## Seminars and Colloquia by Series

### Modeling Avian Influenza and Control Strategies in Poultry

Series
Mathematical Biology Seminar
Time
Wednesday, October 22, 2014 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Hayriye GulbudakSchool of Biology, GaTech
The emerging threat of a human pandemic caused by high-pathogenic H5N1 avian in uenza virus magnifies the need for controlling the incidence of H5N1 in domestic bird populations. The two most widely used control measures in poultry are culling and vaccination. In this talk, I will discuss mathematical models of avian in uenza in poultry which incorporate culling and vaccination. First, we consider an ODE model to understand the dynamics of avian influenza under different culling approaches. Under certain conditions, complex dynamical behavior such as bistability is observed and analyzed. Next, we model vaccination of poultry by formulating a coupled ODE-PDE model which takes into account vaccine-induced asymptomatic infection. In this study, the model can exhibit the "silent spread" of the disease through asymptomatic infection. We analytically and numerically demonstrate that vaccination can paradoxically increase the total number of infected when the efficacy is not sufficiently high.

### A mathematical model of immune regulation: why we aren't all dead from autoimmune disease

Series
Mathematical Biology Seminar
Time
Wednesday, September 3, 2014 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
James MooreSoM GaTech
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.

### Patient-Specific Computational Fluid Dynamic Simulations for Predicting Inferior Vena Cava Filter Performance

Series
Mathematical Biology Seminar
Time
Monday, April 28, 2014 - 13:00 for 1 hour (actually 50 minutes)
Location
IBB 1128
Speaker
Suzanne M. ShontzDepartment of Mathematics and Statistics, Mississippi State University.

Please Note: 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.

### CANCELLED: Pathogen strategies and the shape of epidemics

Series
Mathematical Biology Seminar
Time
Wednesday, April 23, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Zoi RaptiUniversity of Illinois at Urbana-Champaign
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.

### Spatial epidemic models: lattice differential equation analysis of wave and droplet-like behavior

Series
Mathematical Biology Seminar
Time
Wednesday, March 12, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Chi-Jen WangIowa State
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.

### Systems Biology of Epidemiology: From Genes to Environment

Series
Mathematical Biology Seminar
Time
Wednesday, March 5, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Professor Juan GutierrezUGA
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.

### Obtaining Protein Energetics Using Adaptive Steered Molecular Dynamics

Series
Mathematical Biology Seminar
Time
Wednesday, February 19, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Rigoberto HernandezGT Chem &amp;amp; Biochem
The behavior and function of proteins necessarily occurs during nonequilibrium conditions such as when a protein unfolds or binds. The need to treat both the dynamics and the high-dimensionality of proteins and their environments presents significant challenges to theoretical or computational methods. The present work attempts to reign in this complexity by way of capturing the dominant energetic pathway in a particular protein motion. In particular, the energetics of an unfolding event can be formally obtained using steered molecular dynamics (SMD) and Jarzynski’s inequality but the cost of the calculation increases dramatically with the length of the pathway. An adaptive algorithm has been introduced that allows for this pathway to be nonlinear and staged while reducing the computational cost. The potential of mean force (PMF) obtained for neuropeptide Y (NPY) in water along an unfolding path confirmed that the monomeric form of NPY adopts the pancreatic-polypeptide (PP) fold. [J. Chem. Theory Comput. 6, 3026-3038 (2010); 10.1021/ct100320g.] Adaptive SMD can also be used to reconstruct the PMF obtained earlier for stretching decaalanine in vacuum at lower computational cost. [J. Chem. Phys. 136, 215104 (2012); 10.1063/1.4725183.] The PMF for stretching decaalanine in water solvent (using the TIP3P water potential) at 300K has now been obtained using adaptive SMD. [J. Chem. Theory Comput. 8, 4837 (2012); 10.1021/ct300709u] Not surprisingly, the stabilization from the water solvent reduces the overall work required to unfold it. However, the PMF remains structured suggesting that some regions of the energy landscape act partially as doorways. This is also further verified through a study of the hydrogen-bond breaking and formation along the stretching paths of decaalanine in vacuum and solvent. (Rescheduled from Feb 12th.)

### Modeling inoculum dose dependent patterns of acute virus infections

Series
Mathematical Biology Seminar
Time
Monday, February 10, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Professor Andeas HandelDepartment of Epidemiology and Biostatistics, College of Public Health, UGA
Inoculum dose, i.e. the number of pathogens at the beginning of an infection, often affects key aspects of pathogen and immune response dynamics. These in turn determine clinically relevant outcomes, such as morbidity and mortality. Despite the general recognition that inoculum dose is an important component of infection outcomes, we currently do not understand its impact in much detail. This study is intended to start filling this knowledge gap by analyzing inoculum dependent patterns of viral load dynamics in acute infections. Using experimental data for adenovirus and infectious bronchitis virus infections as examples, we demonstrate inoculum dose dependent patterns of virus dynamics. We analyze the data with the help of mathematical models to investigate what mechanisms can reproduce the patterns observed in experimental data. We find that models including components of both the innate and adaptive immune response are needed to reproduce the patterns found in the data. We further analyze which types of innate or adaptive immune response models agree with observed data. One interesting finding is that only models for the adaptive immune response that contain growth terms partially independent of viral load can properly reproduce observed patterns. This agrees with the idea that an antigen-independent, programmed response is part of the adaptive response. Our analysis provides useful insights into the types of model structures that are required to properly reproduce observed virus dynamics for varying inoculum doses.

### Rescheduled for March 12: Spatial epidemic models: lattice differential equation analysis of wave and droplet-like behavior

Series
Mathematical Biology Seminar
Time
Friday, January 31, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Chi-Jen WangIowa State
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.

### Intra-Host Adaptation and Antigenic Cooperation of RNA Viruses: Modeling and Computational Analysis.

Series
Mathematical Biology Seminar
Time
Wednesday, January 22, 2014 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles Bld Room 005
Speaker
Pavel SkumsCDC
Understanding the mechanisms responsible for the establishment of chronic viral infections is critical to the development of efficient therapeutics and vaccines against highly mutable RNA viruses, such as Hepatitis C (HCV). The mechanism of intra-host viral evolution assumed by most models is based on immune escape via random mutations. However, continuous immune escape does not explain the recent observations of a consistent increase in negative selection during chronic infection and long-term persistence of individual viral variants, which suggests extensive intra-host viral adaptation. This talk explores the role of immune cross-reactivity of viral variants in the establishment of chronic infection and viral intra-host adaptation. Using a computational prediction model for cross-immunoreactivity of viral variants, we show that the level of HCV intra-host adaptation correlates with the rate of cross-immunoreactivity among HCV quasispecies. We analyzed cross-reactivity networks (CRNs) for HCV intra-host variants and found that the structure of CRNs correlates with the type and strength of selection in viral populations. Based on those observations, we developed a mathematical model describing the immunological interaction among RNA viral variants that involves, in addition to neutralization, a non-neutralizing cross-immunoreactivity. The model describes how viral variants escape immune responses and persist, owing to their capability to stimulate non-neutralizing immune responses developed earlier against preceding variants. The model predicts the mechanism of antigenic cooperation among viral variants, which is based on the structure of CRNs. In addition, the model allows to explain previously observed and unexplained phenomenon of reappearance of viral variants: for some chronically infected patients the variants sampled during the acute stage are phylogenetically distant from variants sampled at the earlier years of infection and intermixed with variants sampled 10-20 years later. (Joint work with Y. Khudyakov, Z.Dimitrova, D.Campo and L.Bunimovich)