Wednesday, September 30, 2009 - 11:00 , Location: Skiles 269 , Jan Medlock , Clemson University , firstname.lastname@example.org , Organizer:
The recent emergence of the influenza strain (the "swine flu") and delays in production of vaccine against it illustrate the importance of optimizing vaccine allocation. Using an age-dependent model parametrized with data from the 1957 and 1918 influenza pandemics, which had dramatically different mortality patterns, we determined optimal vaccination strategies with regard to five outcome measures: deaths, infections, years of life lost, contingent valuation and economic costs. In general, there is a balance between vaccinating children who transmit most and older individuals at greatest risk of mortality, however, we found that when at least a moderate amount of an effective vaccine is available supply, all outcome measures prioritized vaccinating schoolchildren. This is vaccinating those most responsible for transmission to indirectly protect those most at risk of mortality and other disease complications. When vaccine availability or effectiveness is reduced, the balance is shifted toward prioritizing those at greatest risk for some outcome measures. The amount of vaccine needed for vaccinating schoolchildren to be optimal depends on the general transmissibility of the influenza strain (R_0). We also compared the previous and new recommendations of the CDC and its Advisory Committee on Immunization Practices are below optimum for all outcome measures. In addition, I will discuss some recent results using mortality and hospitalization data from the novel H1N1 "swine flu" and implications of the delay in vaccine availability.
Wednesday, April 15, 2009 - 11:00 , Location: Skiles 255 , Igor Belykh , University of Georgia , Organizer:
Wednesday, April 8, 2009 - 11:00 , Location: Skiles 255 , Shandelle Henson , Andrews University , Organizer:
Oscillator synchrony can occur through environmental forcing or as a phenomenon of spontaneous self-organization in which interacting oscillators adjust phase or period and begin to cycle together. Examples of spontaneous synchrony have been documented in a wide variety of electrical, mechanical, chemical, and biological systems, including the menstrual cycles of women. Many colonial birds breed approximately synchronously within 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 (the “Fraser Darling effect”). It has been unknown, however, whether avian ovulation cycles can synchronize on a daily timescale within the annual breeding pulse. We will discuss socially-stimulated egg-laying synchrony in a breeding colony of glaucous-winged gulls using Monte Carlo analysis and a discrete-time dynamical system model.
Mathematical and experimental considerations of density and physiological state effects on antimicrobial susceptibilityWednesday, April 1, 2009 - 11:00 , Location: Skiles 255 , Klas Udekwu , Emory University , Organizer:
The treatment of bacterial infections with antibiotics is universally accepted as one of (if not THE) most significant contributions of medical intervention to reducing mortality and morbidity during last century. Despite their widespread use over this extended period however, basic knowledge about how antibiotics kill or prevent the growth of bacteria is only just beginning to emerge. The dose and term of antibiotic treatment has long been determined empirically and intuitively by clinicians. Only recently have antibiotic treatment protocols come under scrutiny with the aim to theoretically and experimentally rationalize treatment protocols. The aim of such scrutiny is to design protocols which maximize antibiotics’ efficacy in clearing bacterial infections and simultaneously prevent the emergence of resistance in treated patients. Central to these endeavors are the pharmacodynamics, PD (relationship between bug and drug), and the pharmacokinetics, PK (the change antibiotic concentration with time) of each bacteria : drug : host combination. The estimation of PD and PK parameters is well established and standardized worldwide and although different PK parameters are commonly employed for most of these considerations, a single PD parameter is usually used, the minimum inhibitory concentration (MIC). MICs, also utilized as the criteria for resistance are determined under conditions that are optimal to the action of the antibiotic; low densities of bacteria growing exponentially. The method for estimating MICs which is the only one officially sanctioned by the regulatory authority (Clinical and Laboratory Standards Institute) defines conditions that rarely obtain outside of the laboratory and virtually never in the bacteria infecting mammalian hosts. Real infections with clinical symptoms commonly involve very high densities of bacteria, most of which are not replicating. These populations are rarely planktonic but rather reside as colonies or within matrices called biofilms which sometimes include other species of bacteria. In the first part of my talk, I will present newly published data that describes the pharmacodynamic relationship between the sometimes pathogenic bacterium Staphylococcus aureus and antibiotics of six classes and the effects of cell density on MICs. By including density dependent MIC in a standard mathematical model of antibiotic treatment (from our lab), I show that this density-dependence may explain why antibiotic treatment fails in the absence of inherited resistance. In the second part of my talk I will consider the effects of the physiological state of clinical isolates of S. aureus on their susceptibility to different antibiotics. I present preliminary data which suggests that the duration of an infection may contribute adversely to an antibiotics chance of clearing the infection. I conclude with a brief discussion of the implications of the theoretical and experimental results for the development of antibiotic treatment protocols. As a special treat, I will outline problems of antibiotic treatment that could well be addressed with some classy mathematics.
Wednesday, March 25, 2009 - 11:00 , Location: Skiles 255 , Ruslan Rafikov , Medical College of Georgia , Organizer:
The stress condition calls for an adequate activity of key enzymatic systems of cellular defense. Massive protein destabilization and degradation is occurring in stressed cells. The rate of protein re-synthesis (DNA->RNA->protein) is inadequate to adapt to rapidly changing environment. Therefore, an alternative mechanism should exist maintaining sufficient activity of defense enzymes. Interestingly, more than 50% of enzymes consist of identical subunits which are forming multimeric interface. Stabilization of multimers is important for enzymatic activity. We found that it can be achieved by the formation of inter-subunit covalent bridges in response to stress conditions. It shows an elegance of the structure design that directs selective subunits linkage and increases enzyme's robustness and chances of cell survival during the stress. In contrast, modification of aminoacids involved in linkage leads to protein destabilization, unfolding and degradation. These results describe a new instantaneous mechanism of structural adaptation that controls enzymatic system under stress condition.
Wednesday, March 11, 2009 - 11:00 , Location: Skiles 255 , Dirk Brockmann , Northwestern University , Organizer:
Human Mobility in our globalised world has reached a complexity and volume of unprecedented degree. More than 60 million people travel billions of kilometres on more than 2 million international flights each week. Hundreds of millions of people commute on a complex web of highways and railroads most of which operate at their maximum capacity. Human mobility is responsible for the geographical spread of emergent human infectious diseases and plays a key role in human mediated bioinvasion, the dominant factor in the global biodiversity crisis. I will report on the recent discovery of scaling laws in global human traffic (obtained from online bill-tracking at www.wheresgeorge.com) and mathematical models that can account for it. I will present a complex network perspective on multi-scale human traffic networks, report on their statistical properties and show that they can be used to identify geographically coherent communities that only vaguely resemble administrative ones. The approach provides an operational segmentation of maps into a hierarchical set of effective regions and boundaries based on human behavior. I will briefly talk about European transportation networks, geocaching and trackable items.
Wednesday, March 4, 2009 - 11:00 , Location: Skiles 255 , Sean Ellermeyer , Kennesaw State University , Organizer:
We consider a class of age-structured population models in which the central modeling assumption is simply that the birth rate depends on the size of the adult population. For the most part, we in fact assume that the birth rate is a monotone non-decreasing function of the adult population size. Despite the simplicity of our modeling assumptions (or perhaps because of it), we will see that this class of models admits a wide variety of solutions (exponentially growing, lineary growing, periodic, etc.) Much of the analysis of these models can be carried out using elementary techniques and we present some specific examples in which explicit solutions (which are elementary functions) can be generated. We also consider some questions related to the inverse problem for these models.
Wednesday, February 25, 2009 - 11:00 , Location: Skiles 255 , Yuriy Mileyko , School of Biology, Georgia Tech , Organizer:
The expression dynamics of interacting genes depends on the topology of the regulatory network, the quantitative nature of feedbacks and interactions between DNA, RNA and proteins, and the biochemical state of the intracellular and surrounding environment. In this talk we show that dynamics of a gene regulatory network can also depend sensitively on the copy number of genes and promoters. Genetic regulatory networks include an overrepresentation of subgraphs commonly known as network motifs. We consider positive feedback, bistable feedback, and toggle switch motifs and show that variation in gene copy number can cause a sequence of saddle-node bifurcations in the corresponding differential equations models, which leads to multiple orders of magnitude change in gene expression. A similar analysis of a 3-gene motif with successive inhibition (the ``repressilator'') reveals that changes in gene copy number can also cause a Hopf bifurcation, thus leading to a qualitative switch in system behavior among oscillatory and equilibrium dynamics. Importantly, we show that these bifurcations exist over a wide range of parameter values, thus reinforcing our claim that copy number is a key control parameter in the expression dynamics of regulatory networks.
Wednesday, January 28, 2009 - 11:00 , Location: Skiles 255 , Mike Boots , University of Sheffield , Organizer:
Transient (Electro)Chemical Imaging of Reacting Interfaces - Physical Concepts and Mathematical ChallengesWednesday, December 3, 2008 - 11:00 , Location: Skiles 255 , Andrei Fedorov , School of Mechanical Engineering, Georgia Tech , Organizer:
In this presentation I will outline physical principles of two analytical techniques, the Scanning ElectroChemical Microscopy (SECM) and Scanning Mass Spectrometry (SMS), which can be used to obtain the spatially resolved images of (bio/electro)chemically active interfaces. The mathematical models need to be employed for image interpretation and mapping measured quantities (e.g., an electrode current in SECM) to biochemically relevant quantities (e.g., kinetics of exocytotic signaling events in cellular communications), and I will review the key ideas/assumptions used for the model formulation and the main results of analysis and simulations. In conclusion, an alternative approach to spatially-resolved imaging based on the multi-probe array will be introduced along with intriguing opportunities and challenges for mathematical interpretation of such images.