1 Schedule of Events Friday, October 14 6:00 pm - 9:30 pm Registration 7:00 pm - 8:00 pm Opening and Invited Presentation, SSMB 129 Patterns of Synchrony: From Animal Gaits to Binocular Rivalry Marty Golubitsky 8:00 pm - 9:30 pm Welcome Reception and Poster Session, SSMB 129/Atrium Understanding Adipocyte Dynamics through Mathematical Modeling Katrina Johnson, et al. Mathematically Modeling the Caulobacter crescentus Cell Nattanicha Wattananimitgul Teaching Nonlinear Dynamics to Biology Freshmen Improves Math Interest and Physics Performance Jane Shevtsov, et al. Analyzing the Cell Receptor Sequences of Patients with Celiac Disease Alanna P. Gary Modeling the Spread of the Zika Virus at the 2016 Olympics Triona S. Matheson, et al. Mathematical Modeling of Vaccine Noncompliance Jordan A. Bauer A Hysteresis-like Effect for Insect Control Strategies Bismark Oduro WORMSPREAD: An Individual-based Model of Invasive Earthworm Population Dynamics George Wesley Armstrong Mathematical Model of Swimmer’s Itch with Praziquantel Treatment Kelly R. Buch Synchronization of Coupled Neurons via Robust Feedback Hector Puebla, et al. Influence of Awareness that Results from Direct Exposure on the Spread of Epidemics Ying Xin Modeling the circadian Clock: Per3 Provides Molecular Support for Behavioral Observations Ha T. Vu Comparing the Effects of General and Selective Culling on Chronic Wasting Disease (CWD) Prevalence Elliott J. Moran Mathematical Modeling, Analysis and Computation of the Interaction between Human Sub Populations and Vector-borne Zika Transmission during the Summer 2016 Olympics Pradyuta Padmanabhan, et al. On the Duplexing of DNA’s Genetic and Geometric Codes Alex Kasman Management Strategies in a Malaria Model Combining Human and Transmission- Blocking Vaccines Eric Numfor
Transcript
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Schedule of Events
Friday, October 14 6:00 pm - 9:30 pm Registration 7:00 pm - 8:00 pm Opening and Invited Presentation, SSMB 129
Patterns of Synchrony: From Animal Gaits to Binocular Rivalry Marty Golubitsky
On the Expected Number of Crossings in a Tanglegram
Eva Czabarka
Ideal Free Distributions with Limited Perception and
Population Dynamics Igor Erovenko, et al.
An Agent-Based Model for Integrated Pest Management
with Periodic Control Strategies Timothy Comar
Designing and Mentoring in a Research Experience for
Undergraduates Alex Capaldi
Exploring an Immunology Model for Devil Facial Tumor
Disease Adjo Tameklo, et al.
8:45
-9:1
5
Genome Rearrangement: Graphs and Matrices Jeffrey Davis
Migrations Under Biased Perception: The Distribution of Specialists and Generalists in a Heterogeneous Landscape with Variably Discounted Resources
Jonathan T. Rowell, et al.
The Dynamics of an Integrated Pest Management Model with
Refuge Effect Miranda Henderson
Adventures in Teaching Agent-Based Modeling
Erin N. Bodine
Impact of Devil Facial Tumor Disease on the Tasmanian Devil
Age Structure Christopher Bruno, et al.
9:15
-9:4
5
Markov Chains on Graphical Models of Gene Regulation
Megan Bernstein
Territorial Movement Game Jan Rychtar
Mathematical Models and Optimal Control for Alternative
Pest Management to Alfalfa Agroecosystems Mohammed Yahdi
A Framework for the Teaching of Modeling for Biologists
Drew LaMar, et al.
Quantifying Life: A Computational Approach to
Teaching Mathematics to Biology Students
Dmitry Kondrashov
9:45
-10:
15
Efficient Quartet Systems Joseph Rusinko
Development of Honesty in Repeated Signaling Games
Michael I. Leshowitz
Sensitivity Analysis of Pest Eradication and Permanence
Solutions in a Model for Integrated Pest Management
Timothy Comar, et al.
Quantitative Reasoning-Mathematical Modeling in the
Sciences Robert L. Mayes, et al.
Influence of Preventative Measures to Eradicate the
Spread of the Zika Arbovirus Pradyuta Padmanabhan, et al.
10:15 am - 10:30 am Break
10:3
0 am
- 12
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pm
Tech
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IV
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10:3
0-11
:00
Exploring the Space of RNA
Secondary Structures Heather C. Smith
Modeling Mating Encounters in Insects: the Molecular Collisions Framework and the Associated
Numerical Correction Luis F. Gordillo
Evolving Healthy Populations Nina H. Fefferman
Strategies to Avoid Overfitting of MCMC Bayesian Learning in some Biological Applications
Diego M. García
11:0
0-11
:30
Bounds on the Expected Size of
the Maximum Agreement Subtree
Colby Long, et al.
Using Cellular Automata to Model the Gun Violence Epidemic in Chicago, IL
Shelby Scott
Modeling the Effect of Avian Stage-dependent Vector
Exposure on Enzootic West Nile Virus Transmission and Control
Suzanne Robertson
General Equations for Natural Selection Under Complete
Dominance Kasthuri Kannan, et al.
11:3
0-12
:00
Fractal Analysis of DNA
Sequences Christian G. Arias, et al.
Systemic Influences on the Inflammatory Phase of Wound
Healing Rebecca Segal
Hybrid Modeling for Forecasting Population
Dynamics John H. Lagergren
Finding Cliques in Ant Networks (or Twitter):
Isolating Behavioral Clusters Through an Unsupervised Two Stage Network Segmentation
John D. McKay
12:0
0-12
:30
Toric Neural Ideals and
Stimulus Space Visualization Elizabeth Gross
Stability Analysis of a Prey Refuge Predator-Prey Model
with Allee Effect Unal Ufuktepe
Rock, Paper, Scissors, Ooops Unintended Consequences and Uncertain Metric for Control in
Non-Hierarchical Ecologies Benjamin Morin
Stability and "Hidden Periodicity" in a Discrete,
Probabilistic Two-state Lattice Model of Intracellular Cardiac
Calcium Robert Rovetti
1:00 pm - 2:30 pm Closing Banquet and Invited Presentation, SSMB 129 Species Coexistence in Stochastic Environments
Sebastian J. Schreiber
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Keynote Presentation Friday, October 14 7:00 PM – 8:00 PM
SSMB 129
Patterns of Synchrony: From Animal Gaits to Binocular Rivalry
Marty Golubitsky MBI, Ohio State University
This talk will review previous work on quadrupedal gaits and recent work on a generalized model for binocular rivalry proposed by Hugh Wilson. Both applications show how rigid phaseshift synchrony in periodic solutions of coupled systems of differential equations can help understand high level collective behavior in the nervous system.
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Plenary Presentation Saturday, October 15
8:00 AM – 9:00 PM SSMB 129
Mind the Gap: Is Biomathematics Education Keeping up with Research?
Raina Robeva
Sweet Briar College Over the last decade, methods from modern algebra and discrete mathematics, including graph theory, Boolean networks, polynomial dynamical systems, hidden Markov models, Petri nets, Groebner bases, and more, have been used with great success for solving a wide range of biological problems. Examples span a spectrum of areas and applications: signaling networks and gene regulation; genome assembly; DNA, RNA and protein models and folding; neural networks and neural codes; biochemical reaction networks; cancer models; drug resistance and control; ecological networks and food webs, just to mention a few. The available literature is already massive and growing at a rapid pace, clearly showing that algebraic methods have become essential for mathematical biology. Relatively little progress has been made, however, in introducing those approaches to the mainstream undergraduate mathematical biology curriculum, even though for many of them the level of mathematical sophistication and the nature of the material are entirely appropriate. Thus, while some classical mathematical biology topics requiring difference equations, differential equations, and continuous dynamical systems have already successfully worked their way into classes and standard curriculum, discrete and algebraic techniques have remained relatively invisible. The talk will highlight some of those challenges and present ideas and curricular resources for bridging the gap.
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Plenary Presentation Sunday, October 16 1:00 PM – 2:30 PM
SSMB 129
Species Coexistence in Stochastic Environments
Sebastian Schreiber University of California, Davis
Stochastic fluctuations in temperature, precipitation and a host of other environmental factors occur at multiple spatial and temporal scales. As the survival and reproduction of organisms, whether they be plants, animals, or viruses, depend on these environmental factors, these stochastic fluctuations often drive fluctuations in population abundances. This simple observation leads to a fundamental question in population biology. Namely, “under what conditions do stochastic environmental fluctuations hinder or facilitate the maintenance of biodiversity?” This question is particularly pressing in light of global climate models predicting increasing temporal variation in many climatic variables over the next century. One fruitful approach to tackling this question from population biology is the development and analysis of models accounting for nonlinear feedbacks among species, population structure, and environmental stochasticity. In this talk, I will discuss progress in the development of a mathematical theory for stochastic coexistence where the dynamics of the interacting species are encoded by random difference equations and coexistence corresponds to the limit points of empirical measures being bounded away from an extinction set. I will illustrate the theory with empirical based examples involving checkerspot butterflies, Kansas prairies, and northern pike in Lake Windemere. Limitations of the theory and future challenges will be discussed.
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Presentation Abstracts
Dynamics of a Two Vector, Two Pathogen, Single Host Model
Caleb L. Adams
Radford University In this talk, the speaker will present recent theoretical results from the dynamics of a two-vector, two-pathogen, single host model. A system of ordinary differential equations is used to model the dynamics of two vector-borne pathogens (Rickettsia parkeri and Rickettsia amblyommii) that are increasingly found within tick populations of Virginia spread by two species of ticks (Amblyomma maculatum and Dermacentor variabilis), within a single host system. Three methods of transmission are included in the model: vector-borne, transovarial, and co-feeding. Results of numerical simulations are presented and determine a range of parameter values which lead to coexistence of the two pathogens and values which lead to the extinction of one pathogen and persistence of the other.
Bifurcation and Competitive Exclusion in a Malaria Model with Time Delay
Ephraim Agyingi, Tamas Wiandt, and Matthias Ngwa
Rochester Institute of Technology
We present a mathematical model of the transmission dynamics of two species of malaria with time lag. The model is equally applicable to two strains of the same malaria species. The reproduction number of the model is obtained and used as a threshold parameter to study the persistence or extinction of a species. Numerical simulations demonstrating bifurcation for prolonged delay values and competitive exclusion by the species with a larger reproduction number are provided.
An Environmental Impact Evaluation Model Generated by Compound Probability Distributions
Devin Akman1 and Olcay Akman2
1University of Illinois at Urbana-Champaign; 2Illinois State University
The problem of empirically identifying the underlying distribution of a parameter in a compound distribution has not been satisfactorily addressed in the fields of environmental effect and frailty modeling. We introduce Particle Swarm Optimization as a method to generate an approximate distribution by minimizing the error of the associated marginal distribution. We demonstrate the correctness of our approach via Monte Carlo methods.
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Spectral Graph Theory and New Stability Measures for Deterministic Gene Regulatory Networks
Fusun Akman1 and Devin Akman2
1Illinois State University; 2University of Illinois at Urbana-Champaign
We analyze the deterministic Boolean dynamics of a generic GRN with n genes by studying the asymmetric adjacency matrix of its phase space consisting of 2𝑛 states, and obtain exact formulas for many parameters of the GRN, including the number and sizes of its attractors using spectral graph theory techniques. We also introduce new stability measures with respect to stochastic perturbations and investigate the effects of canalizing Boolean update functions with simulations.
Fractal Analysis of DNA Sequences
Christian Arias1,2, Pedro Moreno1, Carlos Tellez1 1Universidad del Valle-Colombia; 2Georgia Institute of Technology
Fractality is a feature that measures the degree of fracturing and self-similarity of an object at different scales, it provides a value that helps describe the internal structure of the object. Initially, it was used in the analysis of waves and images, but it soon became clear that it was useful in other disciplines, specifically for the study of complex systems. DNA sequence analysis presents great challenges, particularly because of the complexity which is necessary for the algorithms that compare these very large sequences. The fractal and multifractal characterization helps simplify this complexity by facilitating the process of correlation between these structures and biological characteristics. Here we show how to apply this characterization to DNA sequences and the results of these characterization studies on C. Elegans and homo sapiens genomes.
WORMSPREAD: An Individual-based Model of Invasive Earthworm Population Dynamics
George Wesley Armstrong
Colgate University
Invasive earthworm species, such as Lumbricus rubellus, can cause changes to forest soils, which may result in reduced forest biodiversity. Individual Based Modeling (IBM) offers a way to predict the spread of invasive species, and can provide insight for control. We developed an individual-based, spatially explicit, population dynamics model (WORMSPREAD) using the NetLogo environment. The user interface is designed to be easy to learn and flexible enough to incorporate new data. WORMSPREAD allows ecologists and conservationists to better understand how variations in landscape structure and demographic parameters affect predicted earthworm abundance and distribution. Results can help determine where to concentrate conservation efforts and control strategies. An example study of the spread of L. rubellus in a portion of the Adirondack Park, New York State, illustrated challenges to the implementation of WORMSPREAD for this and other species. In particular, more data on the relationship between species demography and environmental conditions are needed – even for this common and well-studied species. The computational demands of IBMs over spatial and time scales relevant to management also may be limiting. WORMSPREAD can be used to predict population growth in real landscapes, with real variation in environmental conditions. However, it will only lead to accurate predictions if the underlying physiological and behavioral traits of the invading species are known. Indeed, our assessment of these traits for L. rubellus indicate that more data are needed for this species, and the situation is likely to be worse for less well-studied species. A better understanding of earthworm physiology and behavior will increase the efficacy of this and other efforts to model the spread of invasive earthworms.
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How Steep is Steep? Learning Curves in Training Undergraduates to do Fluid-structure Interaction Modeling
Nicholas A. Battista
University of North Carolina at Chapel Hill
Computational Fluid Dynamics (CFD) is often regarded as a difficult subject in its own right, let alone when attempting to get undergraduates involved in CFD-related research. However, this should not shy away neither research mentors or undergraduates from pursuing this avenue of research. We have been able to successfully work with undergraduates across a variety of majors, such as biostatistics, biology, math, and engineering, although varying degrees of time have been necessary to prepare students to get started. In this presentation, we will discuss some methods and techniques we have used for accelerating student involvement in fluid-structure interaction (FSI) research, even when the undergraduate students do not have sufficient backgrounds in computing, math modeling, or differential equations.
Mathematical Modeling of Vaccine Noncompliance
Jordan Bauer Valparaiso University
Vaccine scares can prevent individuals from complying with a vaccination program. When compliance is high, the critical vaccination proportion is close to being met, and herd immunity occurs, bringing the disease incidence to extremely low levels. Thus, the risk to vaccinate may seem greater than the risk of contracting the disease, inciting vaccine noncompliance. A previous behavior-incidence ordinary differential equation model shows both social learning and feedback contributing to changes in vaccinating behavior, where social learning is the perceived risk of vaccinating and feedback represents new cases of the disease. In our study, we compared several candidate models to more simply illustrate both vaccination coverage and incidence through social learning and feedback. The behavior model uses logistic growth and exponential decay to describe the social learning aspect as well as different functional forms of the disease prevalence to represent feedback. Each candidate model was tested by fitting it to data from the pertussis vaccine scare in England and Wales in the 1970s. Our most parsimonious model shows a superior fit to the vaccine coverage curve during the scare.
Markov Chains on Graphical Models of Gene Regulation
Megan Bernstein Georgia Institute of Technology
It is a common problem to study conditional dependencies that best fit data. For example, to find gene regulation through data on gene expression. Bayesian networks model conditional dependencies as a directed acyclic graph (DAG). However, many DAGs model the same conditional dependence information. The equivalence classes of DAGs modeling the same dependencies are called essential graphs and can be drawn as partially directed graphs. This talk concerns a Markov chain for random sampling of DAGs in the equivalence class of an essential graph. Conditions for fast and slow mixing will be given.
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Adventures in Teaching Agent-Based Modeling
Erin N. Bodine Rhodes College
As agent-based modeling has become more prominent in mathematical biology research, many math and life-science professors are experimenting with introducing agent-based modeling into the classroom. Agent-based modeling can be a powerful tool for introducing the concepts of mathematical and computational modeling and demonstrating how to link models to data. This talk will present the incorporation of agent-based modeling into a discrete math modeling class at Rhodes College including getting students started with NetLogo, common student difficulties with model implementation and thinking in terms of algorithms instead of equations, how to keep your grading load manageable, and how to assess student learning. Additionally, this talk will review the insights gained from participating in the QUBES Hub Mentoring Network on Teaching Quantitative Biology with Agent-Based Models and NetLogo.
Social Structure Algorithms for a Yellow-bellied Marmot Population Model
Erin N. Bodine1 and Anne E. Yust2 1Rhodes College; 2The New School
A long-term study (1976-2008) of a yellow-bellied marmot (Marmota flaviventris) population in the Upper East River Valley in Gunnison County, Colorado reveals a dramatic population increase from 2000 to 2008 when compared to the growth rate of the population over previous years. The increase has been attributed to changing climate conditions which have lead the marmot population to hibernate for shorter periods of time thereby allowing them more time to gain weight (and store fat) which has caused an increase in their likelihood to survive hibernation and their probability in successfully reproducing post-hiberation. We have modeled the yellow-bellied marmot population using an agent-based model (ABM) which accounts for population structure (matrilineal harems), movement between localities within a population, and the link between shorter winters and the rates of survival and reproduction. Here we present the relevant details of yellow-bellied marmot population biology and the development of an algorithm to simulate the dynamics of the population’s social structure over time.
Impact of Devil Facial Tumor Disease on the Tasmanian Devil Age Structure
Christopher Bruno and Vashni Vasquez
University of St. Francis
The Tasmanian devil population has significantly declined since the emergence of a lethal tumor disease called Devil Facial Tumor Disease (DFTD) in 1996 and DFT2 in 2014. These are two of four known transmissible cancers, with no documented origin or cause. Strategies such as selective culling, isolation, translocation, captive breeding, road fencing, and vaccines are currently being used by researchers to preserve the devil population. The ultimate purpose of this research is to identify the target age group of the devils to implement an effective vaccine. In this talk, we will present a system of ordinary differential equations to explore how the disease is affecting the age structure of the wild devil population.
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Mathematical Model of Swimmer’s Itch with Praziquantel Treatment
Kelly R. Buch Southern Illinois University
Swimmers itch is a water-borne, emerging disease caused by parasites known as avian schistosomes. Typically, these parasites use birds as definitive hosts, but will mistakenly infect a wide-range of dead-end hosts, including humans. When parasite larvae penetrate the skin of humans they initiate an allergic reaction that causes itching and discomfort that can last for weeks to months. Previous research has shown that the Common Merganser serves as a key host for schistosomes in the Midwest, with infection rates exceeding 60% in some regions. While most efforts at schistosome control have focused on other hosts in the parasites life cycle (snails), recent attempts have been made to target waterfowl using the anti-parasitic drug, Praziquantel. Based on this novel approach, we developed a mathematical model to explore the effects of Praziquantel dose and treatment frequency on the occurrence of swimmers itch in a typical Midwestern lake. We modeled susceptible and infected mergansers (both juvenile and adult), and snails using first order differential equations and introduced aspects of Praziquantel treatment into the system. Results from this model help to identify treatment regimens which lower merganser infection rates and ultimately reduce the occurrence of swimmers itch.
Creating Networks: A Research Experience for Undergraduates
Amy Buchmann, Bryce Bullock, Jason Georgis, Amanda Skellington Tulane University
Abstract not available.
Designing and Mentoring in a Research Experience for Undergraduates
Alex Capaldi
Valparaiso University
The Valparaiso Experience in Research by Undergraduate Mathematicians (VERUM) is an NSF funded REU with more than 10 years of history. VERUM is designed as a first research experience for students with an interest in mathematics who are unsure whether they should pursue graduate studies or a career in a math related field. This presentation will explain the structure of our REU as well as elaborate on the mentoring techniques that are used during the program.
Can Culling Barred Owls Save a Declining Northern Spotted Owl Population?
Alex Capaldi1*, Erin N. Bodine2
1Valparaiso University, 2Rhodes College
Data collected over the past 25 years has revealed that the Northern Spotted Owl (Strix occidentalis caurina) population of the Oregon Coast region is being displaced by an invasive Barred Owl (Strix varia) population. A component of the present U.S. Fish and Wildlife Service recovery plan is the culling of Barred Owls from Spotted Owl habitat. Using information theory to perform a model selection, we fit the most parsimonious ordinary differential equation species competition model to the data to determine growth rates and competition parameters. We then augment the model to incorporate Barred Owl culling and determine the minimum culling rate required to completely eliminate the Barred Owl population as well as
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the amount of time required to achieve such an elimination over a range of culling rates. Our analysis shows that even with the culling of Barred Owls, there exists no coexistence equilibrium given the current growth rates and competition parameters, and thus complete elimination of the Barred Owl population is required for the conservation of the Spotted Owl population. Furthermore, the effort required to cull the Barred Owl population is high showing a bleak but not hopeless outlook for this Spotted Owl population. Given the high culling rate necessary, we recommend a robust cost-benefit analysis of the program be conducted of which our study is a first step.
The Interaction of Calcium and Metabolic Oscillations in Pancreatic β-cells
Mary Aronne1, Samantha Clapp2*, Soohwan Jung3, Abigail Kramer4, William Wang5, Janita
Patwardhan1, Bradford E. Peercy1, and Arthur Sherman6 1University of Maine, 2Georgia College and State University, 3Edmonds Community College, 4Kent State University, 5Vanderbilt University, 6Laboratory of Biological Modeling, National Institutes of
Health
Diabetes is a disease characterized by an excessive level of glucose in the bloodstream, which may be a result of improper insulin secretion. Insulin is secreted in a bursting behavior of pancreatic β-cells in the islets of Langerhans, which is affected by oscillations of cytosolic calcium concentration. We used the Dual Oscillator Model to explore the role of calcium in calcium oscillation independent and calcium oscillation dependent (CaD) modes as well as the synchronization of metabolic oscillations in electrically coupled β-cells. We also implemented a synchronization index in order to better measure the synchronization of the β-cells within an islet. We observed that voltage or calcium coupling result in increased synchronization and are more effective in CaD modes. Furthermore, we studied heterogeneous modes of coupled β-cells, their arrangements in the islets, and their synchronization. We saw that increasing calcium coupling or increasing voltage coupling in heterogeneous cases increases synchronization; however, in certain cases increasing both voltage and calcium coupling causes desynchronization, primarily in voltage. To better represent an entire islet, we altered previous code by further optimizing run-time and memory usage to allow for a greater number of cells to be simulated for a longer period of time.
An Agent-Based Model for Integrated Pest Management with Periodic Control Strategies
Timothy D. Comar and Elizabeth Rodriguez
Benedictine University
We consider an agent-based model (ABM) for integrated pest management (IPM). The model incorporates stage structure for both the pest species and the predator species. The two control strategies of augmentation of the predator species and application of pesticide and the pest births occur periodically at possibly different frequencies. Moreover, the amount of augmentation depends on the ratio of the population densities of the pests and predators. We determine conditions under which pest eradication occurs and under which both species persist. We further investigate how varying the frequencies of the control strategies affects the amounts pesticide and augmentation needed to obtain pest eradication or persistence. To provide further insight to the dynamics of the ABM, we compare the model to analogous impulsive differential equation model that exhibits similar behavior, for which we prove conditions for the global asymptotic stability of the pest eradication solution and the permanence of the systems.
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Sensitivity Analysis of Pest Eradication and Permanence Solutions in a Model for Integrated Pest Management
Timothy D. Comar1, Olcay Akman2, Daniel Hrozencik3
1Benedictine University, 2Illinois State University, 3Chicago State University
We investigate the dynamics of deterministic and stochastic models for integrated pest management. The stochastic version incorporates competing stochastic elements in the prey birth rate. We prove the conditions under which solutions to the deterministic model are permanent, which correspond to economically viable solutions with minimal negative impacts. We also perform sensitivity analysis for certain model parameters for both pest eradication and permanent solutions.
On the Expected Number of Crossings in a Tanglegram
Eva Czabarka University of South Carolina
Leaf-labeled binary trees (a.k.a. phylogenetic trees) and tanglegrams are of interest to biologists. For a rooted binary tree on 𝑛 leaves, any subset of 𝑘 leaves induces a rooted binary tree by taking all paths connecting these leaves, placing the new root on the vertex closest to the original root of the tree, and suppressing all non-root degree two vertices in the resulting tree. The inducibility of a 𝑘-leaf rooted binary tree in an 𝑛-leaf rooted binary tree is the proportion of 𝑘-subsets of leaves that induce a tree isomorphic to that tree; the inducibility of any rooted binary tree is the limit superior of its inducibility in any sequence of binary trees. We show a number of results on the inducibility of certain types of binary trees that we use to estimate the expected crossing number of tanglegrams. A tanglegram is a pair of rooted binary trees on the same number of leaves with a fixed matching on the leaves; its crossing number is the minimum number of crossings we can have when we draw this in the plane such that the two binary trees are drawn as plane trees and the crossings are only allowed on the edges corresponding to the given matchings. The tanglegram crossing number is used to estimate relevant biological quantities (e.g. in parasite-host trees). We show that the expected value of tangregram crossing number in a random tanglegram on 𝑛-leaf trees is Θ(𝑛2), i.e. as large as possible. Joint work with László Székely and Stephan Wagner. Density-Dependent Leslie Matrix Modeling for Logistic Populations with
Steady-State Distribution Control Andrew M. Davis and Bruce Kessler
Western Kentucky University
The Leslie matrix model allows for the discrete modeling of population age-groups whose total population grows exponentially. Many attempts have been made to adapt this model to a logistic model with a carrying capacity, with mixed results. This presentation describes a new model for logistic populations that tracks age-group populations with repeated multiplication of a density-dependent matrix constructed from an original Leslie matrix, the chosen carrying capacity of the model, and a chosen steady-state age-group distribution. The total populations from the model converge to a discrete logistic model with the same initial population and carrying capacity, and growth rate equal to the dominant eigenvalue of the Leslie matrix minus 1.
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Discrete Models of Newt Population Declines Due to Severe Drought and Invasive Crayfish
Courtney L. Davis and Timothy A. Lucas
Pepperdine University
We introduce discrete mathematical models for studying the population dynamics of the California newt (Taricha torosa), a species of special concern in California. Recent declines and local extinctions of native California newt populations in Santa Monica Mountain (SMM) streams motivate our investigation of the impact of drought and invasive crayfish (Procambarus clarkii) on newt population sizes. Multiple studies predict Californias severe drought conditions currently underway will persist and even increase in duration and severity. In addition, invasive crayfish have decimated native newt reproduction in SMM streams. We construct two nonlinear systems of discrete equations that include demographic parameters such as survival rates for newt life stages and egg production, which depend upon habitat availability and rainfall. We estimate these demographic parameters using 15 years of stream survey data collected from Cold Creek in the SMM. Our models capture the observed decline of the studied newt population and replicate crayfish trapping data. The first model makes predictions about how the length and severity of drought can affect the likelihood of persistence and the time to critical endangerment of a newt population. With our second model, we evaluate the persistence or the time to extinction for newt populations under crayfish trapping regimes when varying the quantity of trapping resources, frequency of trapping implementation, and susceptibility of the crayfish population to trapping. Predictions made with both models inform restorative efforts and crayfish management.
Genome Rearrangement: Graphs and Matrices
Joshua Cooper1 and Jeffrey Davis2* 1University of South Carolina, 2Emory University
We apply matrix theory over F2 to understand the nature of so-called “successful pressing sequences” of black-and-white vertex-colored graphs. These sequences arise in computational phylogenetics, where, by a celebrated result of Hannenhalli and Pevzner, the space of sortings-by-reversal of a signed permutation can be described by pressing sequences. In particular, we offer several alternative linear-algebraic and graph-theoretic characterizations of successful pressing sequences, describe the relation between such sequences, and provide bounds on the number of them. We also offer several open problems that arose as a result of the present work.
Evolving Healthy Populations
Nina H. Fefferman University of Tennessee, Knoxville
Social species inherently experience greater risks of infectious disease outbreaks than do solitary species. The greater the reliance on social function for continued survival/reproduction, the greater the risks participating individuals face of catching infections from each other. Studies that have explored the evolution of social systems frequently show how selection that favors cooperation/the emergence of sociality is predicated on repeated interactions (at least over generations), but as expected repetition of contact increases, so do the social benefits and so do the disease risks. In this talk, we’ll show how selective pressure to minimize disease transmission risks can favor particular types of individual social behaviors over others, while still allowing for very similar individual‐ and group‐level benefits from sociality.
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Strategies to avoid overfitting of MCMC Bayesian learning in some biological applications
Diego García and Irene Tischer Universidad del Valle-Colombia
Model learning from observed data is typically affected by overfitting, because in order to find the model’s best parameter set, all relations between data are used indifferently whether they represent relevant or noisy interactions. Bayesian networks are widely used in biological modeling (e.g. networks of gene interactions), given that they allow representing graphically and determining statistically the dependence /independence relations between considered variables. A frequent approach in Bayesian learning is Markov Chain Monte Carlo simulation (MCMC), where a set of viable networks are explored by a random walk which converges to a network fitted optimally to data with respect to the likelihood or similar evaluation function. Here we propose various strategies to mitigate overfitting in Bayesian learning by MCMC in order to reduce the resulting models’ complexity. They either apply constraints inside the MCMC simulation or consider post-optimal operations. We show the effectiveness of these strategies in some biological applications.
Analyzing the γδ T Cell Receptor Sequences of Patients with Celiac Disease
Alanna P. Gary
University of Chicago Celiac disease is linked to increased intestinal proportions of T cells expressing a γδ T cell receptor (γδ TCR), which constitute only a small fraction of the overall T-cell population in healthy individuals. To elucidate the relationship these γδ TCRs have with celiac disease, we analyze sequences sampled from the blood and intestines of patients with celiac disease, patients who manage their celiac disease with a gluten-free diet, and disease-free control subjects. An array of sequence- and structure-based approaches is used to investigate what distinguishes the γδ TCRs of healthy patients from those with celiac disease. First, we characterize the diversity of the subjects’ γδ TCR repertoires using the Morisita-Horn similarity index, which quantifies the overlap in the sets of γδ TCR sequences present in a pair of samples. Second, we investigate the chemical properties of the sequences in a non-position-specific manner. For example, we compare the proportions of charged, hydrophobic, aromatic, etc. residues comprising the sequences of each group. Next, we utilize a variety of methods to search for motifs, or repeated patterns, in the sequences; for instance, we implement the Smith-Waterman algorithm to locally align all possible pairs of sequences to cluster similar sequences. Finally, we analyze theoretical structures of these γδ TCRs produced by the ModWeb homology modeling server.
Modeling Mating Encounters in Insects: the Molecular Collisions Framework and the Associated Numerical Correction
Luis F. Gordillo
Utah State University Ideal gas models are a paradigm used in Biology for the phenomenological modeling of encounters between individuals of different types. These models have been used to approximate encounter rates given densities, velocities and distance within which an encounter certainly occurs. When using mass action in two-sex populations, however, it is necessary to recognize the difference between encounters and mating encounters. While the former refers in general to the (possibly simultaneous) collisions between particles,
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the latter represents pair formation that will produce offspring. In this talk I will show how an easy dimensional reduction argument and simulated data help to discriminate between the two cases. In addition, variability in mating encounter rates (due to environmental stochasticity) is numerically explored through random fluctuations on the new mass action proportionality constant. The simulations show how the conditioned time to extinction in a population subject to a reproductive Allee effect is affected.
A Numerical Investigation of a Simplified Human Birth Model
Roseanna Gossman1, Alexa Baumer2, Lisa Fauci1, Megan C. Leftwich2 1Tulane University, 2George Washington University
This work uses a simplified numerical model to explore the forces on an infant during human birth. Numerical results are compared with the results of a physical model which represents the fetus moving through the birth canal using a rigid cylinder (fetus) that moves at a constant velocity through the center of a passive elastic tube (birth canal). The entire system is immersed in a highly viscous fluid; low Reynolds number allows the Stokes equations to approximate fluid behavior. The pulling force necessary to move the rigid inner cylinder at a constant velocity through the tube is measured, and considered along with the time-evolving behavior of the elastic tube. The discrete tube through which the rigid cylinder passes has macroscopic elasticity matched to the tube used in the physical experiment. The buckling behavior of the elastic tube is explored by varying velocity, length, and diameter of the rigid cylinder, and length of the elastic tube. More complex geometries as well as peristaltic activation of the elastic tube can be added to the model to provide more insight into the relationship between force and velocity during human birth. Neural Networks: Using Biomarkers to Inform Diagnosis, Classification of
Disease and Approach to Therapy
Paula Grajdeanu Shenandoah University
While renal biopsy it is still the gold standard for the diagnostic of renal interstitial inflammation, some noninvasive diagnostic studies have been proposed to help categorize interstitial inflammation. Urine samples collected at the time of biopsy are tested to provide confirmatory evidence of interstitial inflammation, though the diagnostic value of these tests remains unclear. Because the pathogenesis of interstitial inflammation is extremely complex in nature, classical analytical models are limited in their ability to elucidate the nonlinear biomarkers interplay that underlies the interstitial inflammation. We propose to develop artificial neural networks to predict renal interstitial inflammation outcomes based on patient urine tests. The neural networks will be trained with patient data for which the interstitial inflammation was scored by a renal pathologist from renal biopsies. The neural networks can then be used to classify new patients. Furthermore, new patient data will be incorporated into older version of the model to refine predictions.
Toric Neural Ideals and Stimulus Space Visualization
Elizabeth Gross San Jose State University
A neural code 𝒞 is a collection of binary vectors of a given length n that record the co-firing patterns of a set of neurons. Our focus is on neural codes arising from place cells, neurons that respond to geographic stimulus. In this setting, the stimulus space can be visualized as subset of ℝ2 covered by a collection 𝒰 of convex sets such that the arrangement 𝒰 forms an Euler diagram for 𝒞. There are some methods to determine whether such a convex realization 𝒰 exists; however, these methods do not describe how to
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draw a realization. In this talk, we will look at the problem of algorithmically drawing Euler diagrams for neural codes using toric ideals. In particular, we will show how these objects are related to the theory of piercings in information visualization. This is joint work with Nida Kazi, Obatake and Nora Youngs.
Making Waves: a Computational Swimming Lamprey with Sensory Feedback
Christina Hamlet1, Eric D. Tytell2, Lisa J. Fauci3, Kathleen A. Hoffman4
1Bucknell University, 2Tufts University, 3Tulane University, 4University of Maryland-Baltimore County
The lamprey is a model organism for both neurophysiology and locomotion studies. This talk will present an integrative, multiscale, computational swimming lamprey driven by a central pattern generator (CPG) modeled as a chain of coupled oscillators. The CPG drives muscle kinematics in fluid-structure interactions implemented in an immersed boundary framework to produce the emergent swimming mode. Body curvature changes provide feedback to the CPG. Effects of feedback to the neural activation on swimming performance are estimated and examined.
The Dynamics of an Integrated Pest Management Model with Refuge Effect
Miranda Henderson
Illinois State University
Pest control has become increasingly difficult in crops as pests develop resistance to traditional methods. Recently, the combination of biological, chemical, and cultural, known as integrated pest management (IPM), has been used in order to control these pests at low levels. However, some of these pests are in refuge and are not exposed to these methods. Here, we introduce an IPM model with refuge effect to study how the refuge effect influences the dynamics of this system. We are particularly interested in the stability of this system and identify permanence of the system in order to apply this knowledge to the control of pests.
Mathematical Modeling in Collaborative Courses: the Soup to Nuts Experience
Sarah Hews and Christina Cianfrani
Hampshire College
The Integrated Sciences First Year Program (ISFP) is a new initiative at Hampshire College that aims to challenge students to learn about complex systems and systems thinking, to improve quantitative skills, to make connections among fields of science, to design innovative collaborative projects, and to create a vibrant science community. ISFP, currently using a new Living Building on campus as a model system, consists of fall collaborative courses (ISFP I), a spring design projects course (ISFP II), and a summer research experience (ISFP III). ISFP I in particular presents an opportunity for science students to learn the benefits of modeling and for the mathematics students to learn applications of their skills. Students met with their respective classes twice a week learning field specific skills and met all together once a week to complete interdisciplinary labs where students collected and used data. This talk will focus on the
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collaborative courses offered during Fall 2015: Water, Carbon, and Nutrient Flows in a Living Building, Modeling Systems in a Living Building, and Microbes in a Living Building. I will cover design, implementation, and assessment of the collaborative courses, general takeaways from the entire ISFP, and preliminary reflections from the current Fall 2016 courses.
Comparison of Eupatorium reinosum and Eupatorium perfoliatum under Stochastic Reproduction
Daniel Hrozencik1, Olcay Akman2, Lina Niu2
1Chicago State University, 2Illinois State University Rare flowering plains in North America are of particular concern to conservation biologist that are interested in preserving species diversity. Possible impact of inherent demographic characteristics leading to rarity and potential extinction, are still not completely understood. For instance, rare species may be more sensitive to demographic stochasticity than more abundant species. In this talk we investigate whether a rare species Eupatorium reinosum, is more adversely affected by stochastic reproduction than a related common species, Eupatorium perfoliatum. We use empirical data to construct stochastic Leslie matrices to compare different populations within each species. Then the stochastic Leslie matrices will be used to determine population dynamics and predict population growth.
Data-Driven Mathematical Modeling for Seniors at the University of
Maryland
Brian Hunt University of Maryland
I will discuss a senior-level modeling course for mathematics majors at the University of Maryland. The course was recently redesigned to emphasize the use of real data, by C. D. Levermore, W. Czaja, E. Slud, and me. I will describe some of the data sets we use, what our students do with them, and how we organize group work and other aspects of the course.
Understanding Adipocyte Dynamics through Mathematical Modeling
Katrina Johnson and Fred Adler University of Utah
Adipocytes are the primary cell type in adipose tissue and are responsible for limiting the exposure of other tissues to lipid accumulation during the postprandial state and providing energy during periods of fasting. Obesity is characterized by the expansion of fat mass due to a positive energy imbalance. Obesity is associate with chronic inflammation and can lead to the development of insulin resistance and diabetes. Large adipocytes are more fragile and prone to dysfunction. Adipocyte dysfunction is a proposed mechanism of obesity associated inflammation. Understanding the relationship between inflammation and obesity is a multi-scale problem that includes interactions on the intracellular, intercellular, and tissue levels. In this project I model the size and population dynamics of adipocytes with a system of ordinary and partial differential equation. Using this model I explore how maintenance of the preadipocyte population via proliferation and ability of preadipocytes to maintain and increase the adipocyte population via differentiation contribute to obesity. Lipogenesis and lipolysis are regulated by the adipokines, cytokines, and hormones in the adipose tissue and this milieu changes during obesity associated inflammation. I use
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this model to explore how the rates of lipogenesis and lipolysis contribute to size and/or number of adipocytes. The development and validation of this model provides a foundation for exploring the intercellular dynamics of adipocytes and other stromal vascular cells in adipose tissue.
Vaccination Strategies for Small Worlds Winfried Just1, Hannah L. Callender2
1Ohio University, 2University of Portland The development of optimal vaccination strategies leads to interesting mathematical problems. This talk will give an overview of a forthcoming book chapter that presents several such open problems in a form suitable for undergraduate research projects. In these problems it is assumed that the contact network can be represented by a small-world network. Through a sequence of background information and preliminary exercises, we take the readers to the point where they can engage in bona fide research on these questions.
General Equations for Natural Selection Under Complete Dominance
Kasthuri Kannan and Adriana Heguy New York University
In theoretical and mathematical biology, natural selection is generally considered in totality as an implicit function of time. Although this has helped achieve statistical equations for natural selection (initially by Fisher and later by Price), non-statistical equations on how evolution would proceed, at all times, under complete dominance have not been described. This talk will focus on deriving general equations for natural selection under complete dominance for all allele frequencies. We invoke a key theorem from mathematical analysis, namely, the inverse function theorem, to derive these equations. We demonstrate the validity of the equations by studying the allele frequencies of mutations in oncogenes as they exhibit dominant behavior. Consistent with population genetics model of fitness, the selection function fits a gamma distribution curve that accurately describes the trend of the mutant allele frequencies. As general and relative formulas for natural selection operating at all frequencies, these equations show that selection exhibits linear behavior favoring dominant alleles and behaves like power-law against the recessive alleles, at all times, explaining why natural selection is a strong force.
On the Duplexing of DNA’s Genetic and Geometric Codes
Alex Kasman College of Charleston
It is well known that a sequence of DNA bases is translated into a sequence of amino acids in living cells. More recently it has been discovered that the sequence of DNA bases also influences the geometry of the molecule. This is a natural example of “duplexed codes”, sending two different coded messages with the same signal. This project (a “work in progress”) seeks to investigate the efficiency of this duplexing. Through numerical computations and graphical representations, we will compare the duplexing of these two natural codes with hypothetical (unnatural) alternatives. The goal is not only to better understand the natural duplexing, but moreover to determine whether there is evidence that this influenced the evolution of the genetic code.
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Quantifying Life: A Computational Approach to Teaching Mathematics to Biology Students
Dmitry Kondrashov
University of Chicago
Computational programming is an effective approach for teaching mathematical concepts by making them interactive and visual. I have developed a set of materials for teaching mathematical modeling, such as Markov models and dynamical systems, for biology students with no prior programming experience and a high school mathematics background. These include R programming exercises and projects, demonstrations using Shiny R applications, and a textbook (Quantifying Life) that is organized by increasing programming complexity. I will demonstrate examples of programming projects, Shiny apps, and share teaching experiences, including feedback from student questionnaires. I will also describe the process of publishing with an academic press and discuss different avenues for dissemination of educational materials.
Hybrid Modeling for Forecasting Population Dynamics
John Lagergren, Amanda Reeder, Franz Hamilton, Ralph Smith, Kevin Flores North Carolina State University
We present a novel hybrid approach for forecasting dynamical systems and demonstrate our methodology on population data from cannibalistic flour beetles. In our proposed method, a portion of a mechanistic model’s equations are used to predict a subset of the variables while a model-free prediction method is used to predict the remaining. The direct benefit of this is a reduction in complexity of the required parameter estimation problem which leads to an overall increase in prediction accuracy of future population behavior. Utilizing a Bayesian parameter estimation framework, we implemented uncertainty quantification analysis and found that the increase in prediction accuracy, afforded by our hybrid approach, is associated with lower levels of parameter correlations and Fisher Information Matrix rank deficiency. Though demonstrated on beetle population dynamics, our approach can be generalized to forecasting any ecological system in which multivariate time series data are available.
A Framework for the Teaching of Modeling for Biologists
Drew LaMar1 and Carrie Diaz Eaton2 1College of William and Mary, 2Unity College
Here we present a framework for teaching models and modeling to biologists. We examine disciplinary strengths in examining biological questions and encourage that differing disciplinary approaches are seen as part of a larger picture of this framework. We define model representations in the rule of five and modeling as the act of moving between representations. We provide examples to illustrate and acknowledge language can interfere with helping students make connections between and within disciplines. We then use this framework to inform instructional approaches for biology students. This work was conducted as part of “Unpacking the Black Box: Teaching Quantitative Biology” Working Group at the National Institute for Mathematical and Biological Synthesis (NIMBioS), sponsored by the National Science Foundation through NSF Award #DBI1300426, with additional support from The University of Tennessee, Knoxville.
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Codon Bias, DNA Transcription Forks, and Kink-Solitons
Alex Kasman and Brenton LeMesurier* College of Charleston Charleston
The transcription of DNA into messenger RNA (and eventually into protein) involves the motion of the transcription fork – a short region in which the two strands separate – along the chromosome in a specified direction. This motion clearly has superficial similarity to the motion of solitons, localized nonlinear wave phenomena that behave like particles. In fact, Salerno has proposed a model in which the transcription fork takes the form of a kink-soliton of the discrete Sine-Gordon equation. An interesting aspect of this model is that the dynamics depend explicitly upon the DNA sequence. Prior research by Salerno and others has shown, for instance, that the sequences at the start of coding regions have the property that they will force a stationary soliton profile to begin traveling in the right direction. Here we consider the question of the effect that the sequence will have on the continued motion of that soliton through the coding region. It is shown, through numerical solution of mathematical models, that the choice of codon for an amino acid or the presence of a non-coding intron can either allow or prevent the transcription fork from completing its task. This suggests the possibility of a previously unrecognized role for nonlinear dynamics in codon selection. In this work in progress, we consider successively more complex and accurate mathematical models of DNA strands, to assess the robustness of the phenomenon seen in the simplest discrete Sine-Gordon models, and to determine how much detail the mathematical models must include in order to give scientifically relevant results.
Development of Honesty in Repeated Signaling Games
Michael I. Leshowitz University of North Carolina at Greensboro
A symbiotic relationship inherently depends on the development of a reliable information channel. This network provides an unintended opportunity for rouge agents to reap benefits by counterfeiting honest signals. In a plant-pollinator system, plants have a multitude of potential signals, primarily visual and olfactory. Some signals are a biproduct of rewards, while other can be positively correlated through pollinator conditioning. Successful pollinators cross reference signals with prior experiences in order to determine the integrity of their sender. We examine the parameters of honest signaling as high-yield and low-yield plants compete for visitation rates in a repeated Sir Philips Sidney Game.
Maintenance of the pH Gradient in the Gastric Mucus Layer
Owen L. Lewis The University of Utah
The gastric mucus is a complex gel-like layer of various proteins and solutes coating the epithelial surface of the stomach. This layer is widely recognized to serve a protective function, shielding the epithelium and the rest of the gastric mucosa from the extremely low pH and digestive enzymes present in the stomach lumen. Often described as a “diffusion barrier” the mucus layer is thought to hinder the transport of diffusive species from the lumen, to the stomach wall. However, there is still a lack of consensus on the mechanism by which the mucus layer hinders lumen-to-wall transport while allowing acid and enzymes secreted from the mucosa unimpeded transport to the lumen. Using a model of two-phase fluid motion
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coupled with electro-diffusion, we test one hypothesis. Furthermore, we explore what regulatory mechanisms are necessary to segregate an acidic stomach lumen from a pH neutral stomach wall.
Bounds on the Expected Size of the Maximum Agreement Subtree
Colby Long1, Daniel Irving Bernstein2, Lam Si Tung Ho3, Mike Steel4, Katherine St. John5, Seth Sullivant2
1The Ohio State University, 2North Carolina State University, 3UCLA, 4University of Canterbury, 5Lehman College City University of New York
We prove polynomial upper and lower bounds on the expected size of the maximum agreement subtree of two random binary phylogenetic trees under both the uniform distribution and the Yule-Harding distribution. This positively answers a question posed in earlier work by Bryant, McKenzie, and Steel.
Modeling the Spread of the Zika Virus at the 2016 Olympics
Triona S. Matheson, Brian Satterthwaite, Hannah L. Callender University of Portland
The Zika Virus (ZIKV) is an arbovirus that is spread by mosquitoes of the Aedes genus and causes mild fever-like symptoms. It is also strongly associated with Microcephaly, a condition that affects the development of the brain of a fetus. With the recent emergence of Zika in Brazil, we developed an agent based model to track mosquitoes, locals and tourists throughout the 18 days of the 2016 Olympics in Rio de Janeiro in order to determine how the Olympics would affect the spread of the virus. The disease states of each individual were tracked throughout each simulation. There are many unknowns regarding the spread and prevalence of Zika, and as many as 80% of infected individuals are not aware of their infectious status. We therefore discuss results of experiments where several parameters were varied, including the rate at which mosquitoes successfully bite humans, the percent of initially infected mosquitoes, the size of the human population, and the size of the mosquito population. From these experiments we offer projections on the possible severity of Zika spread throughout the Olympics.
Quantitative Reasoning - Mathematical Modeling in the Sciences
Robert L. Mayes Georgia Southern University
This session is part of an invited session: The Teaching of Modeling. The session will present pilot research being conducted in undergraduate biology courses at multiple universities. A brief overview of quantitative reasoning in the sciences will be provided, including presentation of a Quantitative Reasoning learning progression framework with three progress variables: Quantitative Act and Literacy, Quantitative Interpretation, and Quantitative Modeling. Two measures associated with the quantitative learning progression will be shared: 1) QA-QL measure of ability to quantify variables within a biological context and ability to apply arithmetic and algebraic skills within context; 2) QI-QM measure of ability to interpret quantitative biological models and understanding of building quantitative models. The QA-QL measure has the potential to be a diagnostic assessment of students’ basic quantitative reasoning ability, providing formative feedback to the instructor which informs the need for supplemental instruction in quantitative skills or just-in-time teaching of quantitative skills. Addressing gaps in students’ quantitative reasoning ability is fundamental to meaningful implementation of modeling in the sciences. The QI-QM measure is designed as a formative pre-post assessment of students’ ability to apply models to determine trends, make
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predictions, translate between models, and make revisions to a model, as well as the ability of students’ to create their own models and reason with those models. Preliminary data from a pilot of the assessments will be presented.
Finding Cliques in Ant Networks (or Twitter) Isolating Behavioral Clusters Through an Unsupervised Two Stage Network Segmentation
John McKay
Pennsylvania State University Ants have had incredible ecological success in part due to their efficient organization of work, a feat achieved by having flexible task allocation networks. These decentralized networks rely on individual workers making crucial decisions without complete knowledge of the colony overall. Research has been done on the idea that task participation can be one way that workers share information locally to organize themselves for the colony, i.e. what task an ant is doing may change its behavior in ways that increase/decrease the amount of communication other tasks. This model relies on an assumption that the finest layer of this in/out group dynamic is indeed task participation. We hypothesize that this may be too much of an a priori distinction and present a novel manner in which to discern proper behavioral clusters of ecological networks based on a "friends of friends" approach. In our two stage network segmentation, we cluster on communication links between a population of nodes and their mutual connections and then perform a feature selection on each cluster to find the most representative members, those who are most similar to every member of their group. To illustrate our algorithm, we utilize Twitter as a data-rich surrogate for an ecological setting and perform a network segmentation on a single user. In this setting, we use followership in place of communication links and “friends of friends” of the account to establish the network. Thus, with the feature selection, we are able to parse out distinct groups with unique behavioral patterns. Using Phylogenetic Trees to Measure the Impact of Background Selection
on Population Diversity
Garrett Mitchener College of Charleston
If a species has a large, fragile, important genetic network, there will be many possible mutations that break it. Each time one of these mutations appears, the organism carrying it is much less likely to reproduce successfully, resulting in a loss of genetic diversity in the population. A way of measuring this loss is through the construction of weighted phylogenetic trees. I will present an artificial life simulation of a species tasked with transmitting information across a narrow synapse. The species must evolve a relatively large gene network to perform this task, and many of the possible mutations cause it to malfunction. Eventually a complete solution evolves and reaches fixation. That root population is then branched. The branches continue to evolve, and genetic distances between branches are measured. From those distances, a weighted phylogenetic tree is constructed. For reference, a second copy of the root population is branched, but continues evolving without the transmission task, so it experiences almost no selection. This second branched population shows more genetic diversity, and the branch weights on the phylogenetic tree are longer. Comparing the results of the population evolving under these two conditions yields an estimate of how strongly the nearly-neutral drift of unrelated genes is disturbed by selective pressure not to break the information-processing genetic network. This phenomenon may affect human genetics. Humans are less genetically diverse than other great apes. Based on this simulation, it is at least plausible that weak selection not to break the genetic network responsible for language may have contributed to that reduction in genetic diversity.
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Comparing the Effects of General and Selective Culling on Chronic Wasting Disease (CWD) Prevalence
Elliott J. Moran Unity College
This study looked at the effect of culling on the spread of Chronic Wasting Disease (CWD). CWD is a transmissible spongiform encephalopathy (TSE) with an unknown derivation and no antidote. Without any type of intervention, the long-term consequence of CWD lead to extirpation of Cervidae. Culling is the primary method used to control Chronic Wasting Disease. Studies suggest that selective culling of infected individuals could be a more effective method of reducing CWD prevalence, however, the two methods have not been directly compared. A series of ordinary differential equations will be used to create a model that reflects CWD in free-ranging Cervidae populations. This model compares general culling and selective culling of infected individuals using qualitative and numerical techniques to identify outcomes, give insight towards management prescriptions, and understand long term population dynamics as they related to different culling regimes.
Rock, Paper, Scissors, Ooops Unintended Consequences and Uncertain Metrics for Control in Non-Hierarchical Ecologies
Ben Morin
Vassar College In this exploratory talk on preliminary work I build simple models of cyclic hierarchies for consumptive (Predator-Prey like) or exclusionary (Competition) interactions between species. Many models for such ecologies have existed, but when one models control of such systems. I will show conditions and metrics where the desire to promote the persistence of one species (e.g., "rock" in a rock-paper-scissors like interaction) may result in a deleterious outcome for them with some metrics and beneficial with others. The derivation of these systems, while relying on classic Lotka-Volterra and Verhulst functional forms, will focus on mechanisms as to make the mode of control clear. These theoretical considerations have applications not only in the context of ecological control of species for which we derive ecoservices but also in the control of infectious disease where complex interactions lead to unclear succession chains. Analysis of Steady States for Classes of Reaction-Diffusion Equations with
U-shaped Density Dependent Dispersal on the Boundary
1Auburn University at Montgomery, 2University of North Carolina at Greensboro We consider positive solutions to equations of the form
−∆𝑢 = 𝜆𝑢(1 − 𝑢), 𝑥 ∈ Ω,
𝜕𝑢𝜕𝜂 + 𝛾√𝜆(𝑢 − 𝐴)2𝑢 = 0, 𝑥 ∈ 𝜕Ω,
where λ > 0, γ > 0, A ∈ (0, 1) are parameters, Ω is a bounded domain in ℝ𝑛;𝑛 ≥ 1 with smooth boundary ∂Ω and 𝜕𝑢𝜕𝜂 is the outward normal derivative. Such models arise in the study of population dynamics in a habitat Ω when the population exhibits U-shaped density dependent dispersal on the boundary. We analyze the
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persistence of the population (existence, non-existence, uniqueness and multiplicity of positive solutions) as the patch size (λ) and the hostility of the outside matrix (γ) vary. We obtain results when Ω = (0, 1) via a quadrature method, and when Ω is any bounded domain in ℝ𝑛;𝑛 > 1 by the method of sub-super solutions.
The Kinetics of Type 1 Interferons During Influenza Virus Infection
Maggie Myers
St. Jude Children’s Research Hospital Influenza A virus (IAV) infections pose a considerable public health threat and are a leading cause of death. The host immune response works to limit virus growth and quickly resolve the infection. Type 1 interferons (IFN-α, β), in particular, aid viral control by inhibiting the infection of epithelial cells and by stimulating and regulating the activity of immune cells. To investigate the role of type 1 IFNs during IAV infection, we infected groups of mice with influenza A/Puerto Rico/8/34 (PR8) and measured their viral load, IFN concentration, and immune cell populations daily. The data indicated a two-phase decline in virus titers and a double peak in IFN. Because published kinetic models of IFN dynamics fail to reproduce these data, we developed two new models: a two-source immune model and a refractory-state reversion model. In both models, the first wave of IFN is produced from infected epithelial cells. The second wave of IFN in the two-source model is from an immunological source, such as macrophages or dendritic cells. In contrast, the refractory reversion model suggests that the second wave of IFN is produced by epithelial cells that have exited the IFN-induced antiviral state and became infected. Although each model is biologically reasonable, the two-source immune model reproduced more features of our data. The models also provide support for enhanced activity of CD8+ T cells in the presence of IFN. Taken together, these results provide insight into the regulation of host immune responses during IAV infection.
Feline Cat Population Dynamics
Andrew Nevai University of Central Florida
Feline cat populations cause ecological destruction and spread many diseases in places that people live. Here, we describe a mathematical model for their population dynamics. The gender-based model includes kittens, adult females and adult males. A net reproduction number 𝑅0 distinguishes between population extinction (𝑅0 < 1) and population persistence (𝑅0 > 1). This is joint work with J. Sharpe (UCF).
Management Strategies in a Malaria Model Combining Human and Transmission-Blocking Vaccines
Jemal Mohammed-Awel1, Ruijun Zhao2, Eric Numfor3, Suzanne Lenhart4
1Valdosta State University, 2Minnesota State University Mankato, 3Augusta University, 4University of Tennessee, Knoxville
A new mathematical model studying control strategies of malaria transmission is formulated and analyzed. The existence of a backward bifurcation is established analytically in the absence of vaccination, and numerically in the presence of vaccination. Optimal control strategies, using vaccination and vector control are investigated to gain qualitative understanding on how the combination of vaccination and vector control should be used to reduce disease prevalence in a malaria endemic setting.
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A Hysteresis-like Effect for Insect Control Strategies
Bismark Oduro Ohio University
Insecticide spraying remains one of the most widely used control strategies for vector-borne diseases such as Chagas disease. Drawbacks include harmful side effects of the insecticide and the fact that it confers only temporary protection to treated units. We investigate ODE-based models of type SIRS with a reservoir to elucidate strategies that would maximize the amount of protection in the long run for a given amount of available insecticide. The models indicate a hysteresis-like effect were two different endemic levels can be maintained at the same cost. The effect predicts that initially highly aggressive intervention will allow to maintain lower endemic levels at the same average cost in the long run. We prove that the effect is fairly robust under fine-graining of the basic model to incorporate more biological details.
Mathematical Modeling, Analysis and Computation of the Interaction between Human Sub Populations and Vector-borne Zika Transmission
During the Summer 2016 Olympics
Pradyuta Padmanabhan1 and Padmanabhan Seshaiyer2 1The Foxcroft School, 2George Mason University
Zika Virus which is primarily transmitted through the Aedes aegypti mosquitoes has led to multiple recent outbreaks in many sub-tropical regions of the Latin American and Caribbean countries. While Zika was thought earlier as primarily a vector-borne disease that is transmitted from the mosquito vector to humans through their bite, recent cases of infection have established the potential for direct transmission through sexual contact in addition to vector transmission. These outbreaks spread even more rapidly in these countries when they host a significant international event such as the recent Olympics 2016 held in Rio de Janeiro, Brazil. According to the Centers for Disease Control and Prevention, the celebratory atmosphere at such events as the Olympics may encourage travelers to engage in risky sex, especially if they are drinking or using drugs. In this work, we study the interaction of three sub groups of human populations that include the visitor population to Rio, the native population of Rio and a population of sex workers in this Olympic event. Besides the transmission of Zika from the infected members in all three populations through sexual contact, the model also incorporates infection through a vector transmission. Specifically, an enhanced SEIR compartmental model is proposed and the final size relation for an epidemic in the subdivided population with preferred mixing patterns is numerically implemented. The basic reproduction number for specific subclasses is derived and a benchmark study for a specific data set of parameters in the model from Brazil is also examined.
Influence of Preventive Measures to Eradicate the Spread of the Zika Arbovirus
Pradyuta Padmanabhan1 and Padmanabhan Seshaiyer2
1The Foxcroft School, 2George Mason University Recently, the Zika arbovirus transmitted through the Aedes aegypti mosquitoes has been shown to be transmitted to humans, not only through vector transmission, but also through sexual contact. While there is a lot of research currently being conducted to find vaccines for the treatment of the disease, other methods of prevention and eradication of the disease recommended by the Center for Disease Control and Prevention include using insecticide treated bed nets (ITN) and indoor residual spraying (IRS). The ITNs developed using chemicals such as pyrethroids, can maintain effective levels of insecticide for a long time
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as well as repel mosquitoes. Since the mosquitoes tend to rest inside houses after biting humans, IRS applied to homes that do not have adequate screening or air conditioning is recommended. Also, exposure to insecticides reduces the mosquito density and lifespan of individual mosquitoes which in turn helps to reduce disease transmission. In this work, we investigate an enhanced mathematical model that incorporates ITNs and IRS as methods for eradication of Zika. Specifically, we develop an ordinary differential equation system that builds on classical SEIR epidemiological models, with added constraints for the two preventive measures, namely ITN and IRS. We derive the basic reproduction number analytically and compute the final size for the epidemic for various conditions involving ITNs and IRS numerically. We present ranges for combination of compliance and efficacy for ITNs and IRS that can potentially eradicate the disease.
Zombies, Predatory Wasps and Consciousness
James K. Peterson Clemson University
In anesthetia, a percentage of patients continue to experience the trauma of the surgery despite being anesthisized. Such patients are a form of zombie and there is a need for brain models which can detect this state using measurements that are available in the operating theater. The altered state of consciousness is obtained by the careful administration of a variety of drugs and in many respects is similar to the altered state of behavior induced by a predatory wasp injection of a potent neural cocktail into their cockroach or spider prey. These external events reprogram the host into a new behavioral pattern. Since all of the usual neural modules are present, we can posit that these external inputs alter the usual connections between the functioning neural modules allowing the full brain outputs to change. We explore these ideas using graphs of computational nodes that are assembled into a brain model. We discuss a model of signalling that is built from ideas from computational homology. Within that framework, neural cocktail signals are modeled using Betti decompositions and that information is used to create a new type of computational node in a general graph model of a cognitive system. The Betti node decomposition is a direct sum of simple groups and we posit that the structure of that direct sum is a measure of consciousness level which can be altered by the injection of a toxin or an anathestic drug. Since the notion of normal behavior is important here, we discuss how we can ask intelligent questions about how the normal behavior – a kind of dynamical attractor – is shifted to the new state.
Modeling Cross-Species Extrapolation of Inhalation Anthrax for Risk Assessment Purposes
Megan O. Powell
University of St. Francis
Inhalation anthrax is a disease cause by spores deposited in the deep lung that subsequently germinate and replicate once taken up by immune system cells. Anthrax is of concern as a potential bioterrorism weapon, and recent melting in the Arctic has allowed dormant spores have affected humans and wildlife alike in Siberia. Research on high and low-dose exposure has been done on animals, namely rabbits, and non-human primates, but cannot be done on humans. Therefore, cross-species extrapolation models can be invaluable for risk assessment purposes. In this talk, I will discuss models that have been explored by the National Institute for Mathematical and Biological Synthesis (NIMBioS) Inhalation Anthrax Working Group in an effort add to the potential tools used by those making risk assessment decisions.
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Synchronization of Coupled Neurons via Robust Feedback
The synchronization of individual neurons is a central topic in understanding the rhythmicity of living organisms in neurosciences. The synchronization problem consists of making two or more systems oscillate in a synchronized way. In this case we require that the signals are identical, at least asymptotically when t→∞. By using a robust feedback control approach, we provide a method for synchronization of coupled neurons. Simulation results are presented for two case studies. We hope that our control approach can be useful to both study and gain insight of the effect of electrical stimulation of nerve cell, which has a range of clinical applications.
Robust Feedback Control based on Low Order Models with Uncertainty Estimation for a class of Biomedical Problems
Héctor Puebla1, Miguel A. Gutiérrez-Limón1, Eliseo Hernández-Martínez2, Alejandra Velasco-
In the last two decades, considerable effort has been directed toward the development of control schemes for biomedical applications aimed to provide physicians with a reliable and practical polices for drug dose. The development of mathematical models for biomedical problems has impulse model-based control designs. However, model-based control for biomedical applications is a challenging problem due significant model uncertainties as well intra and inter-patient variability. In this work, we are addressing a model-based robust feedback control approach for a class of biomedical applications. Our control design is based on a low-order step response model enhanced with estimation of model uncertainties due model reduction and uncertainties in model parameters. The control design is addressed using a simple robust control approach that has two features for practical application of the resulting controller: (i) a systematic consideration of uncertainty that leads to a controller with a good robustness properties, (ii) an equivalent linear control structure with simple tuning rules that could be implemented in practice. Numerical simulations on two case studies, glucose regulation in diabetes type 1 and the regulation of virion particles in HIV.
Modeling the Effect of Avian Stage-dependent Vector Exposure on Enzootic West Nile Virus Transmission and Control
Suzanne Robertson
Virginia Commonwealth University
West Nile virus (WNV) is major public health concern in the United States. Seasonal WNV outbreaks have been widely observed to be associated with the end of the avian nesting season. Newly hatched birds, or nestlings, have less feather coverage and fewer defense mechanisms than older birds, rendering them more vulnerable to mosquitoes. While total avian population size increases throughout the season, nestling abundance declines at the end of the brooding season. We investigate how this temporal variation in host stage abundance, along with the differential exposure of these stages to mosquito bites, may structure enzootic WNV transmission with a novel mathematical model incorporating avian (host) stage-structure and within-species heterogeneity in the form of stage-specific mosquito (vector) biting rates. Currently, the main control methods for WNV are mosquito larvicide and adulticide. We use optimal control as well as genetic algorithms to explore the viability of nestling vaccination as a new form of WNV control.
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Stability and “Hidden Periodicity” in a Discrete, Probabilistic Two-state Lattice Model of Intracellular Cardiac Calcium
Robert Rovetti
Loyola Marymount University We examine a discrete-time, probabilistic two-state lattice model with nearest-neighbor interactions, based on the intracellular calcium release system of cardiac cells. In numerical simulations of a 10,000-node lattice, the entire system can exhibit quasi-period-2 behavior (alternans) that corresponds to physiological conditions leading to arrhythmia and sudden cardiac death. However, under certain conditions, the lattice can “split” into two regions which individually exhibit periodic behavior but are in opposite phase, thereby cancelling each other out in the ensemble average. The result is a “hidden periodicity” which corresponds to the physiological case of subcellular alternans. We discuss conditions under which this splitting can occur.
Migrations Under Biased Perception: The Distribution of Sepcialists and Generalists in a Heterogeneous Landscape with Variably Discounted
Resources
Jonathan T. Rowell1, Garrett M. Street2, Igor Erovenko1* 1University of North Carolina Greensboro, 2Mississippi State University
The dispersal of organisms through their environment is influenced by multiple factors including the quantity and quality of resources and the presence of competitors; however, the perception of these factors can be compromised. In this talk, we explore population distributions that arise when individuals may be perceptually biased and discount some regions of available resources due to palatability, the local camouflaging of resources, or other external aspects of the environment that diminish apparent local desirability. The imbalance in growth and dispersal for these specialists leads to standing solutions with internal directional migration. When bias‐free generalists are introduced to existing specialist populations (or the reverse), the evolution of the community assemblage depends strongly upon the initial location of the novel group. Additionally, specialists are at risk of marginalization or elimination under slowly traveling waves of vegetative transformation.
Efficient Quartet Systems
Joseph Rusinko Hobart and William Smith Colleges
Quartet trees that are displayed by larger phylogenetic trees are common inputs to phylogenomic reconstruction algorithms. We introduce the Efficient Quartet System to represent a phylogenetic tree with a subset of the quartets displayed by the tree which encode all of the topological information of the tree. We demonstrate that Efficient Quartet Systems effective inputs for quartet amalgamation algorithms when trying to reconstruct species trees and supertrees.
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Territorial Movement Game
Jan Rychtar The University of North Carolina at Greensboro
The important biological problem of how groups of animals should allocate themselves between different habitats, has been modeled extensively. Such habitat selection models have usually involved infinite well mixed populations. In particular, the problem of allocation over a number of food patches when movement is not costly, the ideal free distribution (IFD) model is well-developed. Here we generalize (and solve) a habitat selection game for a finite structured population. We show that habitat selection in such a structured population can have multiple stable distributions (in contrast to the equivalent IFD model that is practically unique). We also define and study a ”predator dilution game” where unlike in the habitat selection game, individuals prefer to aggregate (to avoid being caught by predators due to the dilution effect) and show that this model has a unique solution when movement is unrestricted.
Experimenting with Mathematical Biology
Rebecca Sanft and Anne Walter University of North Carolina at Asheville
St. Olaf College recently added a Mathematical Biology concentration to its curriculum. The core course, Mathematics of Biology, was redesigned to include a wet laboratory. The labs required students to collect data and implement the essential modeling techniques of formulation, implementation, validation, and analysis. The four labs investigated population growth, enzyme kinetics, glucose-insulin feedback and random walks/diffusion. Based on assessment data, having the lab and class juxtaposed was an effective way to reinforce mathematical concepts and encourage collaboration among students with different majors. We discuss key factors that permitted this course’s development, the continuing challenges and how this model might be adapted to other venues. Using Cellular Automata to Model the Gun Violence Epidemic in Chicago,
IL
Shelby Scott University of Tennessee, Knoxville
In 2013, the CDC reported that 3.5 per 100,000 deaths resulted from firearm induced homicide. Despite overall national reductions in fatal and nonfatal shootings since the 1990s, gun violence remains a major problem in communities nationwide, including Chicago, Illinois. Gun violence has often been referred to as an “epidemic,” but limited research exists comparing the issue to a disease. We hypothesize that a cellular automata (CA) epidemic model can appropriately determine the conditions that lead to an outbreak of gun violence and expose some underlying causes of propagation. A CA model consists of an array of cells, each with a defined state. With each time step, the cellular states are updated based on fairly simple rules. We simulate gun violence by combining tenets of SEIR models with spatially explicit CA models. We show that a modified sand pile model can approximate the spread of violence in Chicago. This model serves as a predictive tool to determine where outbreaks of violence might take place, as well as an extrapolative tool for explaining why and how these acts of violence occur.
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Systemic Influences on the Inflammatory Phase of Wound Healing
Rebecca Segal, Angela Reynolds, Robert Diegelmann, Racheal Cooper Virginia Commonwealth University
Wound healing and tissue repair is a complex, multi-phase process. Even in healthy individuals, it is difficult to quantify the different components involved in the successful healing of a wound. The inflammatory phase is particularly important to understand because dysfunction in this phase leads to undesirable patient outcomes. In order to understand the inflammatory phase in more detail, we developed an ordinary differential equation model that accounts for two systemic mediators that are known to modulate this phase, estrogen (a protective hormone during wound healing) and cortisol (a hormone elevated after trauma that slows healing). Including the effects of estrogen and cortisol is a necessary step to creating a patient specific model that accounts for gender and trauma. This inflammatory phase model will later become the inflammatory subsystem of our full wound healing model, which includes fibroblast activity, collagen accumulation and remodeling.
Teaching Nonlinear Dynamics to Biology Freshmen Improves Math Interest and Physics Performance
Jane Shevtsov, Alan Garfinkel, William Conley, Kevin Eagan, Erin Sanders and Blaire van
Valkenburgh University of California, Los Angeles
Since Fall 2013, UCLA has been offering a two-course sequence, Life Sciences 30AB (LS 30), which students can complete for major credit instead of the traditional Calculus for Life Sciences curriculum, Math 3A-C. The LS30 courses focus on modeling biological systems using differential equations. Mathematical topics include state spaces, vector fields, trajectories, Euler's method, equilibria and stability, nullclines, bifurcations, limit cycles, chaos, linear stability analysis and optimization. The fundamental concepts of calculus and linear algebra are also covered but memorization of technical formulas is not emphasized. In addition, there is a computer lab component in which students learn programming and use simulation to study biological models.
LS 30 dramatically increases students’ interest in math. While 81% of students say their interest in the subject was low to medium before an LS 30 class (A or B), at the end of the class, 92% say their interest is medium to high. We also monitored student performance in subsequent physics courses, for which math is a prerequisite. 30.5% of students who took LS 30 received an A or A+ in physics, compared to 13.5% of students who completed Math 3. Only 2.8% of LS 30 students received a C- or lower in physics, compared to 12.4% of Math 3 students. After adjusting for student preparation and demographic characteristics, we still nd LS 30 students scoring 0.4 grade points higher than Math 3 students in physics. We hypothesize that this e ect may be attributed to LS 30 students' extensive exposure to modeling.
Spatiotemporal Protein Patterns in Dividing Bacterial Cells
Blerta Shtylla Pomona College
During division bacterial cells must equally split their components. However, due to their small size these cells do not possess complex machinery to help equipartition cell contents and to also place the division plane at the correct location prior to physical cell separation. Instead biochemical reactions must use to guide the spatial and temporal separation of cell components. In this talk, we discuss mathematical models that capture the spatial and temporal localization of proteins involved in the division of Caulobacter
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crescentus bacteria. Using PDE models we show that these species can not only be used to equally separate bacterial genetic material but can also be used to correctly place the division plane at the midcell prior to division. Model analysis shows that the model can generate oscillatory behavior, which turns out to be in alignment with recent experimental data.
Rodents of Unusual Sperm
Julie Simons1, Paul Cripe2, Owen Richfield2
1The California Maritime Academy, 2Tulane University Cooperative swimming behavior in sperm is a phenomenon observed in many species of rodents and marsupials. These behaviors involve swimming in pairs or groups, often with a mechanical link between individuals. In particular, some species of opossum have sperm often swim cooperatively as a pair, with heads fused together. While this behavior has been well-documented, it is unknown how it contributes to fertilization potential. In some experimental work, it has been shown that groups swim faster than individuals. On the other hand, a significant portion of the sperm engaged in collective swimming are rendered unable to fertilize the oocyte because of damage caused by the collective swimming itself. In this talk, we will introduce an undergraduate research project investigating the potential advantages to cooperative swimming behavior in low Reynolds number (viscous) fluid flow. We will highlight our mathematical and computational methodology, as well as how to engage undergraduates with minimal computational or physics background. Interestingly, our results indicate there are fluid mechanical advantages for cooperative swimming behaviors that coincide with similar geometries observed in biological studies. We postulate these results may provide evidence for an evolutionary advantage to cooperative swimming in sperm.
Exploring the Space of RNA Secondary Structures
Heather C. Smith
Georgia Institute of Technology When a strand of RNA folds onto itself, the resulting secondary structure gives information about the function of the molecule. We use combinatorial objects, such as non-crossing perfect matchings and plane trees, to model the possible secondary structures of a strand of RNA. Meanders are another combinatorial object of interest in comparing secondary structures as they are a pair of non-crossing perfect matchings which form a single closed curve when drawn on opposites sides of a single horizontal line. We discuss a number of interesting mathematical problems found at this interface of discrete mathematics and molecular biology.
Human Exposure Modeling using SHEDS
Luther Smith1 and Graham Glen2 1Alion Science and Technology, Inc., 2ICF International
The Stochastic Human Exposure and Dose Simulation (SHEDS) modeling framework was developed for EPA’s Office of Research and Development (ORD). The SHEDS models are stochastic time/activity-based multi-media, -pathway, and -chemical microenvironmental models used to estimate pollutant exposures through various mechanisms. While the specifics of the SHEDS models are dependent on their applications, the inhalation, dermal, non-dietary ingestion, and dietary ingestion pathways have all been incorporated and the media have included air, surfaces, and soil and dust. Chemical concentrations are based on user supplied inputs and are tracked within microenvironments via decay, chemical applications, and fugacity calculations. Here, overviews of the SHEDS-Multimedia and SHEDS-HT models are presented.
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Model inputs were developed from a variety of sources such as modeled air pollution concentrations, physical and chemical properties of pollutants, human physiological parameters (e. g., absorption coefficients), census data, and specific product information. As the models are stochastic, the model inputs were developed in the form of statistical variability and uncertainty distributions. The presentation will include brief discussion of some modeling aspects incorporated during development, such as correlation of input variables, energy expenditure adjustments for EPOC/fatigue, sensitivity analyses, and adaptation of an existing fugacity model.
Extracting Biochemical Parameters from Protein Distributions of Vascular Cells
Partha Srinivasan
Cleveland State University
Using quantitative data collected from adult rat aortic smooth muscle cell cultures in vitro, we analyze the various distributions of proteins which are synthesized during the formation of extracellular matrix, like collagen and tropoelastin. We compare these results to the theoretical 2-stage model developed in (Friedman, et al. 2006, Shahrezaei, et al. 2008) for protein synthesis, under the assumption that the time these proteins take to decay is significantly longer than their corresponding mRNA. As might be expected, we do not find any simple linear correlation between the cell proliferation and protein synthesis. However, using the theoretical model mentioned above, we are able to extract biochemical parameters that may not be easy to measure experimentally, such as the number of proteins translated during an mRNA lifetime.
Optimal Control of Vaccination Rate in an Epidemiological Model of Clostridium difficile Transmission
Brittany Stephenson*, Cristina Lanzas, Suzanne Lenhart, Judy Day
University of Tennessee, Knoxville
The spore-forming, gram-negative bacteria Clostridium difficile can cause severe intestinal illness. A striking increase in the number of cases of C. difficile infection (CDI) among hospitals has highlighted the need to better understand how to prevent the spread of CDI. We begin by first extending a compartmental model of nosocomial C. difficile transmission to include vaccination. From there, we apply optimal control theory to determine the time-varying optimal vaccination rate that minimizes a combination of disease prevalence and spread in the hospital population as well as cost, in terms of time and money, associated with vaccination. Various hospital scenarios are considered, such as times of increased antibiotic prescription rate and times of outbreak, to see how such scenarios modify the optimal vaccination rate. By comparing total costs with a constant vaccination rate to those with a time-varying optimal vaccination rate, we determine in which scenarios a time-varying rate of vaccination would be preferred over a constant one.
Interdisciplinary Undergraduate Research in Biofluids
Eva M. Strawbridge James Madison University
Applications of fluid dynamics to math biology, by its very nature, exists at the interface of the two fields and often necessitates the coupling of experiment and theory. In practice this all too often means people who engage in one collaborating with those engaged in the other, leaving undergraduate research students
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firmly rooted on one side of this divide. As a result, this approach appears to propound the statement: ``Don’t look at the man behind the curtain!’’ In this talk I will discuss how we have incorporated experiment and mathematical theory together using both mathematical and experimentally driven questions in the JMU WORM Lab as well as some of the successful projects which have come out of this group.
Ideal Free Distributions with Limited Perception and Population Dynamics
Garrett M. Street1, Igor Erovenko2, Jonathan T. Rowell2
1Mississippi State University, 2University of North Carolina at Greensboro
The distribution of animals around their environment is one of the cornerstones of ecology. The ideal free distribution (IFD) describes the distribution of animals which are “ideal,” meaning they are assumed to always go to the patch where their intake is highest, and “free” in that they can enter any patch without restriction or cost in terms of time or energy. However, experiments show that there is a bias for overusing poor patches and underusing good patches in many animals. Considerable effort has been devoted to studying potential causes for departures from IFD. One of such possible causes is perceptual constraints – animals might not be able to distinguish between good and bad patches. By incorporating population dynamics into the model we show that if animals reproduce according to their resource uptake, then highly fecund animals still approach IFD even if their perception of patches is limited.
Mathematical Modeling of Cellular Blebbing Dynamics
Wanda Strychalski Case Western Reserve University
Cell migration plays an essential role in many important biological processes such as wound healing, cancer metastasis, embryonic development, and the immune response. Recent advances in microscopy have led to an increasing number of qualitative observations of cell migration in 3D environments that closely mimic physiological conditions. In particular, they showed that some cells such as leukocytes, embryonic cells, and cancer cells, migrating through 3D matrices adopt an amoeboid phenotype characterized by round, liquid-filled, pressure-driven protrusions. Blebs are one type of protrusion these cells use to migrate in different environments. A dynamic computational model of the cell is presented to simulate recent experiments of blebbing cells. Model results show that complex rheology of cytoplasm is essential to explain experimental observations.
A 2-D Compartmental Model for Multi-capillary Supply
Liang Sun, Junkoo Park, Alessandra L. Barrera Georgia Gwinnett College
Oxygen diffusion for time-dependent diffusion and consumption can be measured for small tissue regions containing a single capillary. An all or none model is reflected by myocardial infarction where necrotic regions are clearly demarcated. However if there is more than one capillary, the problem becomes very difficult; since the boundary of the ischemic area is no longer circular and is not known a priori. A geometric compartmental model using the Fick’s method will be presented for multi-capillary supply. Our method is to approach the steady-state by a transient process, which paradoxically may be more efficient than the steady state problem.
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Using Citizen Science and Remote Sensing Data to Model Hummingbird Migration
Sarah R. Supp1, Laura J. Graham2, Frank A. La Sorte3, Tina A. Cormier4, Gil Bohrer5, Donald
Powers6, Susan Wethington7, Kevin Guay4,5, Patrick Jantz4, Scott Goetz4, Catherine H. Graham2 1University of Maine, 2Stony Brook University, 3Cornell University, 4Woods Hole Research Center,
5The Ohio State University, 6George Fox University, 7Hummingbird Monitoring Network Understanding migration behavior and variation through time represents a complex problem for biologists. The constraints on migration may differ among seasons (spring versus autumn), as birds track resources, favorable weather or atmospheric conditions, and may have different needs at their destination (breeding versus wintering grounds). Environmental and weather conditions vary among years and seasons, and may impact the magnitude of variation in hummingbird migration routes and timing. Citizen-science projects, such as eBird (www.ebird.org), now allow researchers to track population movement of migratory species. eBird provides vast amounts of observation data and presents an opportunity to gain a population-level perspective on species movement patterns. In addition, data aggregation efforts such as Movebank (www.movebank.org) allow researchers to easily integrate environmental datasets from distributed resources to evaluate the impact of environmental and atmospheric variables on species occurrence. Because of their small body size, high metabolic rates, and dependence on nectar resources, hummingbirds may deviate substantially from other bird species in their migratory routes, timing, and response to environmental or weather factors. Using generalized additive models for location, shape, and scale (gamlss) in program R, we model 8 years of eBird data (2008-2015) from 5 North American latitudinal migrating hummingbird species. For each species we determine the environmental and weather variables most correlated with migratory route in spring vs. autumn for each year and evaluate the explanatory power of physiological constraints on hummingbird geospatial location and ability to respond to changes in environmental and weather parameters. We compare the patterns in spring vs. autumn routes, and also characterize the degree of annual variation in environmental conditions, migration route and timing.
Exploring an Immunology Model for Devil Facial Tumor Disease
Adjo Tameklo and Kait Weihofen University of St. Francis
Tasmanian devil facial tumor disease (DFTD) is a transmissible cancer affecting a large number of Tasmanian devils in southern Australia. This cancer has proven to be neither viral or bacterial in nature, but it is known to transmit rapidly within the Tasmanian devil community. The lack of genetic diversity and their inability to differentiate between their own cells and foreign cells is one of the main reasons that they cannot combat the disease. The rate at which the disease is transmitted is high when the devils engage in biting during play or mating. In this talk, we will discuss the contact the rate of the disease among the devil population, the immunology/pathology and a possible model to help explore different vaccination methods for the disease. Teaching Systems Biology of the Circadian Clock with Journal Articles and
Matlab
Stephanie R. Taylor Colby College
I will describe a two course sequence that I teach in the computer science department at a small liberal arts college. The goal of the first course is to introduce students to the basics of mathematical modeling of biological systems. Students study topics including 1) modeling kinetics with ordinary differential
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equations, 2) motifs in biological systems, 3) numerical solution of ODEs, 4) parameter-fitting through optimization to match model output to data, and 5) parametric sensitivity analysis. To provide a theme, all projects are centered on the gene regulatory network controlling the circadian clock. Student read relevant journal articles, present them in class, and write Matlab code related to the topics in the course as well as to several of the articles. In the second course, students spend a semester extending the work of a recently published journal article. In this course, they engage in a literature search, design Matlab programs, and, in many cases, analyze circadian time-course data. By the end of the two courses, students are able to relate the mathematics to the biology in a meaningful way. Stability Analysis of a Prey Refuge Predator-Prey Model with Allee Effects
Unal Ufuktepe1, Burcin Kulahcioglu2, and Sinan Kapcak1
1American University of the Middle East, 2Izmir University of Economics
We study the impact of the Allee effect and prey refuge on the stability of a discrete time predator prey model. In this study, we focus on stability behavior of the system with the Allee effect in predator, prey and both populations by using center manifold theorem and type of bifurcations. Based on our analytical and numerical results, we observe that the Allee effects stabilizes the systems dynamics in a moderate value of the prey refuge.
On the Perfect Reconstruction of the Structure of Dynamic Networks
Alan Veliz-Cuba University of Dayton
The network inference problem consists in reconstructing the structure or wiring diagram of a dynamic network from time-series data. Even though this problem has been studied in the past, there is no algorithm that guarantees perfect reconstruction of the structure of a dynamic network. In this talk I will present a framework and algorithm to solve the network inference problem for discrete-time networks that, given enough data, is guaranteed to reconstruct the structure with zero errors. The framework uses tools from algebraic geometry. Modeling of the Human Circadian Clock: per3 Provides Molecular Support
for Behavioral Observations
Ahmet Ay1, Soo Bin Kwon2, Krista K. Ingram1, Amanda R. Liberman1, Ha T. Vu1* 1Colgate University, 2University of California, Los Angeles
The human circadian clock controls daily patterns of sleep-wake and activity cycles. Circadian clock malfunctions can lead to serious pathologies, ranging from obesity and diabetes to cancer. The human circadian clock consists of a core negative feedback loop: period genes (per13) and cryptochromes12 (cry1-2) are activated by the BMAL1-CLK protein complexes: the translated PER and CRY proteins in turn inhibit the transcription of BMAL1-CLK. The per3 gene is often believed to be unimportant to this network, since the biological clock continues to function in the absence of per3. However, recent research has causally linked per3 to numerous sleep disorders and behavioral conditions. Here, we developed for the first time a comprehensive mathematical model of the human circadian clock consisting of nine genes, including per3. We performed parameter searches to demonstrate that our model can reproduce the dynamics of the human circadian clock in more than ten mutant conditions. Using our model we also
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predicted the circadian clock dynamics in four recently discovered per3 mutant genetic backgrounds that have been linked to human sleep and behavioral disorders. Our results support the current experimental observations that shows per3 gene is important for the correct functioning of the circadian clock, and suggests that further research has to be done on per3 gene for true understanding of human circadian clock.
Mathematically Modeling the Caulobacter crescentus Cell
Nattanicha Wattananimitgul
Pomona College
During division, bacterial cells must equally partition their contents. However, due to their small size these cells do not possess complex machinery to help with division, instead biochemical reactions must be used to guide the spatial and temporal separation of cell components. Here we present a whole cell stochastic mathematical model that captures the spatial and temporal localization of proteins involved in the division of Caulobacter crescentus bacteria in a realistic cell model that incorporates important geometrical effects. We show that these species can be used to equally separate bacterial genetic material during division. Influence of Awareness that Results from Direct Experience on the Spread
of Epidemics
Ying Xin Ohio University
Here we study ODE epidemic models with spread of awareness, assuming that a certain proportion of the hosts will become aware of the ongoing outbreak upon recovery. This study builds on W. Just and J. Saldaña’s work in (Just, et al. 2016), and is conducted under the same framework, while addressing the influence of the awareness gained from direct experience of the disease. In [1], the authors investigated the question whether preventive behavioral response triggered by awareness of the infection is sufficient to prevent future flare-ups from low endemic levels if awareness decays over time. They showed that if all the hosts experienced infection return directly to the susceptible compartment upon recovery, such oscillations are ruled out in Susceptible-Aware- Infectious-Susceptible models with a single compartment of aware hosts, but can occur if two distinct compartments of aware hosts who differ in their willingness to alert other susceptible hosts are considered. Qualitatively, the models studied here produce the same results when we assume that recovery from the disease may or even will convey awareness from direct experience.
Mathematical Models and Optimal Control for Alternative Pest Management to Alfalfa Agroecosystems
Mohammed Yahdi
Hartnell College
Alfalfa is the most cultivated forage legume in the world supporting dairy and cattle productions, and with growing export market for U.S. farmers. The Potato Leafhopper (PLH) is a pest that costs serious and costly damages to the host-plant alfalfa in traditional monoculture fields. Moreover, chemical pesticides are increasingly costly and unsafe. It is critical to explore natural and sustainable alternative pest management strategies to reduce PLH abundance and damage to alfalfa while making them viable by considering production and revenues levels for farmers. Based on actual field experiments, this project developed mathematical models, computer simulations and optimal control theory for sustainable, revenue effective and environmentally safe strategies that minimize alfalfa-plant damage from PHL pests. The models
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incorporated enemies hypothesis (natural predators), polyculture farming (growing other plants with alfalfa), and movement-risk hypothesis (moving pests are vulnerable to predators), that have been shown to be effective in field experiments (Straub et al.). Mathematical models including twelve size and time-dependent parameters were created using systems of differential equations. They were shown to accurately fit results from open-field experiments and were used to predict outcomes for polyculture scenarios not covered by these experiments. A sensitivity analysis established the relative importance of each parameter. Optimal control theory results showed sustainable and viable designs of plant-diversity levels that minimize the alfalfa damage, preserve the nutritional efficacy of the harvests, minimize production costs, and maximize farmers’ profit over several years of the alfalfa life cycles.
Predator-Prey Dynamics with Intraspecific Competition and an Allee Effect in the Predator Population
Anne E. Yust1, Erin N. Bodine2
1The New School, 2Rhodes College The study of the Allee effect on the stability of equilibria of predator-prey systems is of recent interest to mathematicians, ecologists, and conservationists. Many theoretical models that include the Allee effect result in an unstable coexistence equilibrium. However, empirical evidence suggests that predator-prey systems that exhibit density dependent growth at small population densities still can achieve coexistence in the long term. In this talk, I will review an often cited model that incorporates an Allee effect in the predator population and results in an unstable coexistence equilibrium, and then I will present a novel extension to this model that includes a term that models intraspecific competition within the predator population. The additional term penalizes predator population growth for large predator densities relative to the prey density. Standard methods of equilibrium analysis show that there exist biologically reasonable parameter sets which produce a stable coexistence equilibrium for the modified model.
