October 911, 2009
Huntsville, Alabama
About the Conference
The general theme of the conference will be on the theory, modeling, and analysis of the temporal dynamics of biological populations. A special emphasis at this second conference will be placed on the modeling of epidemics. Mathematical modeling and analysis can be used to give insight and better understanding of the dynamics of biological populations. Mathematical models are built on tradeoffs between biological accuracy and mathematical tractability. Of particular importance are the effects on a population's dynamics of modeling assumptions concerning spatial or temporal heterogeneities or concerning heterogeneities among the characteristics of individuals within the population and how these characteristics affect the way they interact with their environment. The invited speakers will address a wide variety of theoretical issues, applications (ecological, epidemiological, etc.), and case studies that illustrate the connection of models with data.
Conference Organizers
Conference Coordinator
 Jia Li, Department of Mathematical Science, University of Alabama in Huntsville, li@math.uah.edu
Scientific Advisory Committee
 Jim Cushing, Department of Mathematics, the University of Arizona (Chair)
 Thomas Banks, Center for Research in Scientific Computation, North Carolina State University
 Fred Brauer, Department of Mathematics, the University of British Columbia
 Carlos CastilloChavez, Department of Mathematics and Statistics, Arizona State University
 Karl Hadeler, Lehrstuhl für Biomathematik, University of Tübingen
 Mac Hyman, Theoretical Division, Los Alamos National Laboratory
Organizing Committee
 Jia Li, Department of Mathematical Science, University of Alabama in Huntsville (Chair), li@math.uah.edu
 Jim Cushing, Department of Mathematics, the University of Arizona, cushing@math.arizona.edu
 Saber Elaydi, Department of Mathematics, Trinity University, selaydi@trinity.edu
Sponsors
Publication
Speakers will be invited to submit papers for possible publication in special issues of JBD and JDEA that will be devoted to the conference.
Conference Schedule
Friday, Oct. 9  Saturday, Oct. 10  Sunday, Oct. 11  
8:00 AM  Registration  Registration  Registration  
8:30 AM  Room 107 Opening Remarks, President Williams (UAH) 

8:45 AM  Room 107 Horst Thieme (Chair: Banks) 
Room 107 Lou Gross (Chair: Hyman) 
Room 107 Alun Lloyd (Chair: Cushing) 

9:45 AM  Break  Break  Break  
Room 109 (Chair: Gumel) 
Room 103 (Chair: Elaydi) 
Room 105 (Chair: Burns) 
Room 109 (Chair: Yakubu) 
Room 103 (Chair: Nisbet) 
Room 158 (Chair: Ruan) 
Room 109 (Chair: Lenhart) 
Room 103 (Chair: Wolkowicz) 
Room 158 (Chair: Smith) 

10:00 AM  Lou  Sacker  Banks  Hyman  Ackleh  Huang  Feng  Olofsson  Burns 
10:30 AM  Hadeler  Hayward  Nisbet  Song  X. Li  Ai  Bourouiba  Dib  Weiss 
11:00 AM  Break  Break  Zhao  Boushaba  Kostova  
11:15 AM  Brauer  Henson  Nevai  Martcheva  Smith  Deng  End of Conference at 11:30 AM!  
11:45 AM  Gaff  Robertson  Maroun  Tridane  Wolkowicz  B. Li  
12:15 PM  Lunch on Your Own  Lunch on Your Own  
1:15 PM  Registration  Registration  
1:45 PM  Room 107 Heesterbeek (Chair: Hadeler) 
Room 107 Jianhong Wu (Chair: Brauer) 

2:45 PM  Break  Break  
Room 109 (Chair: Martcheva) 
Room 103 (Chair: Henson) 
Room 105 (Chair: Sacker) 
Room 109 (Chair: Lou) 
Room 103 (Chair: Ackleh) 
Room 158 (Chair: Huang) 

3:00 PM  Chitnis  Liu  Lenhart  Bortz  Mickens  H. Wang  
3:30 PM  Ruan  Cushing  Ding  Dukic  Rael  J.X. Li  
4:00 PM  Break  Break  
4:15 PM  Xu  Jang  Rong  Eladdadi  Hong  Zou  
4:45 PM  Wesley  Yakubu  Gumel  Sindi  Leite  Shuai  
5:20 PM  Room 107 NSF Programs Related to Mathematical and Computational Biology Kostova (NSF) 

6:00 PM 7:30 PM 
Room 301 Reception and Poster Session 
Printable Format
Conference Speakers and Participants
Confirmed Plenary Speakers
 Lou Gross, Departments of Ecology and Evolutionary Biology and Mathematics, University of Tennessee
 Hans Heesterbeek, Faculty of Veterinary Medicine, Utrecht University
 Alun Lloyd, Department of Mathematics, North Carolina State University
 Horst Thieme, School of Mathematics and Statistics, Arizona State University
 Jianhong Wu, Department of Mathematics and Statistics, Center for Disease Modeling, York University
Invited Speakers
 Azmy Ackleh, Department of Mathematics, University of Louisiana at Lafayette
 Shangbing Ai, Department of Mathematical Sciences, University of Alabama in Huntsville
 Thomas Banks, Center for Research in Scientific Computation, Center for Quantitative Science in Biomedicine, North Carolina State University
 David Bortz, Department of Applied Mathematics, University of Colorado
 Lydia Bourouiba, Department of Mathematics and Statistics, York University
 Khalid Boushaba, Department of Mathematics, Iowa State University
 Fred Brauer, Department of Mathematics, University of British Columbia
 John Burns, Department of Mathematics, Virginia Tech
 Nakul Chitnis, Malaria Modeling Team, Swiss Tropical Institute, Liverpool School of Tropical Medicine
 Jim Cushing, Department of Mathematics, University of Arizona
 Keng Deng, Department of Mathematics, University of Louisiana at Lafayette
 Youssef Dib, Department of Mathematics and Physics, University of Louisiana at Monroe
 Wandi Ding, Department of Mathematical Sciences, Middle Tennessee State University
 Vanja Dukic, Department of Health Studies, University of Chicago
 Amina Eladdadi, Department of Mathematics, College of Saint Rose
 Zhilan Feng, Department of Mathematics, Purdue University
 Holly Gaff, Virginia Modeling, Analysis and Simulation Center, Old Dominion University
 Abba Gumel, Department of Mathematics, University of Manitoba
 Karl Hadeler, Lehrstuhl f'r Biomathematik, University of T'bingen
 Jim Hayward, Department of Biology, Andrews University
 Shandelle Henson, Department of Mathematics, Andrews University
 Dawei Hong, Department of Computer Science, Rutgers University
 Wenzhang Huang, Department of Mathematical Sciences, University of Alabama in Huntsville
 Mac Hyman, Department of Mathematics, Tulane University
 Sophia Jang, Department of Mathematics and Statistics, Texas Tech University
 Tanya KostovaVassilevsk, DMS, National Science Foundation
 Maria Leite, Department of Mathematics, University of Oklahoma
 Suzanne Lenhart, Department of Mathematics, University of Tennessee
 Bingtuan Li, Department of Mathematics, University of Louisville
 Jia Li, Department of Mathematical Sciences, University of Alabama in Huntsville
 Jiaxu Li, Department of Mathematics, The University of Louisville
 XueZhi Li, Department of Mathematics, Xingyang Normal University
 Rongsong Liu, Department of Mathematics, University of Wyoming
 Yuan Lou, Department of Mathematics, Ohio State University
 Maia Martcheva, Department of Mathematics, University of Florida
 Mariette Maroun, Department of Mathematics and Physics, University of Louisiana at Monroe
 Ron Mickens, Department of Physics, Clark University
 Andrew Nevai, Department of Mathematics, University of Central Florida
 Roger Nisbet, Department of Ecology, Evolution and Marine Biology, University of California, Santa Barbara
 Peter Olofsson, Department of Mathematics, Trinity University
 Rosalyn Rael, Department of Ecology and Evolutionary Biology, University of Michigan
 Suzanne Robertson, Mathematical Biosciences Institute, Ohio State University
 Libin Rong, Theoretical Biology and Biophysics, LANL
 Shigui Ruan, Department of Mathematics, University of Miami
 Robert Sacker, Department of Mathematics, University of Southern California
 Zhisheng Shuai, Department of Mathematical and Statistical Sciences, University of Alberta
 Suzanne Sindi, Center for Computational Molecular Biology, Brown University
 Hal Smith, Department of Mathematics and Statistics, Arizona State University
 Baojun Song, Department of Mathematical Sciences, Montclair State University
 Abdessamad Tridane, Department of Applied Sciences and Mathematics, Arizona State University at the Polytechnic Campus
 Haiyan Wang, Division of Mathematical and Natural Sciences, Arizona State University
 Howie Weiss, Department of Mathematics, Georgia Tech
 Curtis Wesley, Department of Mathematics, Louisiana State University at Shreveport
 Gail Wolkowicz, Department of Mathematics and Statistics, McMaster University
 Dashun Xu, Department of Mathematics, Southern Illinois University, Carbondale
 AbdulAziz Yakubu, Department of Mathematics, Howard University
 Shan Zhao, Department of Mathematics, University of Alabama
 Xingfu Zou, Department of Applied Mathematics, University of Western Ontario
Poster Presenters
 Erin Bodine, Department of Mathematics, University of Tennessee
 Thanate Dhirasakdanon, School of Mathematics and Statistics, Arizona State University
 Heather Finotti, Department of Mathematics, University of Tennessee
 Zhun Han, School of Mathematics and Statistics, Arizona State University
 Kim Meyer, Department of Mathematics, University of Louisville
 Thembinkosi Mkhatshwa, Department of Mathematics, Marshall University
 Anna Mummert, Department of Mathematics, Marshall University
 Sherry Towers, Department of Applied Statistics, Purdue University
 Roy Trevino, School of Mathematics and Statistics, Arizona State University
 Xiaohong Wang, Mathematical, Computational & Modeling Sciences Center, Arizona State University
 Xiuquan Wang, Department of Mathematics, Southern Illinois University, Carbondale
 Mohammed Yahdi, Department of Mathematics and Computer Science, Ursinus College
 Yiding Yang, Department of Mathematics, Purdue University
 Feng Yu, Department of Statistics and Epidemiology, RTI International
 Peng Zhong, Department of Mathematics, University of Tennessee
Participants
 Joy Agee, Department of Biology, University of Alabama in Huntsville
 Folashade Agusto, National Institute for Mathematical & Biological Synthesis, University of Tennessee
 Barbara BenitezGucciardi, Department of Mathematics, Houston Baptist University
 Fengjuan Chen, Department of Mathematics, Zhejiang Normal University
 Amina Dozier, Department of Mathematical Sciences, University of Alabama in Huntsville
 Sean Ellermeyer, Department of Mathematics and Statistics, Kennesaw State University
 Michael Kelly, National Institute for Mathematical & Biological Synthesis, University of Tennessee
 Douglas Langille, Department of Mathematical Sciences, University of Alabama in Huntsville
 Michael Lawton, Department of Ecology and Evolutionary Biology, University of Tennessee
 Nianpeng Li, Department of Mathematics, Howard University
 Junliang Lu, Department of Mathematical Sciences, University of Alabama in Huntsville
 Shushuang Man, Department of mathematics & computer science, Southwest Minnesota State University
 Marco Martinez, Department of Mathematics, University of Tennessee
 Myla Menitt, Department of Mathematical Sciences, University of Alabama in Huntsville
 Jing Qing, Department of Mathematics, University of Miami
 Paul Salceanu, Department of Mathematics, University of Louisiana at Lafayette
 Deirdre Watts, Department of Mathematical Sciences, University of Alabama in Huntsville
 Aaron Willmon, Department of Mathematics, Walter State Community College
Titles and Abstracts
Plenary Speakers
Integrating into the Future
Dr. Louis Gross
Departments of Ecology and Evolutionary Biology and Mathematics, University of Tennessee
NIMBioS and the Math/Biology Interface One indicator of the potential for mathematical approaches to enhance research across the biological sciences is the increased funding in this area by agencies such as the NSF. The advent of the National Institute for Mathematical and Biological Synthesis, as a second major NSFfunded center at this interface (MBI being the other), provides evidence that the field is not only deserving of enhanced support, but additionally that there are advantages to multiple approaches to foster the growth of these interdisciplinary interactions. NIMBioS provides multiple routes for increased research and educational connections between these fields and to foster connections as well to other areas such as computation and social science. I will describe the opportunities that NIMBioS provides, give examples of the research and educational initiatives already underway, and provide some personal thoughts about future directions in both the development of general theory and the application to important practical issues.
The Construction and Use of Next Generation Matrices for Compartmental Epidemic Systems
Dr. Hans Heesterbeek
Faculty of Veterinary Medicine, University of Utrecht
The basic reproduction number $R_{0}$ is arguably the most important quantity in infectious disease epidemiology. The nextgeneration matrix (NGM) is the natural basis for the definition and calculation of $R_{0}$ where finitely many different categories of individuals are recognised. I clear up confusion that has been around in the literature concerning the construction of this matrix, specifically for the most frequently used socalled compartmental models. I present a detailed easy recipe for the construction of the NGM from basic ingredients derived directly from the specifications of the model. We show that two related matrices exist which we define to be NGM with large domain and the NGM with small domain. The three matrices together reflect the range of possibilities encountered in the literature for the characterisation of $R_{0}$. I show how they are connected and how their construction follows from the basic model ingredie! nts, and establish that they have the same nonzero eigenvalues, the largest of which is the basic reproduction number $R_{0}$. Although I present formal recipes based on linear algebra, the construction of the NGM by way of direct epidemiological reasoning is strongly encouraged, using the clear interpretation of the elements of the NGM and of the model ingredients. I present a selection of examples as a practical guide to the methods. Finally, I will show several applications of nextgeneration matrices for epidemiological systems, notably the possible insights that can be gained from sensitivity analysis of $R_{0}$ using the NGM. The largest part of this lecture is based on recent joint work with Odo Diekmann (Utrecht) and Mick Roberts (Auckland): The construction of nextgenenation matrices for compartmental epidemic systems (Diekmann, Heesterbeek & Roberts, submitted). The latter part is based on the paper: Elasticity analysis in epidemiology: an application to tickborne infections (Matser, Hartemink, Heesterbeek, Galvani & Davis; Ecology Letters, 2009, in press)
Modeling Genetic Strategies for Controlling Mosquito Borne Diseases
Dr. Alun Lloyd
Department of Mathematics, North Carolina State University
Mosquito borne infections, most notably malaria and dengue, kill over a million people every year. Traditional control measures (such as insecticides) against these infections in developing countries have had mixed success. A novel avenue of attack involves the production and release of mosquitoes that have been manipulated or genetically engineered to be less able, or even unable, to transmit infection. The manipulated mosquitoes will, however, be less fit than native (wildtype) mosquitoes, and so would not be expected to spread in the wild. Selfish genesones that are able to "bend" the laws of Mendelian inheritance, getting transmitted to a higher fraction of offspring than would be expectedhave been suggested as a way of overcoming this problem, driving the desired trait into wild populations. Mathematical modeling is playing an important role in several largescale projects that are currently under way to assess the feasibility of these genetic techniques. In this talk I shall discuss the biology of some of the approches and the accompanying modeling work, illustrating how a number of different models are being used as the projects move along the path from labbased studies to possible field deployment.
Population Persistence without a Compact Attractor
Dr. Horst R. Thieme
School of Mathematical and Statistical Sciences, Arizona State University
(Joint work with Hal L. Smith)
The theory of persistence is designed to provide an answer to such questions as which species, in a mathematical model of interacting species, will survive over the long term. In a mathematical model of an epidemic, will the disease drive a host population to extinction or will the host persist? Can a disease remain endemic in a population? Persistence theory can give a mathematically rigorous answer to these questions: it establishes an positive longterm lower bound for the component of a dynamical system such as population size or disease prevalence; if persistence is uniform, this lower bound does not depend on the initial state of the system.
Persistence theory conveniently uses the language of dynamical systems, notably semiflows on metric spaces. A powerful but also restricting assumption is the existence of a compact attractor of points. This assumption excludes, among other things, the consideration of growing populations. This talk explores how much it can be relaxed. The LotkaVolterra predatorprey system shows that some features of a compact attractor must be retained for uniform persistence. Applications are presented to the spread of infectious diseases in growing populations and to dividing cells in a chemostat with agedependent resource uptake and division rates.
Migratory Birds and Avian Influenza Outbreak: Models and Satellite Surveillance Data for Spatiotemporal Dynamics of H5N1 Spread
Dr. Jianhong Wu
Department of Mathematics and Statistics, Centre for Disease Modeling, York University
Virulent outbreaks of Highly Pathogenic Avian Influenza since 2005 have raised the question about the roles of migratory and wild birds in this disease's transmission dynamics. Despite increased monitoring, the role of wild waterfowl as the primary source of the highly pathogenic H5N1 has not been clearly established, and the consequence of outbreaks of HPAI among species of wild birds for the local and nonlocal ecology where migratory species are established has not been quantified. Understanding the entangled dynamics of migration and the disease dynamics is key to planning of prevention and control strategies for humans, migratory birds and the poultry industry. This talk will introduce the various factors involved in the spatial spread of H5N1 in Asia and present the results of a few dynamical models of seasonal migration linking the local dynamics during migratory stopovers to the largerscale migratory routes. The effect of repeated epizootic at specific migratory stopovers for Barheaded geese (Anser indicus) will be discussed as an illustration of the ecological impact of H5N1 outbreaks. Issues relevant to the coexistence and interaction of low and high pathogenic strains will be addressed, and some challenging problems in the theory of monotone periodic processes and nonlinear dynamical systems described by delay differential equations with periodic coefficients will be presented.
(This talk is based on projects in collaboration with Lydia Bourouiba, Venkaka Duvvuri, Stephen Gourley, Rongsong Liu and Sasha Alexandra Teslya.)
Invited Talks
Competitive Exclusion in a DiscreteTime, StageStructured Population Model
Dr. Azmy Ackleh
Department of Mathematics, University of Louisiana at Lafayette
We develop and analyze a discretetime stagestructured population model that describes the competition of two similar species. We show that if one of the species has invasion reproductive number greater than one and the other has invasion reproduction number less than one, then competitive exclusion occurs and the winner species is the one with the larger invasion reproductive number.
Stationary Periodic and Homoclinic Solutions for 1D Nonlocal Reactiondiffusion Equations
Dr. Shangbing Ai
Department of Mathematical Sciences, University of Alabama in Huntsville
Spatially periodic patterns for 1D nonlocal reactiondiffusion equations arise from various biological models. The problem reduces to study periodic and homoclinic solutions of differential equations with perturbations containing convolution terms. We consider the case that the system is timereversible. Assuming the unperturbed system has a family of periodic orbits surrounded by a homoclinic orbit, we establish the persistence of these solutions for the perturbed system.
Estimation of Cell Proliferation Dynamics Using CFSE Data
Dr. H. T. Banks
Center for Research in Scientific Computation, Center for Quantitative Science in Biomedicine, North Carolina State University
Advances in fluorescent labeling of cells as measured by flow cytometry have stimulated recent illuminating quantitative studies of proliferating populations of cells. We discuss our recent efforts on a new class of mathematical models based on fluorescence intensity as a structure variable to describe the evolution in time of proliferating cells labeled by carboxyfluorescein succinimidyl ester (CFSE). Early models and several extensions/modifications are discussed. Suggestions for improvements are presented and analyzed with respect to statistical significance for better agreement between model solutions and experimental data. These investigations reveal that the new decay/label loss and time dependent effective proliferation and death rates which we introduce do indeed provide improved fits of the model to data as well as new understanding of the data itself. Statistical models for the observed variability/noise in the data are discussed with implications for uncertainty quantification. The resulting new cell dynamics models should prove useful in proliferation assay tracking and modeling, with applications in numerous areas of disease progression (such as cancer, HIV and other viruses, etc.) well as in microbiology.
Fragmentation and Aggregation of Bacterial Emboli
Dr. David Bortz
Department of Applied Mathematics, University of Colorado
Klebsiella pneumoniae is one of the most common causes of intravascular catheter infections, potentially leading to lifethreatening bacteremia. These bloodstream infections dramatically increase the mortality of illnesses and often serve as an engine for sepsis. Our current model for the dynamics of the sizestructured population of aggregates in a hydrodynamic system is based on the Smoluchowski coagulation equations.
In this talk, I will discuss the progress of several investigations into properties of our model equations. In particular, I will focus on: a) accurate characterization of the fractal properties for the aggregates, b) a differential geometry approach to fragmentation modeling, and (time permitting) c) selfsimilar solutions to the equations.
Effect of CrossImmunity between High and Low Pathogenic Strains of Avian Influenza in Wild Birds at Seasonal Migration Stopovers
Dr. Lydia Bourouiba
Department of Mathematics and Statistics, York University
Many species of wild birds are identified to be highly susceptible to the highly pathogenic strain of H5N1 despite being known as natural reservoirs of low pathogenic avian influenza viruses. Understanding the disease dynamics of avian in uenza in wild birds at various stopovers of their seasonal migration is important for the evaluation of both the role of wild birds in the spread of H5N1, and the ecological impact of H5N1 outbreaks on these species.
Recent experimental studies identified a temporary crossimmunity between low pathogenic and the high pathogenic H5N1 strains in certain species of wild birds. The data focused on species of birds which are more susceptible to these strains. In this talk, I will discuss the impact of this crossimmunity observed at the individual bird level on the population as a whole. The effect of the seasonal prevalence of the low pathogenic strains on the change of the highly pathogenic strain disease dynamics will be discussed in the context of previous epidemics observed in bird populations.
This talk is based on projects in collaboration with Sasha Alexandra Teslya and Jianhong Wu.
A Mathematical Feasibility for the Use of Aptamers in Chemotherapy and Imaging
Dr. Khalid Boushaba
Department of Mathematics, Iowa State University
A challenge for drug design is to create molecules with optimal function that also partition efficiently into the appropriate in vivo compartment(s). This is particularly true in cancer treatments because cancer cells upregulate their expression of multidrug resistant transporters, which necessitates a higher concentration of extracellular drug to promote sufficiently high intracellular concentrations for cell killing. Pharmacokinetics can be improved by ancillary molecules, such as cyclodextrins, that increase the effective concentrations of hydrophobic drugs in the blood by providing a hydrophobic binding pocket. However, the extent to which the extracellular concentration of drug can be increased is limited. A second approach, different from the "push" mechanism just discussed, is a "pull" mechanism by which the effective intracellular concentrations of a drug is increased by a molecule with an affinity for the drug that is located inside the cell. Here we propose and give a proof in principle that intracellular RNA aptamers might perform this function. The mathematical model considers the following: Suppose I denotes a drug (inhibitor) which must be distributed spatially throughout a cell, but tends to remain outside the cell due the transport properties of the cell membrane. Suppose that E, a deleterious enzyme that binds to I, is expressed by the cell and remains in the cell. Here we evaluate the use of an intracellular aptamer with affinity for the inhibitor (I) to increase the efficiency of inhibitor transport across the cell membrane. We show that this outcome will occur if (1) the aptamer neither binds too tightly nor too weakly to the inhibitor than the enzyme and (2) the aptamer is much more diffusible in the cell ytoplasm than the enzyme. We illustrate these possibilities with numerical aimulations. The ability of the aptamer to increase the intracellular concentration of aptamer ligand (inhibitor in the above case) could also be put to use for imaging the cell. Thus, we propose and show by simulation that an intracellular aptamer can be enlisted for an integrated approach to increasing inhibitor effectiveness and imaging aptamerexpressing cells.
Backward Bifurcations in a Simple Disease Transmission Model
Dr. Fred Brauer
Department of Mathematics, University of British Columbia
We describe a simple disease transmission model with demographics, imperfect vaccination, and recovery with temporary immunity. We derive a necessary condition for the existence of a backward bifurcation which can not be satisfied if the immunity is permanent. For sufficiently rapid disease dynamics, this condition is also sufficient.
Sensitivity Analysis of Cancer Models with Proliferating and Quiescent Cells
Dr. John A. Burns
Interdisciplinary Center for Applied Mathematics, Virginia Tech
In this presentation we discuss a model of tumor growth that includes quiescence cells and the immune system response to a cyclephasespecific drug. Tumor cells can be divided into proliferating or cycling cells and nonproliferating or quiescent cells. A cell is considered "cancerous" when it has lost its ability to regulate cell growth and division leading to a rapid uncontrolled growth of malignant cells. The model considers three populations of cancer cells and the immune system. The three populations considered in this talk are the quiescence cells, the tumor cells during interphase and the tumor cells during mitosis. Delay differential equations are used to model the system to take into account the phases of the cell cycle. We then focus on a particular method (the Sensitivity Equation Method) for computing the model sensitivities and use these sensitivities to help predict the long term behavior of the model with and without drug treatment.
Mathematical Modeling of Malaria Epidemiology and Control
Dr. Nakul Chitnis
Malaria Modeling Team, Swiss Tropical Institute, Liverpool School of Tropical Medicine
Malaria interventions are usually prioritized using efficacy estimates from intervention trials, without considering the context of existing intervention packages or long term dynamics. We use numerical simulation of mathematical models of malaria in humans and mosquitoes to provide robust quantitative predictions of effectiveness of different strategies in reducing transmission, morbidity and mortality. We link individualbased stochastic simulation models for malaria in humans with a deterministic model for mosquito infection and survival, incorporating variations in host exposure to infectious bites, naturally acquired immunity to infection and disease, effects of coinfection, and variations in human infectiousness. We can reasonably well reproduce malariological patterns in endemic areas, including nonmonotonic relationships between parasite prevalence and disease incidence with host age and force of infection; and provide quantitative relationships between malaria morbidity and mortality, and increasing coverage of vector control interventions, intermittent preventive treatment in infants, and different vaccines.
The Fundamental Bifurcation Theorem and Darwinian Matrix Models
Dr. J. M. Cushing
Department of Mathematics, University of Arizona
Stability of a Delay Equation Arising from a JuvenileAdult Model
Dr. Keng Deng
Department of Mathematics, University of Louisiana at Lafayette
We consider a delay equation that has been formulated from a juvenileadult population model. We give conditions on the vital rates to ensure local stability of the positive equilibrium. We also show that under certain conditions the trivial equilibrium is asymptotically stable. We then make numerical simulations to describe the rich dynamical behavior of the model.
VIVO and VITRO HSV_1 Infections, LatencyReactivation by Systems Theory Approach
Dr. Youssef Dib
Department of Mathematics and Physics, University of Louisiana at Monroe
A nonlinear methematical model for HSV1 viral infections will be produced from its background. Differential cell are the host of this virus. Once infected, this differential cell would survive as long as it host this virus. It is assumed that both HSV1\'s DNA and Nuclear DNA in the differential cell depend on Thyroid Hormone liganded with its receptore. Numerical simulation proving the biological relevence will be shown. In addition, future research direction for this model will be discussed.
Optimal Control for a Tick Disease Model Using Hybrid ODE Systems
Dr. Wandi Ding
Department of Mathematical Sciences, Middle Tennessee State University
We are considering an optimal control problem for a type of hybrid system involving ordinary differential equations and a discrete time feature. One state variable has dynamics in only one season of the year and has a jump condition to obtain the initial condition for that corresponding season in the next year. The other state variable has continuous dynamics. Given a general objective functional, existence, necessary conditions and uniqueness for an optimal control are established. We apply our approach to a ticktransmitted disease model with age structure in which the tick dynamics changes seasonally while hosts have continuous dynamics. The goal is to maximize diseasefree ticks, minimize infected ticks through an optimal control strategy of treatment with acaricide. Numerical examples are given to illustrate the results.
Tracking Influenza Using Particle Learning Algorithms
Dr. Vanja Dukic
Department of Health Studies, University of Chicago
In this talk we introduce a novel approach, based on the particle learning (PL) methodology, for classic epidemics models from the family of the susceptibleexposedinfectedrecovered (SEIR) models. The proposed approach is particularly wellsuited to online learning and surveillance of infectious diseases. As compared to the widely used MCMC (O'Neil and Roberts 1999, Elderd et al. 2006, Leman et al. 2009) and perfect sampling (Fearnhead and Meliglokou 2004) based methods, the PL method, which is based on the clever use of sufficient statistics as added states, is more robust, easier to implement, and readily generalizable to problems with more complex dynamics.
Mathematical Modeling of the Effects of HER2 OverExpression in Breast Cancer
Dr. Amina Eladdadi
Department of Mathematics, The College of Saint Rose
(Joint work with David Isaacson, Department of Mathematical Sciences, Rensselaer Polytechnic Institute)
Members of the type I receptor tyrosine kinase (RTK) family, which consists of the epidermal growth factor receptor (EGFR), HER2 (ErbB2), HER3 (ErbB3) and HER4 (ErbB4) play a crucial role in growth and differentiation of both normal and malignant mammary epithelial cells. The carcinogenic effects of HER2 protein overexpression on cell growth and cell proliferation have been observed in a variety of experimental systems. These observations suggest that HER2 overexpression provides tumor cells with a growth advantage leading to a more aggressive phenotype. Although these effects have been attributed to high levels of HER2expression, there have been no quantitative linkages between HER2 expression levels and the proliferation rate of HER2overexpressing cells. To investigate the effects of HER2 receptor overexpression on cell proliferation, we have developed a mathematical model that describes the proliferative behavior of HER2overexpressing cells as a function of the HER2 expression level. The proliferation model formulates the cell proliferation rate as a function of the cell surface HER2 and EGFR receptor numbers and ligand concentration. The model enables us to simulate the proliferative behavior of the HER2overexpressing cells with various HER2 and EGFR expression levels at various ligand concentrations. Numerical simulations of the model give good agreement with the experimental data in which an increase in HER2 receptors leads to increased cell proliferation.
Modeling the Evolutionary Implications of Influenza Medication Strategies
Dr. Zhilan Feng
Department of Mathematics, Purdue University
(Joint work with J. Glasser, R. Liu, Z. Qiu, D. Xu, and Y. Yang)
Medication and treatment are important measures for prevention and control of influenza. However, the benefit of antiviral use can be compromised if drugresistant strains arise. Consequently, not only the epidemic size may increase with a higher level of treatment but also the viruses may become more resistant to the antiviral drugs. We use a mathematical model to explore the impact of antiviral treatment on the transmission dynamics of influenza. The model includes both drugsensitive and resistant strains. Analytical and numerical results of the model show that the conventional quantity for the control reproduction number is not appropriate to use for gaining insights into the disease dynamics. We derive a new reproduction number by considering multiple generations of infection, and demonstrate that this new reproduction number provides a more reasonable measure for evaluating control programs as well as evolutionary implications of influenza medication strategies.
Optimal Control of TickBorne Disease
Dr. Holly Gaff
Virginia Modeling, Analysis and Simulation Center, Old Dominion University
Human monocytic ehrlichiosis (Ehrlichia chaffeensis ), or HME, is a ticktransmitted, ricksettisal disease with growing impact in the United States. Risk of a tickborne disease such as HME to humans can be estimated using the prevalence of that disease in the tick population. A deterministic model for HME is explored to investigate the underlying dynamics of prevalence in tick populations, particularly when spatial considerations are allowed. Optimal control is applied to this model to identify how limited resources can best be used to reduce the risk of tickborne diseases to humans.
Mathematical Recipe for HIV Elimination in ResourcePoor Settings
Dr. Abba Gumel
Department of Mathematics, University of Manitoba
I will present a model for the transmission dynamics of HIV/AIDS in a population, and show how such a model (and its analyses) could provide a costeffective roadmap for the effective control and/or elimination of HIV in a resourcepoor setting, such as Nigeria.
The Largest Basic Reproduction Number in MultiType Epidemic Models
Dr. Karl Hadeler
Department of Mathematical and Statistical Sciences, Arizona State University
The basic reproduction number for a multigroup epidemic model depends on the distribution of types. Determining the worst case amounts to maximizing the spectral radius ρ(XA) where A is a given nonnegative matrix and X is a variable nonnegative diagonal matrix with trace equal to one. Lower bounds for the maximum can be obtained and improved without computing eigenvalues. Upper bounds can be computed using the max eigenvalue of the matrix A. (Joint work with Ludwig Elsner)
Sociallyinduced Ovulation Synchrony in a Seabird Colony: a DiscreteTime Model
Dr. James L. Hayward
Department of Biology, Andrews University
(Joint work with Shandelle M. Henson, and J. M. Cushing)
Spontaneous oscillator synchrony has been documented in a wide variety of electrical, mechanical, chemical, and biological systems, including the menstrual cycles of women and estrous cycles of Norway rats. In temperate regions, many colonial birds breed seasonally in a time window set by photoperiod; some studies have suggested that heightened social stimulation in denser colonies can lead to a tightened annual reproductive pulse. It has been unknown, however, whether the analogue of menstrual synchrony occurs in birds, that is, whether avian ovulation cycles can synchronize on a daily timescale within the annual breeding pulse. We present data on everyotherday egglaying synchrony in a breeding colony of glaucouswinged gulls (Larus glaucescens) and show that the level of synchrony declined with decreasing colony density. We also discuss a discretetime mathematical model based on the hypothesis that preovulatory luteinizing hormone surges synchronize through social stimulation.
The selective Advantage of Ovulation Synchrony in Colonial Seabirds: a Darwinian Dynamics Model
Dr. Shandelle M. Henson
Department of Mathematics, Andrews University
(Joint work with J. M. Cushing and James L. Hayward)
The existence of sociallyinduced ovulation synchrony in colonial seabirds begs the question of selective advantage. We pose a discretetime population model for colonial seabirds, incorporating a social stimulation parameter that can induce ovulation synchrony during the breeding season. Using the birth rate as a bifurcation parameter, we prove the existence of a transcritical bifurcation of positive periodic solutions, and show that the bifurcation is supercritical in the absence of social stimulation. In the presence of social stimulation, the bifurcation can become subcritical, and the branch of positive solutions bends back to the right, lying above the branch for which there is no social stimulation. If the population model is coupled to a dynamic model for an evolving trait related to social stimulation, the resulting Darwinian dynamics model predicts that the system will evolve to a state for which ovulation synchrony exists.
A New Look at Stochastic Resonance Enhancement of Mammalian Auditory Information Processing
Dr. Dawei Hong
Center for computational and integrative biology, Department of computer science, Rutgers University
Dynamics of an SIS Type of ReactionDiffusion Epidemic Model
Dr. Wenzhang Huang
Department of Mathematical Sciences, University of Alabama in Huntsville
Recently an SIS epidemic reactiondiffusion model with Neumann (or noflux) boundary condition have been proposed and studied by several authors to understand the dynamics of disease transmission in a spatially heterogeneous environment in which the individuals are subject to a random movement. Many important and interesting properties have been obtained: such as the role of diffusion coefcients in defning the reproductive number; the globally stability of diseasefree equilibrium; the existence of positive endemic steady; and the asymptotical profiles of the endemic steady states as one of diffusion coefcients is sufficiently small (or large). In this research we will study a modified SIS diffusion model with the Dirichlet boundary condition. Results on the dynamics of disease transmission and problems on the model will be presented.
Using Models to Help Control the H1N1 Pandemic
Dr. Mac Hyman
Department of Mathematics, Tulane University
We must use all of the tools available to advance epidemic models, from qualitative insight to quantitative predictions, to devise effective strategies to minimize the impact and spread of infectious diseases such as the current H1N1 flu pandemic. I will review the lessons learned from mathematical modeling previous epidemics, with the goal of identifying ways that our mathematical models can be used to help improve the effectiveness of public health interventions measures. In particular, I will describe how mathematical models can estimate the benefits and the costs of projected interventions and project the requirements that an epidemic will place on the health care system.
Dynamics of an AgeStructured Population with Allee Effects and Harvesting
Dr. Sophia Jang
Department of Mathematics and Statistics, Texas Tech University
In this talk we introduce a discretetime, agestructured single population model with Allee effects and harvesting. It is assumed that survival probabilities from one age class to the next are constants and fertility rate is a function of weighted total population size. Global extinction is certain if the maximal growth rate of the population is less than one. The model can have multiple attractors and the asymptotic dynamics of the population depends on its initial distribution if the maximal growth rate is larger than one. An Allee threshold depending on the components of the unstable interior equilibrium is derived when only the last age class can reproduce. The population becomes extinct if its initial population distribution is below the threshold. Harvesting on any particular age class can decrease the magnitude of the possible stable interior equilibrium and increase the magnitude of the unstable interior equilibrium simultaneously.
On the Existence of Error Threshold of the Quasispecies Model
Dr. Tanya Kostova
National Science Foundation
The quasispecies theory was introduced approximately 30 years ago by Eigen and Schuster. It became very popular within the virology community when experimental evidence showed that viruses have so high mutation rates that the viral populations consist of numerous diverse genotypes. It has been widely accepted that the quasispecies model predicts that the fittest genotype (with the highest replication rate) loses dominance when the mutation rate becomes sufficiently high. These conclusions have been largely based on computer simulations and have led to the definition of the so called error threshold. I show that it is easy to construct counter examples where the fittest genotype remains dominant independently of the value of the mutation rate and therefore the error threshold does not exist.
Multistability and Oscillations in Feedback Loops
Dr. Maria Leite
Department of Mathematics, University of Oklahoma
(Joint work with Yunjiao Wang, University of Manchester)
Feedback loops are found to be important network structures in biological systems. Recently, the dynamical role of feedback loops have received extensive attention. In this talk we discuss some of the interesting dynamical features of those loops such as multistability and oscillations.
Optimal Control of Treatments in a Cholera Model
Dr. Suzanne Lenhart
Department of Mathematics, University of Tennessee
While cholera has been a recognized disease for two centuries, there is no strategy for its effective control. We formulate a mathematical model to include essential components such as a hyperinfectious, shortlived bacterial state, a separate class for mild human infections, and waning disease immunity. A new result quantifies contributions to the basic reproductive number from multiple infectious classes. Using optimal control theory, parameter sensitivity analysis, and numerical simulations, a costeffective balance of multiple intervention methods is compared for two endemic populations. Results provide a framework for designing costeffective strategies for diseases with multiple intervention methods.
Spreading Speeds and Traveling Wave Solutions in Partially Monotone Systems
Dr. Bingtuan Li
Department of Mathematics, University of Louisville
Investigating the spreading speeds and traveling waves for spatial multiple species models has been fascinating and challenging. Most of the existing results on spread of species assume that the system is monotone throughout the region of biological interest. In this talk, we will present mathematical results on spatial spread of partially monotone models in the form of reactiondiffusion equations and in the form of integrodifference equations. By a partially monotone model we mean that the model is monotone near an unstable equilibrium from which the spatial transition moves away. In such a model species interact with each other to promote growth and migration in a cooperative manner in one region while they may behave differently in other regions. A partially monotone model may generate complicated dynamics including chaos. We will show results on the socalled "linear determinacy" that equates spreading speed in the full nonlinear model with spread rate in the system linearized about the leading edge of the invasion. We will then show that the spreading speed can be characterized as the slowest speed of a class of traveling wave solutions. We will finally discuss the applications of the general mathematical results to some specific ecological models in which the predatorprey interaction can be incorporated. (Joint work with Hans F. Weinberger, University of Minnesota)
Impact of Mosquito Transgenes on Malaria Transmission
Dr. Jia Li
Department of Mathematical Sciences, University of Alabama in Huntsville
We formulate continuoustime models for interactive wild and transgenic mosquitoes. With fundamental analysis of their dynamics, we introduce the transgenic mosquitoes into a simple compartmental malaria transmission mode l. We study the dynamics of the simple malaria model and the model with the transgenic mosquitoes, and investiga te the impact of transgenic mosquitoes on the malaria transmission.
Delay Dependent Conditions for Global Stability of an Intravenous Glucose Tolerance Test Model
Dr. Jiaxu Li
Department of Mathematics, University of Louisville
Diabetes mellitus has become an epidemic disease in the sense of life style. Detecting the onset of diabetes is one of the fundamental steps in treatment of diabetes including determining the insulin sensitivity and glucose effectiveness. An effective method for this end is the intravenous glucose tolerance test (IVGTT). Several mathematical models have been proposed and some are widely used in clinics. The most recent model proposed by P. Palumbo, S. Panunzi and A. De Gaetano (2007) demonstrates reasonable profiles with their experimental data. To analytically ensure the global stability of the basal equilibrium, several attempts have been made. The existing results are either delay independent conditions or the convergence is for a type of specific solutions. In this talk, we study the global stability and obtain delay dependent conditions to ensure the global and asymptotic stable equilibrium. An easytocheck condition that is an estimate of the upper bound of time delay is given.
An Agestructured TwoStrain Epidemic Model with SuperInfection
Dr. XueZhi Li
Department of Mathematics, Xinyang Normal University
This article focuses on the study of an agestructured twostrain model with superinfection. The explicit expression of basic reproduction numbers and the invasion reproduction numbers corresponding to strain one and strain two are obtained. It is showed that the infectionfree steady state is globally stable if the basic reproductive number R_0 is below one. Existence of strain one and strain two exclusive equilibria is established. Conditions for local stability or instability of the exclusive equilibria of the strain one and strain two are established. Existence of coexistence equilibrium is also obtained under the condition that both invasion reproduction numbers are larger than one. Keywords: agestructured; twostrain epidemic model; superinfection; basic reproduction number; invasion reproduction number, the exclusive equilibrium, the coexistence equilibrium, stability.
A Mathematical Approach to Study the Impact of Predators on the Vegetation Succession
Dr. Rongsong Liu
Department of Mathematics, University of Wyoming
In order to study the role of predator of on the vegetation succession, we use a system of ordinary differential equations to model the interaction among two plant species, herbivores, and predators. The toxindetermined functional response is applied to describe the interactions between plant species and herbivores and Holling Type II functional response is used to model the interactions between herbivores and predators. In order to study how the predators impact the succession of vegetation, we derive the invasion condition. Numerical simulations are conducted to reinforce of analytical results.
Tracking Prey or Tracking Prey's Resource?
Dr. Yuan Lou
Department of Mathematics, Ohio State University
We consider a continuous environment with an arbitrary distribution of resources, randomly diffusing prey that consumes the resources, and predators that consume the prey. Our model introduces a class of movement rules in which the direction of predators\' movement is determined (i) randomly, (ii) by prey density, and/or (iii) by the density of the prey's resource. We find that, for some resource distributions, predators that track the gradient of the prey's resource may have an advantage compared to predators that track the gradient of prey directly.
Permanence of the Water Hyacinth in Northeast Louisiana
Dr. Mariette Maroun
Department of Mathematics and Physics, University of Louisiana at Monroe
The invasive specie of Water Hyacinth was introduced into the United States of America in late 1800. This aquatic plant consists of three different stages. It take over upon introduction into fresh water bodies because of its sexual and assexual reproductive system. From early 1970's till now, scientists have been trying to control it in different manners from chemical to biological. A model will be provided to show that long term control of this plant depends only on its survival.
Avian Influenza: Modeling, Analysis, and Data Fitting
Dr. Maia Martcheva
Department of Mathematics, University of Florida
Low Pathogenic Avian Influenza (LPAI) virus, which circulates in wild bird populations in mostly benign form, is suspected to have mutated into a highly pathogenic (HPAI) strain after transmission to the domestic birds. HPAI has recently garnered worldwide attention because of the ''spillover" infection of this strain from domestic birds to humans  primarily those in poultry industry  causing significant human fatality and thus creating potentially favorable conditions for another flu pandemic. We use an ordinary differential equation model to describe this complex dynamics of the HPAI virus, which epidemiologically links a number of species in a multispecies community. We include the wild bird population as a periodic source feeding infection to the coupled domestic birdhuman system. We also account for mutation between the low and high pathogenic strains. We fit our model to the actual number of human avian influenza cases obtained from WHO, and estimate the relevant reproduction numbers and invasion reproduction numbers. We conclude that low pathogenic avian influenza is maintained in the domestic bird population through "spill over" from wild birds, while high pathogenic avian influenza is endemic in the domestic bird population.
A NSFD Scheme for a Model of Respiratory Virus Transmission
Dr. Ronald Mickens
Department of Physics, Clark Atlanta University
We construct a nonstandard finite difference numerical integration scheme for an SIRS model of respiratory virus transmission. Our work extends that done by A. J. Arenas et al. (Computers and Mathematics with Applications, Vol. 56 (2008), 670678) by using the system's exact conservation law to place constraints on the discretization. The scheme satisfies a positivity condition for all time stepsizes. We note that neither of the latter two conditions holds for the scheme derived by Arenas et al.
Stability of Choice in the Honey Bee NestSite Selection Process
Dr. Andrew Nevai
Department of Mathematics, University of Central Florida
A pair of compartment models for the honey bee nestsite selection process is introduced. The first model represents a swarm of bees deciding whether a site is viable, and the second characterizes its ability to select between two viable sites. The onesite assessment process has two equilibrium states: a disinterested equilibrium (DE) in which the bees show no interest in the site and an interested equilibrium (IE) in which bees show interest. In analogy with epidemic models, basic and absolute recruitment numbers (R0 and B0) are defined as measures of the swarm\'s sensitivity to dancing by a single bee. If R0 is less than one then the DE is locally stable, and if B0 is less than one then it is globally stable. If R0 is greater than one then the DE is unstable and the IE is stable under realistic conditions. In addition, there exists a critical site quality threshold Q* above which the site can attract some interest (at equilibrium) and below which it can! not. There also exists a a second critical site quality threshold Q** above which the site can attract a quorum (at equilibrium) and below which it cannot. The twosite discrimination process, which examines a swarm's ability to simultaneously consider two sites differing in both site quality and discovery time, has a stable DE if and only if both sites\' individual basic recruitment numbers are less than one. Numerical experiments are performed to study the influences of site quality on quorum time and the outcome of competition between a lower quality site discovered first and a higher quality site discovered second.
Stochastic Energy Budgets, IntegrateandFire Models, and Population Dynamics
Dr. Roger Nisbet
Department of Ecology, Evolution and Marine Biology, University of California, Santa Barbara
In many adult animals, energyrich material is accumulated as "reserves" that are eventually converted to reproductive material and released in a pulse. Similarly, achieving reproductive maturity in juveniles typically involves sustained energy allocation, with the onset of reproduction occurring after some threshold level is achieved. These observations have motivated study of a stochastic bioenergetic model involving integration of a varying energy input and firing on achieving some threshold, similar to the well studied integrateandfire (IF) neuron model. The model dynamics in a periodically variable environment give insight on the synchronization of reproduction in many organisms, and I shall show an example involving spawning corals. IF dynamics are also central to stagestructured population models with time varying maturation delays. I shall discuss an application to zooplankton populations.
Growing, Slowing, Growing: A Branching Process Model of How Cells Survive Telomere Shortening
Dr. Peter Olofsson
Department of Mathematics, Trinity University
Telomeres are specialized structures found at the ends of chromosomes. During DNA replication, telomeres shorten and once a critical length is reached, the cell stops dividing and becomes senescent. A cell population that experiences telomere shortening exhibits initial exponential growth, and once senescent cells start dominating the population, growth slows down and the population size levels off resulting in a typical sigmoidshaped growth curve. However, experimental data on the yeast Saccharomyces cerevisiae indicate that some populations regain exponential growth after slowing down. The explanation for this phenomenon is that some cells develop ways to maintain short telomeres and become "survivors." We suggest a bracnhing process model that takes into account random variation in individual cell cycle times, telomere shortening, finite lifespan of mother cells, and the possibility of survivorship. We identify and estimate crucial parameters such as cell cycle mean and variance, and the probability of an individual cell becoming a survivor, and compare our model to experimental data.
Evolutionary Changes in Competitive Outcomes
Dr. Rosalyn Rael
Department of Ecology and Evolutionary Biology, University of Michigan
Evolution is a natural process that can occur on time scales commensurate with ecological dynamics and result in changes in expected outcomes of interactions such as competition. Evolutionary game theory is a modeling technique that combines both ecological dynamics and evolution to form "Darwinian dynamics." With this method, natural selection is viewed as a game, where traits are strategies that affect payoff in the form of species\' fitness. I will give a brief introduction to Darwinian dynamics and describe applications of this modeling approach to twospecies competition. Using evolutionary game theory, we show how evolution can lead to the coexistence of species or other outcomes not expected in the absence of evolution. I will discuss the conditions necessary to see such changes, and show that these results compare well with data from classic flour beetle experiments.
Formation of Spatial Patterns in StageStructured Populations with Density Dependent Dispersal
Dr. Suzanne Robertson
Mathematical Biosciences Institute, Ohio State University
Spatial segregation among life cycle stages has been observed in many stagestructured species, both in homogeneous and heterogeneous environments. We investigate density dependent dispersal of life cycle stages as a mechanism responsible for this separation by using stagestructured, integrodifference equation (IDE) models that incorporate density dependent dispersal kernels. After investigating mechanisms that can lead to spatial patterns in two dimensional JuvenileAdult IDE models, we construct spatial models to describe the population dynamics of the flour beetle species T. castaneum, T. confusum and T. brevicornis and use them to assess density dependent dispersal mechanisms that are able to explain spatial patterns that have been observed in these species.
Asymmetric Division of Activated Latently Infected Cells May Explain the Divergent Decay Kinetics of the HIV Latent Reservoir
Dr. Libin Rong
Theoretical Biology and Biophysics, Los Alamos National Laboratory
Most HIVinfected patients when treated with combination therapy achieve viral loads that are below the current limit of detection of standard assays after a few months. Despite this, virus eradication from the host has not been achieved. Latent, replicationcompetent HIV1 can generally be identified in resting memory CD4+ T cells in patients with "undetectable" viral loads. Turnover of these cells is extremely slow but virus can be released from the latent reservoir quickly upon cessation of therapy. In addition, a number of patients experience transient episodes of viremia, or HIV1 blips, even with suppression of the viral load to below the limit of detection for many years. The mechanisms underlying the slow decay of the latent reservoir and the occurrence of intermittent viral blips have not been fully elucidated. In this study, we address these two issues by developing a mathematical model that explores a hypothesis about latently infect! ed cell activation. We propose that asymmetric division of latently infected cells upon sporadic antigen encounter may both replenish the latent reservoir and generate intermittent viral blips. Interestingly, we show that occasional replenishment of the latent reservoir induced by reactivation of latently infected cells may reconcile the differences between the divergent estimates of the halflife of the latent reservoir in the literature.
Modelling the Transmission Dynamics and Control of Hepatitis B Virus in China
Dr. Shigui Ruan
Department of Mathematics, University of Miami
Hepatitis B is a potentially lifethreatening liver infection caused by the hepatitis B virus (HBV) and is a major global health problem. HBV is the most common serious viral infection and a leading cause of death in mainland China. Around 130 million people in China are carriers of HBV, almost a third of the people infected with HBV worldwide and about 10% of the general population in the country; among them 30 million are chronically infected. Every year, 300,000 people die from HBVrelated diseases in China, accounting for 40  50% of HBVrelated deaths worldwide. Despite an effective vaccination program for newborn babies since the 1990s, which has reduced chronic HBV infection in children, the incidence of hepatitis B is still increasing in China. We propose a mathematical model to understand the transmission dynamics and prevalence of HBV infection in China. Based on the data reported by the Ministry of Health of China, the model provides an approximate estimate of the basic reproduction number R0 =2.406. This indicates that hepatitis B is endemic in China and is approaching its equilibrium with the current immunization programme and control measures. Although China made a great progress in increasing coverage among infants with hepatitis B vaccine, it has a long and hard battle to fight in order to significantly reduce the incidence and eventually eradicate the virus. Keywords: Hepatitis B virus, mathematical modeling, transmission dynamics, basic reproduction number, disease endemic equilibrium.
*Research was partially supported by the State Scholarship Fund of China Scholarship Council (Z.L.), NSFC grant #10825104 and the China MOE Research Grant (W.Z.), and NSF grant DMS0715772 (S.R.)
Global Stability in a MultiSpecies Periodic LeslieGower Model
Dr. Robert Sacker
Department of Mathematics, University of Southern California
The $d$species LeslieGower competition model is studied in which all the parameters are $p$periodic. It is shown that whenever the coupling is small, there is a positive $p$periodic state that is exponentially asymptotically stable and globally attracts all initial states having positive coordinates.
GlobalStability Problems for Coupled Systems Arising in Population Dynamics
Mr. Zhisheng Shuai
Department of Mathematical and Statistical Sciences, University of Alberta
(Joint work with Michael Li)
We study the globalstability problem of equilibria for coupled systems of differential equations arising in population dynamics. Using results from graph theory, we develop a systematic approach to construct global Lyapunov functions/functionals for coupled systems from individual Lyapunov functions/functionals for vertex systems. We apply our general approach to several coupled systems in ecology and epidemiology, for example, single species model with dispersal, predatorprey model with dispersal, and multigroup epidemic model with time delays.
Modeling the Evolution of Repetitive Sequence in DNA
Dr. Suzanne Sindi
Center for Computational Molecular Biology, Brown University
There are families of nearly identical sequences within the genomes of human, fly, worm and every nonmicrobial genome that has been determined. Such sequences were originally hypothesized to be "junk DNA", but biologists continue to find many functions these sequences perform. Several features of repetitive DNA follow power law distributions, a natural question is how such distributions have emerged over time from individual duplication events. I will describe mathematical models that demonstrate how power law and generalized Pareto Law distributions can emerge naturally from random duplication and deletion in a genome.
Lyapunov Exponents and Persistence
Dr. Hal Smith
Department of Mathematics and Statistics, Arizona State University
(Joint work with P. Salceanu)
We will show that Lyapunov exponents can be employed in establishing persistence of discrete and continuoustime finite dimensional dynamical systems.
Transmission of Avian Influenza between Two Patches
Dr. Baojun Song
Department of Mathematical Sciences, Montclair State University
Patch models are constructed and analyzed to study the role of a migratory bird population in the transmission of the highly pathogenic H5N1 strain of avian influenza.
Our discrete models consider a migratory bird population and two local bird populations. The local bird populations live in their own patches and the migratory birds migrate back and forth between patches seasonally. The models are tested by using the prevalence of avian influenza in Mallard Duck by season in United States and Canada from 1974 to 1986. Both our analytic results and simulations predict a pattern of seasonal oscillation of the prevalence of avian influenza in Mallard Duck A variety types of demographic growth modes are discussed. The models for most nonlinear reproductions or nonlinear survive functions undergo double perioddouble bifurcations.
Dynamics of Killer T Cells and Immunodominance in the Influenza Infection
Dr. Abdessamad Tridane
Department of Applied Sciences and Mathematics, Arizona State University at the Polytechnic Campus
Antigenspecific killer T cells ( CD8+ cells ) play an important role in virus clearance. The aim of this talk is to introduce and analyze mathematical models of the dynamics of killer T cells and the differential expansion of antigenspecific CD8+ cell, called immunodominance, in the influenza infection. Understanding qualitative impact of killer T cells is very important for the design of Tcellbased vaccines that promote early virus clearance. The systematical analysis of these model systems show that the behaviors of the models are similar for high killer T cells density generating reasonable dynamics. Our models try to shed some light on possible explanations of the some aspect immunodominance in influenza infection by studying the effect of the epitope of the antigen presented on the surface of the infected cells and the effect of Interferonγ
Traveling Wave Solutions of Delayed ReactionDiffusion Equations
Dr. Haiyan Wang
Division of Mathematical and Natural Sciences, Arizona State University
Traveling wave phenomena in reactiondiffusion equations arise from many biological problems. Combining upper and lower solutions, monotone iterations and fixed point theorems, we study the existence and asymptotic behavior of traveling wave solutions for nonmonotone reactiondiffusion equations with nonlocal delay. Our results extend and improve some related results in the literature.
A Formula for the TimeDependent Transmission Rate in an SIR Model from Data
Dr. Howie Weiss
Department of Mathematics, Georgia Tech
The transmissibility of many infectious diseases varies significantly in time, but has been thought impossible to measure directly. Based on solving an inverse problem for SIRtype systems, we devise a mathematical algorithm to recover the timedependent transmission rate from infection data. We apply our algorithm to historic UK measles data and observe that for most cities the main spectral peak of the transmission rate has a twoyear period. Our construction clearly illustrates the danger of overfitting an epidemic transmission model with a variable transmission rate function.
Models for the Spread of Hantavirus between Reservoir and Spillover Species
Dr. Curtis Wesley
Department of Mathematics, Louisiana State University at Shreveport
The modeling of interspecies transmission has the potential to provide more accurate predictions of disease persistence and emergence dynamics. We describe various models which are motivated by recent work on hantavirus in rodent communities in Paraguay. Each model is a system of ordinary differential equations (ODE) which are developed for modeling the spread of hantavirus between a reservoir and a spillover species. The basic reproduction number is calculated for each model, with global stability results given for some models. Numerical simulations are created that illustrate the dynamics of each model.
Competition in the Presence of a Virus in an Aquatic Environment
Dr. Gail Wolkowicz
Department of Mathematics and Statistics, McMaster University
Recent research has determined that viruses are much more prevalent in aquatic environments than previously imagined. We derive a model of competition between two populations of bacteria for a single limiting nutrient in a chemostat where a virus is present. It is assumed that the virus can only infect one of the populations, the population that would be a more efficient consumer of the resource in a virus free environment, in order to determine whether introduction of a virus can result in coexistence of the competing populations. Criteria for the global stability of the disease free and endemic steady states are obtained. It is also shown that it is possible to have multiple attracting endemic steady states, oscillatory behavior involving Hopf and homoclinic bifurcations, and a hysteresis effect. Mathematical tools that are used include Lyapunov functions, persistence theory, and bifurcation analysis.
Evolution of Schistosome's Drug Resistance and Virulence
Dr. Dashun Xu
Department of Mathematics, Southern Illinois University, Carbondale
Motivited by some recent empirical studies on Schistosoma mansoni, we use a set of ordinary differential and integral equations to investigate the role of drug treatments of human hosts in the evolution of drug resistant parasites. By studying evolutionarily singular strategies (ESS) of parasites, we found that high drug resistance (and low virulence) is likely to develop for high drug treatment rates, which usually tend to promote monomorphism as the evolutionary endpoint. Our study also shows that the coinfection of the intermediate host does not affect the drug resistance and virulence levels of parasites, but tends to destabilize ESS points and hence promote dimorphism or even polymorphism as the evolutionary endpoint.
The Impact of Periodic Proportional Harvesting Policies on TACRegulated Fishery Systems
Dr. AbdulAziz Yakubu
Department of Mathematics, Howard University
We extend the TAC regulated fish population model of Ang et al. to include stock under compensatory and overcompensatory dynamics with and without the Allee effect. We focus on periodic harvesting strategy, a subset of variable proportion harvesting strategies that includes constant harvesting as a special case. Both periodic and constant harvesting strategies have the potential to stabilize complex overcompensatory stock dynamics with or without the Allee effect. Furthermore, we show that both strategies force a sudden collapse of TAC fishery systems that exhibit the Allee mechanism. However, in the absence of the Allee effect, TAC fishery systems decline to zero smoothly under high exploitation. As case studies, we apply the TAC theoretical model framework to Gulf of Alaska Pacific halibut data from the International Pacific halibut Commission (IPHC) annual reports and Georges Bank Atlantic cod data from the North East Fisheries Science Center !(NEFSC) Reference Document 0815. We show that TAC does a good job of preventing the collapse of halibut while cod is endangered. Furthermore, we observe that the likelihood of stock collapse increases with increased weather variability.
Geometric and Potential Driving Formation and Evolution of Biomolecular Surfaces
Dr. Shan Zhao
Department of Mathematics, University of Alabama
In this talk, I will present some geometrical flow equations for the theoretical modelling of biomolecular surfaces in the context of multiscale implicit solvent models. When a less polar macromolecule is immersed in a polar environment, the surface free energy minimization occurs naturally to stabilize the system. This motivates us to propose a new concept, the minimal molecular surface (MMS), for modelling the solventbiomolecule interface. The intrinsic curvature force is used in the MMS model to drive the surface formation and evolution. To further account for the local variations near the biomolecular surfaces due to interactions between solvent molecules, and between solvent and solute molecules, we recently proposed some new potential driven geometric flows, which balance the intrinsic geometric forces with the potential forces induced by the atomic interactions. High order geometric flows are also considered and tested for biomolecular surface modelling. Extensive numerical experiments are carried out to demonstrate the proposed concept and algorithms. Comparison is given to a classical model, the molecular surface. Unlike the molecular surface, biomolecular surfaces generated by our approaches are typically free of geometric singularities. (This is a joint work with Peter Bates and G.W. Wei, Michigan State University).
Dynamics of an Epidemic Model with NonLocal Infections for Diseases with Latency over a Patchy Environment
Dr. Xingfu Zou
Department of Applied Mathematics, University of Western Ontario
Assuming that an infectious disease in a population has a fixed latent period and the latent individuals of the population may disperse, we formulate an SIR model with a simple demographic structure for the population living in an $n$patch environment (cities, towns, or countries, etc.). The model is given by a system of delay differential equations with a fixed delay accounting for the latency and a nonlocal term caused by the mobility of the individuals during the latent period. Assuming irreducibility of the travel matrices of the infection related classes, an expression for the basic reproduction number \\mathcal{R}_0$ is derived, and it is shown that the disease free equilibrium is globally asymptotically stable if $\\mathcal{R}_0<1$, and becomes unstable if $\\mathcal{R}_0>1$. In the latter case, there is at least one endemic equilibrium and the disease will be uniformly persistent. When $n=2$, two special cases allowing reducible travel matrices are considered to illustrate joint impact of the disease latency and population mobility on the disease dynamics. In addition to the existence of the disease free equilibrium and interior endemic equilibrium, the existence of a boundary equilibrium and its stability are discussed for these two special cases.
Poster Presentations
Discrete Time Optimal Control of Species Augmentation: Augment then Grow
Ms. Erin Bodine
Department of Mathematics, University of Tennessee
Stability of the Endemic Coexistence Equilibrium for One Host and Two Parasites
Mr. Thanate Dhirasakdanon
School of Mathematics and Statistics, Arizona State University
For an SI type endemic model with one host and two parasite strains with complete cross protection between the parasite strains, we study the stability of the endemic coexistence equilibrium, where the host and both parasite strains are present. Our model assumes reduced fertility and increased mortality of infected hosts. The model also assume that one parasite strain is exclusively vertically transmitted and cannot persists just by itself. We find several sufficient conditions for the equilibrium to be locally asymptotically stable. One of them is that the horizontal transmission is of densitydependent (massaction) type. If the horizontal transmission is of frequencydependent (standard) type, then, under certain conditions, the equilibrium can be unstable and undamped oscillations can occur. We support and extend our analytical results by numerical simulations and by twodimensional plots of stability regions for various pairs of parameters.
Optimal Control of Growth Coefficient in a Steady State Population Model
Dr. Heather Finotti
Department of Mathematics, University of Tennessee
(Joint work with Ding, Lenhart, Lou, and Ye)
We study the control problem of maximizing the net benefit in the conservation of a single species with a fixed amount of resources. The existence of an optimal control is established and the uniqueness and characterization of the optimal control are investigated. Numerical simulations illustrate several cases, for both one and twodimensional domains, in which several interesting phenomena are found. Some open problems are discussed.
An AgeStructured Setup of the BacteriaBacteriophage Model
Mr. Zhun Han
School of Mathematics and Statistics, Arizona State University
The mathematical model of the bacteriabacteriophage interaction has been an interesting topic since 1960's. In this alternate setup, we introduce an age structure on the infected species and rewrite the model into a combination of delayed differential equations and integral equations. We show that this alternate setup coincides with an existing model. However, by employing this age structure, we may have a better view in the biological sense.
The Spreading Speed and Traveling Wave Solutions of a Spatial Competition Model
Ms. Kim Meyer
Department of Mathematics, University of Louisville
Integrodifference equations are used to model spatial spread of species with nonoverlapping generations. We look at a two species competition model with Ricker's growth functions in the form of integrodifference equations. We investigate spatial dynamics about how an introduced competitor spreads into a habitat preoccupied by a resident species. We found a formula for the so called spreading speed at which the resident species retreats and the introduced species expands in space. We also obtained conditions under which the spreading speed can be characterized as the slowest speed of a class of traveling wave solutions. In addition, we conducted numerical simulations and showed that a traveling wave solution can have a complicated tail. (Joint work with Bingtuan Li)
Mathematical Modeling of SARS with a Focus on SuperSpreading Events (SSEs)
Mr. Thembinkosi Mkhatshwa
Department of Mathematics and Applied Sciences, Marshall University
"Super spreading events" (SSEs) have been cited to have been one of the major factors which were responsible for the spread of severe acute respiratory syndrome (SARS), the first epidemic of the 21st century. The understanding of these SSEs is critical to understanding the spread of SARS. We present a modification of the basic SIR disease model, an SIPR model, which captures the effect of the SSEs.
Modeling Antibiotic Resistant Bacteria in the Mud River, WV
Dr. Anna Mummert
Department of Mathematics, Marshall University
When antibiotics are used by humans, or for livestock or crop production, antibiotic resistant bacteria enters the environment. The antibiotic resistant bacteria wash into rivers, where the antibiotic resistance gene is transferred to naturally occurring bacteria in the river. In this poster we present and study a system of ordinary differential equations that model antibiotic resistant bacteria in rivers. The influence of bacteria entering the river due to nearby land use appears in the model as an external forcing term. The model is compared with data from the Mud River, WV.
Bacteriophage Infection Dynamics:Multiple Host Binding Sites
Mr. Roy Trevino
School of Mathematical and Statistical Sciences, Arizona State University
We construct a stochastic model of bacteriophage parasitism of a host bacteria that accounts for demographic stochasticity of host and parasite and allows for multiple bacteriophage adsorption to host. We analyze the associated deterministic model, identifying the basic reproductive number for phage proliferation, showing that host and phage persist when it exceeds unity, and establishing that the distribution of adsorbed phage on a host is binomial with slowly evolving mean. Not surprisingly, extinction of the parasite or both host and parasite can occur for the stochastic model.
Novel H1N1: Predicting the Course of a Pandemic
Dr. Sherry Towers
Department of Applied Statistics, Purdue University
In April, 2009 a new strain of H1N1 was identified, causing a spring epidemic in Mexico, and a summer wave of infection in the US and elsewhere. Because influenza is seasonal in nature (more infectious in winter than summer in the northern hemisphere), world health officials anticipate a second, larger fall wave, similar to that seen in 1918. We examine the prevalence of H1N1 in the US during summer 2009. In a unique study, we use this information, along with what we know about the seasonal behavior of influenza, to predict the prevalence of influenza during fall 2009, and examine the efficacy of the planned CDC H1N1 vaccination campaign.
Dispersal Behavior with Biased Edge Movement Between Two Different Habitat Types
Ms. Xiuquan Wang
Department of Mathmatics, Southern Illinois Univercity, Carbondale
(Joint work with Drs. Mingqing Xiao, John D. Reeve, Dashun Xu, and James T. Cronin)
we analyze the behavior of the reactiondiffusion model of organisms to study insect diffusion. The main idea is based on some set of hypotheses about the scale and structure of the spatial environment and the way that insects disperse through it to express how the insect responds to edges between two different habitats, therefore, its behavior can be analyzed according to the shape of corresponding distribution curves. By analyzing the reactiondiffusion equations, this also provides a simulation of occupancy mean times for insect in different habitats.
Mathematical Modeling of the VancomycinResistant Enterococci
Dr. Mohammed Yahdi
Department of Mathematics and Computer Science, Ursinus College
A mathematical model of the VancomycinResistant Enterococci (VRE) is introduced. It includes a system of three nonlinear differential equations with three variables connected and twelve parameters, such as fitness costs, rates of colonization, and hygiene compliance. Equilibrium point simulation and outbreak analysis are performed to visualize and measure the impact of the parameters on the spread of the antibiotic resistant VRE, and to provide optimal control strategies.
Effect of Host Heterogeneity on the Coevolution of Parasite and Host
Ms. Yiding Yang
Department of Mathematics, Purdue University
A system of differential equations which models the disease dynamics of schistosomiasis is used to study the evolution of parasite virulence. The model incorporates both the definitive human hosts and two strains of intermediate snail hosts. An agestructure of human hosts is considered to reflect the agedependent transmission rate and agetargeted drug treatment rate. The basic parasite reproductive number R_i of strain i snail hosts is computed, and the invasion reproductive number R_{ij} for strain i snail host when type j snail hosts are at the equilibrium. We establish the criterion for strain i to invade strain j snail host, and the criterion is used to examine the evolutionary dynamics of snail hosts and the parasite.
Modeling Disease Transmission with Age and Spatial Heterogeneities
Dr. Feng Yu
Statistics and Epidemiology, Statistics Research Division, RTI International
We have developed a comprehensive disease epidemic model that takes both ageheterogeneity and spatialheterogeneity into account. The model features an age structure that captures the dynamics of disease epidemic with seasonal effect for various age groups. This model also simulates the impact of migration among geographic locations on disease transmission. In addition, vaccination strategy has been built into the model for disease intervention and control. We implemented the model using the AnyLogicTM software package with graphical user interface for presentation of results and for changing parameters interactively. For illustration purpose, we will use Measles transmission as an example.
Different Orders of Harvesting an Integrodifference Model
Ms. Peng Zhong
Department of Mathematics, University of Tennessee
An optimal control harvesting problem for a population modeled by an integrodifference equation model is considered. The proportion to be harvested is taken to be control. The goal is to find the optimal harvesting control to maximize the profit. The effect of order on optimal control of harvesting on integrodifferential equations is studied.
Conference Location
All talks will be held in the Shelby Center for Science and Technology on the UAHuntsville Campus
Hotels
Tom Bevill Center
550 Sparkman Drive, Huntsville, AL 35899
Located on the UAH Campus
(256) 7219428
Amenities
 Complimentary deluxe continental breakfast
 Shuttle service available
 Business center available for copies, fax machine, computer / printer, ATM, etc.
 Complimentary pass to the University Fitness Center
 Coffee makers with complimentary coffee
 Study area with desk and chair,
 Mini refrigerators, microwAves, iron & iron board, radio/alarm clocks in all the rooms
 Remote control televisions with 70 cable channels
 Telephone with voice mail and data port capability
 Individual thermostatically controlled air conditioning and heat
 All interior corridor entrances
Reservations
Call (256) 7219428 to make reservations. Mention you are attending the conference hosted by the UAH Math Department. Room rates are
 Single Room, NonSmoking/1 Double: $67.00
 Double Room, NonSmoking/2 Double: $71.00
 Double Room, Smoking/2 Double: $71.00
 Junior Suite/1 King: $89.00
Directions
From Huntsville International Airport:
 Start out going north on Glenn Hearn Blvd SW toward John Harrison Dr. SW
 Merge onto I565 E / US 72 Alt E toward Huntsville.
 Take Exit 15 toward Madison Pike / Sparkman Dr / Bob Wallace Ave.
 Take the Sparkman Dr / Bob Wallace Ave ramp.
 Turn left onto Bob Wallace Ave SW / Sparkman Dr NW. continue to follow Sparkman Dr NW.
 End at 550 Sparkman Dr NW
From Birmingham or Nashville
 Take I65 Exit to I565 E / US 72 Alt E toward Huntsville
 Take Exit 15 toward Madison Pike / Sparkman Dr / Bob Wallace Ave.
 Take the Sparkman Dr / Bob Wallace Ave ramp.
 Turn left onto Bob Wallace Ave SW / Sparkman Dr NW. continue to follow Sparkman Dr NW.
 End at 550 Sparkman Dr NW
From Atlanta:
 Merge onto US72 W via the ramp on the left toward Huntsville.
 US72 W becomes I565 W.
 Take the Sparkman Dr / Bob Wallace Ave Exit, Exit 15, toward Madison Pike.
 Keep right at the fork to go on Sparkman Dr NW
 End at 550 Sparkman Dr NW
Hilton Garden Inn
4801 Governors House Drive, Huntsville, AL 35805
Located 1.4 miles from UAH campus
(256) 4301778
Amenities
 One kingsized bed or two queensized beds
 Microwave, refrigerator, coffee maker, iron & ironing board
 Ergonomic Herman Miller Mirra chair, Garden Sleep System bed
 26" flat screen highdefinition television
 Adjustable lighting, desk level electrical outlets
 2 phone lines in each room and voice mail
 Complimentary wired and wireless highspeed Internet access
 Secure PrinterOn remote printing
Reservations
Call (256) 4301778 to make reservations. Mention you are attending the conference hosted by the UAH Math Department. Room rates are
 Single Rooms/King or Queen: $89.00
Directions
From Huntsville International Airport:
 Start out going north on Glenn Hearn Blvd SW toward John Harrison Dr. SW
 Merge onto I565 E / US 72 Alt E toward Huntsville.
 Take Exit 15 toward Madison Pike / Sparkman Dr / Bob Wallace Ave.
 Take the Sparkman Dr/Bob Wallace Ave ramp.
 Merge onto Bob Wallace Ave. SW.
 Turn left onto Governors House Drive SW
 End at 4801 Governors House Drive SW
From Birmingham or Nashville:
 Take I65 Exit to I565 E / US 72 Alt E toward Huntsville
 Take Exit 15 toward Madison Pike / Sparkman Dr / Bob Wallace Ave.
 Take the Sparkman Dr / Bob Wallace Ave ramp.
 Merge onto Bob Wallace Ave. SW.
 Turn left onto Governors House Drive SW
 End at 4801 Governors House Drive SW
From Atlanta:
 Merge onto US72 W via the ramp on the left toward Huntsville.
 US72 W becomes I565 W.
 Take the Sparkman Dr / Bob Wallace Ave Exit, Exit 15, toward Madison Pike.
 Keep right at the fork to go on Sparkman Dr NW
 Turn left onto Governors House Drive SW
 End at 4801 Governors House Drive SW
To UAH Campus:
 Start out going west on Governors House Dr SW toward Bob Wallace Ave SW.
 Turn right onto Bob Wallace Ave SW.
 Bob Wallace Avenue becomes Sparkman Drive.
 Turn right onto UAH campus
Registration and Abstract Submission
There will be a registration fee of $100 per participant except students (with confirmed student status). To register, you need to complete the online form below to provide contact information. You also need to download, print, and complete the registration form, and mail it to the following address:
Attn: Ms. Tami Lang
Department of Mathematical Sciences
Shelby Center Room 258A
University of Alabama in Huntsville
Huntsville, AL 35899
USA
With your registration form, please send a check payable to "Math Department, UAH" denominated in US dollars, no later than September 7, 2009 to the address above. The late registration fee will be $150 after September 7. You may also pay your registration fee by cash or check at the registration desk of the conference with the late registration fee if you wish. Unfortunately, we won't be able to accept credit card or payment online.
**Online Form disabled.
Financial Support
Our National Science Foundation grant has been recommended for funding. The grant stipulates that we provide financial support to a limited number of U.S. based junior faculty, post doctorates, and graduate students. This includes up to $75 for lodging per night (maximum 3 nights) and up to $500 for travel allowance for each person funded. In order to be considered for funding, please print and complete the PDF Application Form, and mail it along with the supporting documents to the address below.
Dr. Jia Li, Chair
Department of Mathematical Sciences
Shelby Center Room 258A
University of Alabama in Huntsville
Huntsville, AL 35899
USA
The supporting documents should include a CV, and for graduate students, a recommendation letter from the student's supervisor. Qualified participants are encouraged to apply.