Other Applied Mathematics Commons^™

Stability Of Modified Host-Parasitoid Model With Allee Effect, Özlem A. Gümüs, A. G. Maria Selvam, R. Janagaraj

Applications and Applied Mathematics: An International Journal (AAM)

This paper deals with a host-parasitoid model subject to Allee effect and its dynamical behavior. Steady state points of the proposed host-parasitoid model are computed. Stability properties are analyzed with eigen values of Jacobian matrix which are determined at the steady states. Theoretical findings are supported by numerical illustrations and enhanced by pictorial representations such as bifurcation diagrams, phase portraits and local amplifications for different parameter values. Existence of chaotic behavior in the system is established via bifurcation and sensitivity analysis of the system at the initial conditions. Various phase portraits are simulated for a better understanding of the qualitative …

Density-Dependent Development Impacts The Success Of Wolbachia-Based Mosquito Control Programs, Alyssa Petroski, Lauren M. Childs, Michael Andrew Robert

Biology and Medicine Through Mathematics Conference

No abstract provided.

On The Properties Of Solutions Of A Cross-Diffusion System With Nonlinear Boundary Flux, Zafar Rakhmonov, Jasur Urunbaev, Bobur Allaberdiyev

Scientific Journal of Samarkand University

In this paper, based on a self-similar analysis and the method of standard equations, the properties of a nonlinear cross-diffusion system coupled via nonlocal boundary conditions are studied. We are investigated the qualitative properties of solutions of a nonlinear system of parabolic equations of cross-diffusion in a medium coupled with nonlinear boundary conditions. It is proved that for certain values of the numerical parameters of the nonlinear cross-diffusion system of parabolic equations coupled via nonlinear boundary conditions, they may not have global solutions in time. Based on a self-similar analysis and the principle of comparing solutions, a critical exponent of …

A Demographic Model Of An Endangered Florida Native Bromeliad (Tillandsia Utriculata), Zoe S. Brookover, Alexandra M. Campbell, Brian D. Christman, Sydney L. Davis, Erin N. Bodine

Spora: A Journal of Biomathematics

The large, long-lived, epiphytic bromeliad Tillandsia utriculata is currently listed as state-endangered in Florida due to significant population reduction from predation by an invasive weevil, Metamasius callizona. We have developed a novel demographic model of a population of T. utriculata in Myakka River State Park (MRSP) in Sarasota, Florida using a stage-structured matrix model. Analysis of the model revealed conditions for population viability over a variety of parameter scenarios. Model analysis showed that without weevil predation the minimum germination rate required for population viability is low (4–16%), and that given a viable population at structural equilibrium we would expect …

Analysis Of An Agent-Based Model For Predicting The Behavior Of Bighead Carp (Hypophthalmichthys Nobilis) Under The Influence Of Acoustic Deterrence, Craig Garzella, Joseph Gaudy, Karl R. B. Schmitt, Arezu Mansuri

Spora: A Journal of Biomathematics

Bighead carp (Hypophthalmichthys nobilis) are an invasive, voracious, highly fecund species threatening the ecological integrity of the Great Lakes. This agent-based model and analysis explore bighead carp behavior in response to acoustic deterrence in an effort to discover properties that increase likelihood of deterrence system failure. Results indicate the most significant (p < 0.05) influences on barrier failure are the quantity of detritus and plankton behind the barrier, total number of bighead carp successfully deterred by the barrier, and number of native fishes freely moving throughout the simulation. Quantity of resources behind the barrier influence bighead carp to penetrate when populations are resource deprived. When native fish populations are low, an accumulation of phytoplankton can occur, increasing the likelihood of an algal bloom occurrence. Findings of this simulation suggest successful implementation with proper maintenance of an acoustic deterrence system has potential of abating the threat of bighead carp on ecological integrity of the Great Lakes.

Individual Based Model To Simulate The Evolution Of Insecticide Resistance, William B. Jamieson

Department of Mathematics: Dissertations, Theses, and Student Research

Insecticides play a critical role in agricultural productivity. However, insecticides impose selective pressures on insect populations, so the Darwinian principles of natural selection predict that resistance to the insecticide is likely to form in the insect populations. Insecticide resistance, in turn, severely reduces the utility of the insecticides being used. Thus there is a strong economic incentive to reduce the rate of resistance evolution. Moreover, resistance evolution represents an example of evolution under novel selective pressures, so its study contributes to the fundamental understanding of evolutionary theory.

Insecticide resistance often represents a complex interplay of multiple fitness trade-offs for individual …

An Agent-Based Modeling Approach For Predicting The Behavior Of Bighead Carp (Hypophthalmichthys Nobilis) Under The Influence Of Acoustic Deterrence, Joey Gaudy, Craig Garzella

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Network Reconstruction Using Computational Algebra And Gene Knockouts, Matthew Macauley

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Simulating Bacterial Growth, Competition, And Resistance With Agent-Based Models And Laboratory Experiments, Anne E. Yust, Davida S. Smyth

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Engaging Undergraduates In Research In Mathematical Biology With Limited Resources, Timothy Comar

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

The Energy-Spectrum Of Bicompatible Sequences, Wenda Huang

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Quantifying Pollen Traits To Build A Mathematical Model Of Pollen Competition - A Biologist's Perspective, Rob Swanson, Alex Capaldi

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Analysis Of An Agent-Based Model For Integrated Pest Management With Periodic Control Strategies, Timothy Comar

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Qualitative Analysis Of A Modified Leslie-Gower Predator-Prey Model With Weak Allee Effect Ii, Manoj K. Singh, B. S. Bhadauria

Applications and Applied Mathematics: An International Journal (AAM)

The article aims to study a modified Leslie-Gower predator-prey model with Allee effect II, affecting the functional response with the assumption that the extent to which the environment provides protection to both predator and prey is the same. The model has been studied analytically as well as numerically, including stability and bifurcation analysis. Compared with the predator-prey model without Allee effect, it is found that the weak Allee effect II can bring rich and complicated dynamics, such as the model undergoes to a series of bifurcations (Homoclinic, Hopf, Saddle-node and Bogdanov-Takens). The existence of Hopf bifurcation has been shown for …

Do Metabolic Networks Follow A Power Law? A Psamm Analysis, Ryan Geib, Lubos Thoma, Ying Zhang

Senior Honors Projects

Inspired by the landmark paper “Emergence of Scaling in Random Networks” by Barabási and Albert, the field of network science has focused heavily on the power law distribution in recent years. This distribution has been used to model everything from the popularity of sites on the World Wide Web to the number of citations received on a scientific paper. The feature of this distribution is highlighted by the fact that many nodes (websites or papers) have few connections (internet links or citations) while few “hubs” are connected to many nodes. These properties lead to two very important observed effects: the …

Determination Of Optimal Parameter Estimates For Medical Interventions In Human Metabolism And Inflammation, Marcella Torres

Theses and Dissertations

In this work we have developed three ordinary differential equation models of biological systems: body mass change in response to exercise, immune system response to a general inflammatory stimulus, and the immune system response in atherosclerosis. The purpose of developing such computational tools is to test hypotheses about the underlying biological processes that drive system outcomes as well as possible real medical interventions. Therefore, we focus our analysis on understanding key interactions between model parameters and outcomes to deepen our understanding of these complex processes as a means to developing effective treatments in obesity, sarcopenia, and inflammatory diseases.

We develop …

Using Canalization For The Control Of Discrete Networks, David Murrugarra

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Extreme Climate Events And The Ecological Dynamics Of Plant-Herbivore Interactions, David C. Elzinga, Christopher A. Klausmeier, William C. Wetzel

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Intercropping In Semi-Arid India: An Analysis Of Risks And Trade Offs, Jack Pringle

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Parameter Sensitivity For In Vitro Anthrax Studies, Yareley Gonzalez, Maria Macias-Bedolla, Megan O. Powell

Spora: A Journal of Biomathematics

Studies done on interactions between spores and macrophages done in vitro show inconsistent results based on experimental protocol and inhibit meaningful extrapolation to in vivo. In this study, we perform a sensitivity analysis of a model representing in vitro studies of interactions between anthrax spores and macrophages to help address the effects of these inconsistencies. We perform both local and global analyses using Latin hypercube sampling and partial rank correlation coefficients. Our analysis indicates the amount of intracellular bacteria over time is most sensitive to the killing of intracellular bacteria by the macrophages and replication of the bacteria inside …

Evaluation Of Drug-Loaded Gold Nanoparticle Cytotoxicity As A Function Of Tumor Tissue Heterogeneity., Hunter Allan Miller

Electronic Theses and Dissertations

The inherent heterogeneity of tumor tissue presents a major challenge to nanoparticle-medicated drug delivery. This heterogeneity spans from the molecular to the cellular (cell types) and to the tissue (vasculature, extra-cellular matrix) scales. Here we employ computational modeling to evaluate therapeutic response as a function of vascular-induced tumor tissue heterogeneity. Using data with three-layered gold nanoparticles loaded with cisplatin, nanotherapy is simulated with different levels of tissue heterogeneity, and the treatment response is measured in terms of tumor regression. The results show that tumor vascular density non-trivially influences the nanoparticle uptake and washout, and the associated tissue response. The drug …

Staged Hiv Transmission And Treatment In A Dynamic Model With Concurrency, Katharine Gurski, Kathleen Hoffman

Biology and Medicine Through Mathematics Conference

No abstract provided.

Brightness Perception Involves Local Adaptation Opposed By Lateral Interaction, Qasim Zaidi, Romain Bachy, Jose-Manuel Alonso

MODVIS Workshop

No abstract provided.

Generating Species Assemblages For Restoration And Experimentation: A New Method That Can Simultaneously Converge On Average Trait Values And Maximize Functional Diversity, David C. Laughlin, Loïc Chalmandrier, Chaitanya Joshi, Michael Renton, John M. Dwyer, Jennifer L. Funk

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

1.Restoring resilient ecosystems in an era of rapid environmental change requires a flexible framework for selecting assemblages of species based on functional traits. However, current trait‐based models have been limited to algorithms that select species assemblages that only converge on specified average trait values, and could not accommodate the common desire among restoration ecologists to generate functionally diverse assemblages.

2.We have solved this problem by applying a nonlinear optimization algorithm to solve for the species relative abundances that maximize Rao's quadratic entropy (Q) subject to other linear constraints. Rao's Q is a closed‐form algebraic expression of functional diversity …

Effect Of Neuromodulation Of Short-Term Plasticity On Information Processing In Hippocampal Interneuron Synapses, Elham Bayat Mokhtari

Graduate Student Theses, Dissertations, & Professional Papers

Neurons convey information about the complex dynamic environment in the form of signals. Computational neuroscience provides a theoretical foundation toward enhancing our understanding of nervous system. The aim of this dissertation is to present techniques to study the brain and how it processes information in particular neurons in hippocampus.

We begin with a brief review of the history of neuroscience and biological background of basic neurons. To appreciate the importance of information theory, familiarity with the information theoretic basics is required, these basics are presented in Chapter 2. In Chapter 3, we use information theory to estimate the amount of …

Homogenization Techniques For Population Dynamics In Strongly Heterogeneous Landscapes, Brian P. Yurk, Christina A. Cobbold

Faculty Publications

An important problem in spatial ecology is to understand how population-scale patterns emerge from individual-level birth, death, and movement processes. These processes, which depend on local landscape characteristics, vary spatially and may exhibit sharp transitions through behavioural responses to habitat edges, leading to discontinuous population densities. Such systems can be modelled using reaction–diffusion equations with interface conditions that capture local behaviour at patch boundaries. In this work we develop a novel homogenization technique to approximate the large-scale dynamics of the system. We illustrate our approach, which also generalizes to multiple species, with an example of logistic growth within a periodic …

Modeling Aggregation Of Proliferating Microglia In Response To Amyloid-Beta In Dementia, Adrienne C. Kinney, Ellen R. Swanson

Spora: A Journal of Biomathematics

Amyloid-beta plaques are prominent biological markers in dementia brains. In response to plaque formation, the brain's immune cells, microglia, become reactive. Microglia are measurable cells that surround amyloid-beta plaques, indicating their location. A system of partial differential equations describes the concentration of microglia in dementia brains by incorporating chemotactic signaling. However, this system fails to incorporate increasing numbers of reactive microglia cells in response to amyloid-beta aggregation. A system of ordinary differential equations describing the number of significant cells and proteins in the brain suggests the amount of reactive microglia increases significantly during the progression of dementia. We couple these …

Development Of Epithelial Tissues: How Are Cleavage Planes Chosen?, Ying Xin

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Medicine: Modeling Disease And Treatment, Lisette Depillis

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Uncovering Functional Relationships In Leukemia, Reginald Mcgee

Biology and Medicine Through Mathematics Conference

No abstract provided.