Jan 1997

Random Processes With Convex Coordinates On Triangular Graphs, J. N. Boyd, P. N. Raychowdhury

Mathematics and Applied Mathematics Publications

Probabilities for reaching specified destinations and expectation values for lengths for random walks on triangular arrays of points and edges are computed. Probabilities and expectation values are given as functions of the convex (barycentric) coordinates of the starting point.

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Computations For A Vibrating System Diagonalize The Variance, J. N. Boyd, P. N. Raychowdhury Jan 1995

Computations For A Vibrating System Diagonalize The Variance, J. N. Boyd, P. N. Raychowdhury

Mathematics and Applied Mathematics Publications

The transformations to diagonalize potential energy matrices for coupled harmonic oscillators will also diagonalize the variance when written in matrix form. After a brief review of a geometrical interpretation of the variance, the transformations are described and an example is given.

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Hankel Transforms In Generalized Fock Spaces, John Schmeelk Jan 1994

Hankel Transforms In Generalized Fock Spaces, John Schmeelk

Mathematics and Applied Mathematics Publications

A classical Fock space consists of functions of the form,ϕ↔(ϕ0,ϕ1,…,ϕq),where ϕ0∈ℂ and ϕq∈Lp(ℝq), q≥1. We will replace the ϕq, q≥1 with test functions having Hankel transforms. This space is a natural generalization of a classical Fock space as seen by expanding functionals having abstract Taylor Series. The particular coefficients of such series are multilinear functionals having distributions as their domain. Convergence requirements set forth are somewhat in the spirit of ultra differentiable functions and ultra distribution theory. The Hankel transform oftentimes implemented in Cauchy problems will be introduced into this setting. A theorem will be proven relating the convergence of …

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A Double Chain Of Coupled Circuits In Analogy With Mechanical Lattices, J. N. Boyd, P. N. Raychowdhury Jan 1991

A Double Chain Of Coupled Circuits In Analogy With Mechanical Lattices, J. N. Boyd, P. N. Raychowdhury

Mathematics and Applied Mathematics Publications

A unitary transformation obtained from group theoretical considerations is applied to the problem of finding the resonant frequencies of a system of coupled LC-circuits. This transformation was previously derived to separate the equations of motion for one dimensional mechanical lattices. Computations are performed in matrix notation. The electrical system is an analog of a pair of coupled linear lattices. After the resonant frequencies have been found, comparisons between the electrical and mechanical systems are noted.

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