- You are here:
- GT Home
- Home
- News & Events

Wednesday, February 17, 2016 - 11:00 ,
Location: Skiles 006 ,
Professor David Gurarie ,
CWRU ,
dxg5@case.edu ,
Organizer:

Schistosoma is a parasitic worm that circulates between human and snail hosts. Multiple biological and ecological factors contribute to its spread and persistence in host populations. The infection is widespread in many tropical countries, and WHO has made control of schistosomiasis a priority among neglected tropical diseases.Mathematical modeling is widely used for prediction and control analysis of infectious agents. But host-parasite systems with complex life-cycles like Schistosoma, pose many challenges. The talk will outline the basic biology of Schistosoma, and the principles employed in mathematical modeling of macro parasites. We shall review conventional approaches to Schistosomiasis starting with the classical work of MacDonald, and discuss their validity and implications. Then we shall outline more detailed “stratified worm burden approach”, and show how combining mathematical and computer tools one can explore real-world systems and make reliable predictions for long term control outcomes and the problem of elimination.

Wednesday, September 30, 2015 - 11:05 ,
Location: Skiles 005 ,
Norbert Stoop ,
MIT ,
Organizer:

Morphogenesis of curved bilayer membranes
Buckling of curved membranes plays a prominent role in the morphogenesis
of multilayered soft tissue, with examples ranging from tissue
differentiation, the wrinkling of skin, or villi formation in the gut,
to the development of brain convolutions. In addition
to their biological relevance, buckling and wrinkling processes are
attracting considerable interest as promising techniques for nanoscale
surface patterning, microlens array fabrication, and adaptive
aerodynamic drag control. Yet, owing to the nonlinearity
of the underlying mechanical forces, current theoretical models cannot
reliably predict the experimentally observed symmetry-breaking
transitions in such systems. Here, we derive a generalized
Swift-Hohenberg theory capable of describing the wrinkling morphology
and pattern selection in curved elastic bilayer materials. Testing the
theory against experiments on spherically shaped surfaces, we find
quantitative agreement with analytical predictions separating distinct
phases of labyrinthine and hexagonal wrinkling patterns.
We highlight the applicability of the theory to arbitrarily shaped
surfaces and discuss theoretical implications for the dynamics and
evolution of wrinkling patterns.

Thursday, February 26, 2015 - 13:30 ,
Location: Skiles 006 ,
David Dynerman ,
University of Wisconsin-Madison ,
Organizer: Christine Heitsch

Cryo-electron microscopy (cryo-EM) is a microscopy technique used to discover the 3D structure of molecules from very noisy images. We discuss how algebra can describe two aspects of cryo-EM datasets. First, we'll describe common lines datasets. Common lines are lines of intersection between cryo-EM images in 3D. They are a crucial ingredient in some 2D to 3D reconstruction algorithms, and they can be characterized by polynomial equalities and inequalities. Second, we'll show how 3D symmetries of a molecule can be detected from only 2D cryo-EM images, without performing full 3D reconstruction.

Wednesday, February 18, 2015 - 11:00 ,
Location: Skiles 005 ,
Shelby Wilson ,
Morehouse College ,
shelby.wilson@morehouse.edu ,
Organizer:

An array of powerful mathematical tools can be used to identify the key underlying components and interactions that determine the mechanics of biological systems such as cancer and its interaction with various treatments. In this talk, we describe a mathematical model of tumor growth and the effectiveness of combined chemotherapy and anti-angiogenic therapy (drugs that prevent blood vessel growth). An array of mathematical tools is used in these studies including dynamical systems, linear stability analysis, numerical differential equations, SAEM (Stochastic Approximation of the Expectation Maximization) parameter estimation, and optimal control. We will develop the model using preclinical mouse data and discuss the optimal combination of these cancer treatments. The hope being that accurate modeling/understanding of experimental data will thus help in the development of evidence-based treatment protocols designed to optimize the effectiveness of combined cancer therapies.

Wednesday, October 22, 2014 - 11:05 ,
Location: Skiles 005 ,
Hayriye Gulbudak ,
School of Biology, GaTech ,
Organizer:

The emerging threat of a human pandemic caused by high-pathogenic H5N1avian inuenza virus magnifies the need for controlling the incidence ofH5N1 in domestic bird populations. The two most widely used controlmeasures in poultry are culling and vaccination. In this talk, I will discussmathematical models of avian inuenza in poultry which incorporate cullingand vaccination. First, we consider an ODE model to understand the dy-namics of avian inuenza under different culling approaches. Under certainconditions, complex dynamical behavior such as bistability is observed andanalyzed. Next, we model vaccination of poultry by formulating a coupledODE-PDE model which takes into account vaccine-induced asymptomaticinfection. In this study, the model can exhibit the \silent spread" of thedisease through asymptomatic infection. We analytically and numericallydemonstrate that vaccination can paradoxically increase the total numberof infected when the ecacy is not suciently high.1

Wednesday, September 3, 2014 - 11:05 ,
Location: Skiles 005 ,
James Moore ,
SoM GaTech ,
Organizer:

The
immune system must simultaneously mount a response against foreign
antigens while tolerating self. How this happens is still unclear as
many mechanisms of immune tolerance are antigen non-specific.
Antigen specific immune cells called T-cells must first bind to
Immunogenic Dendritic Cells (iDCs) before activating and proliferating.
These iDCs present both self and foreign antigens during infection, so
it is unclear how the immune response can be limited to primarily
foreign reactive T-cells. Regulatory T-cells (Tregs) are known to play a
key role in self-tolerance. Although they are antigen specific, they
also
act in an antigen non-specific manner by competing for space and growth factors as well as modifying DC behaviorto
help kill or deactivate other T-cells. In prior models, the lack of
antigen specific control has made simultaneous foreign-immunity and
self-tolerance extremely unlikely. We include a heterogeneous DC
population, in which different DCs present antigens at different levels.
In addition, we include Tolerogenic DC (tDCs) which can delete
self-reactive T-cells under normal physiological conditions. We compare
different mathematical models of immune tolerance with and without Tregs and heterogenous antigen presentation.For each model, we compute the final number of foreign-reactive and self-reactive T-cells, under a variety of different
situations.We find that even if iDCs present more self antigen than foreign antigen, the immune response will be primarily foreign-reactive as long as there is sufficient presentation of self antigen on tDCs. Tregs are required primarily
for rare or cryptic self-antigens that do not appear frequently on tDCs. We also find that Tregs can onlybe effective when we include heterogenous antigen presentation, as this allows Tregs and T-cells of the same
antigen-specificity to colocalize to the same set of DCs. Tregs better aid immune tolerance when they can both compete forspace and growth factors and directly eliminate other T-cells. Our results show the importance of the structure of the
DC population in immune tolerance as well as the relative contribution of different cellular mechanisms.

Monday, April 28, 2014 - 13:00 ,
Location: IBB 1128 ,
Suzanne M. Shontz ,
Department of Mathematics and Statistics, Mississippi State University. ,
Organizer:

Speaker is visiting the School of Biology, Georgia Tech

Pulmonary embolism (PE) is a potentially-fatal disease in which blood clots (i.e., emboli) break free from the deep veins in the body and migrate to the lungs. In order to prevent PE, anticoagulants are often prescribed; however, for some patients, anticoagulants cannot be used. For such patients, a mechanical filter, namely an inferior vena cava (IVC) filter, is inserted into the IVC to trap the blood clots and prevent them from reaching the lungs. There are numerous IVC filter designs, and it is not well understood which particular IVC filter geometry will result in the best treatment for a given patient. Patient-specific computational fluid dynamic (CFD) simulations may be used to predict the performance of IVC filters and hence can aid physicians in IVC filter selection and placement.
In this talk, I will first describe our computational pipeline for prediction of IVC filter performance. Our pipeline involves several steps including image processing, geometric model construction, in vivo stress state estimation, surface and volume mesh generation based on virtual IVC filter placement, and CFD simulation of IVC hemodynamics. I will then present the results of our IVC hemodynamics simulations obtained for two patient IVCs.
This talk represents joint work with several researchers at The Pennsylvania State University, Penn State Hershey Medical Center, the Penn State Applied Research Lab, and the University of Utah.

Wednesday, April 23, 2014 - 11:00 ,
Location: Skiles 005 ,
Zoi Rapti ,
University of Illinois at Urbana-Champaign ,
Organizer: Christine Heitsch

We will introduce a PDE model to investigate how epidemic metrics, such as the basic reproductive ratio R_0 and infection prevalence, depend on a pathogen's virulence. We define virulence as all harm inflicted on the host by the pathogen, so it includes direct virulence (increased host mortality and decreased fecundity) and indirect virulence (increased predation on infected hosts). To study these effects we use a Daphnia-parasite disease system. Daphnia are freshwater crustaceans that get infected while feeding, by consuming free-living parasite spores. These spores after they are ingested, they start reproducing within the host and the host eventually dies. Dead hosts decay releasing the spores they contain back in the water column. Visual predators, such as fish, can detect infected hosts easier because they become opaque, hence they prey preferentially on them. Our model includes two host classes (susceptible and infected), the free-living propagules, and the food resource (algae). Using experimental data, we obtain the qualitative curves for the dependence of disease-induced mortality and fecundity reduction on the age of infection. Among other things, we will show that in order the predator to keep the host population healthy, it needs to (i) detect the infected hosts very soon after they become infected and (ii) show very high preference on consuming them in comparison to the uninfected hosts. In order to address questions about the evolution of virulence, we will also discuss how we defined the invasion fitness for this compartmental model. We will finish with some pairwise invasibility plots, that show when a mutant strain can invade the resident strain in this disease system.

Wednesday, March 12, 2014 - 11:00 ,
Location: Skiles 005 ,
Chi-Jen Wang ,
Iowa State ,
Organizer: Christine Heitsch

Spatially discrete stochastic models have been implemented to analyze cooperative behavior in a variety of biological, ecological, sociological, physical, and chemical systems. In these models, species of different types, or individuals in different states, reside at the sites of a periodic spatial grid. These sites change or switch state according to specific rules (reflecting birth or death, migration, infection, etc.) In this talk, we consider a spatial epidemic model where a population of sick or healthy individual resides on an infinite square lattice. Sick individuals spontaneously recover at rate *p*, and healthy individual become infected at rate O(1) if they have two or more sick neighbors. As *p* increases, the model exhibits a discontinuous transition from an infected to an all healthy state. Relative stability of the two states is assessed by exploring the propagation of planar interfaces separating them (i.e., planar waves of infection or recovery). We find that the condition for equistability or coexistence of the two states (i.e., stationarity of the interface) depends on orientation of the interface. We also explore the evolution of droplet-like configurations (e.g., an infected region embedded in an all healthy state). We analyze this stochastic model by applying truncation approximations to the exact master equations describing the evolution of spatially non-uniform states. We thereby obtain a set of discrete (or lattice) reaction-diffusion type equations amenable to numerical analysis.

Wednesday, March 5, 2014 - 11:00 ,
Location: Skiles 005 ,
Professor Juan Gutierrez ,
UGA ,
jgutierr@uga.edu ,
Organizer:

The traditional epidemiological approach to characterize transmission of infectious disease consists of compartmentalizing hosts into susceptible, exposed, infected, recovered (SEIR), and vectors into susceptible, exposed and infected (SEI), and variations of this paradigm (e.g. SIR, SIR/SI, etc.). Compartmentalized models are based on a series of simplifying assumptions and have been successfully used to study a broad range of disease transmission dynamics. These paradigm is challenged when the within-host dynamics of disease is taken into account with aspects such as: (i) Simultaneous Infection: An infection can include the simultaneous presence of several distinct pathogen genomes, from the same or multiple species, thus an individual might belong to multiple compartments simultaneously. This precludes the traditional calculation of the basic reproductive number. (ii) Antigenic diversity and variation: Antigenic diversity, defined as antigenic differences between pathogens in a population, and antigenic variation, defined as the ability of a pathogen to change antigens presented to the immune system during an infection, are central to the pathogen's ability to 1) infect previously exposed hosts, and 2) maintain a long-term infection in the face of the host immune response. Immune evasion facilitated by this variability is a critical factor in the dynamics of pathogen growth, and therefore, transmission.This talk explores an alternate mechanistic formulation of epidemiological dynamics based upon studying the influence of within-host dynamics in environmental transmission. A basic propagation number is calculated that could guide public health policy.