Biomathematics Seminar, Upcoming Talks

Tuesday, Feb. 8, Little Hall 368, 12:50-1:40 pm
Hal Smith, Arizona State
Bacteriophage predation on bacteria: mathematical models and their analysis
Bacteriophage, phage for short, are viruses that parasitize bacteria. Mathematical modeling of this predator-prey relationship began in the early 1960s with work of Campbell and later in the late 1970s with Stewart, Chao and Levin. These models have proved to be resistant to mathematical analysis due to the presence of nonlinearity and time-delays. For example, sharp conditions for the persistence or extinction of phage do not exist in the literature. I will give a status report on on-going research with collaborators H. Thieme and D. Jones on our work in this area. We have generalized the earlier models to better capture phage biology. Further, we give sharp criteria for persistence and extinction in terms of a basic reproductive ratio for chemostat-based models and for models based on flow reactors where spatial inhomogeneity is present. If time permits, more recent work on the spatial spread of phage infection on immobilized bacteria in a petri dish will be discussed.

Friday, Feb. 11, The Atrium, 4:05-4:55 pm, (Tea served at 3:30)
Linda Allen, Texas Tech
Pathogen Extinction in Stochastic Models of Epidemics and Viral Dynamics
The basic reproduction number R_0 in epidemic models is probably one of the most well-known thresholds in disease dynamics. In stochastic epidemic models, disease elimination (or pathogen extinction) often depends on the magnitude of R_0. For example, in the simple case of an SIS Markov chain model with R_0>1, the probability of pathogen extinction is approximately (1/R_0)^{i_0}, where i_0 is the initial number of infectious individuals. In more complex stochastic epidemic models, such as models with several infectious stages, the probability of pathogen extinction depends on the initial number of infectious individuals in each of the stages. In this presentation, multitype branching process theory is used to derive expressions for pathogen extinction in models of epidemics and viral dynamics. In particular, viral extinction within a host is analyzed as it depends on initial viral dose, the immune response, and the viral reproductive strategy.

Biomathematics Seminar, Spring 2011

Souvik Bhattacharya
Size Structured Predator-Prey Model
In this talk I will introduce a predator-prey model with the prey structured by body size based on reports in the literature that predation rates are prey-size specific. The model is built on the foundation of the one-species physiologically structured models studied earlier. Three types of equilibria are found: extinction, multiple prey-only equilibria and possibly multiple predator-prey coexistence equilibria. The stabilities of the equilibria are investigated. Comparison is made with the underlying ODE Lotka-Volterra model. It turns out that the ODE model can exhibit sustain oscillations if there is an Allee effect in the net reproduction rate, that is the net reproduction rate grows for some range of the prey's population size. In contrast, it is shown that the structured PDE model can exhibit sustain oscillations even if the net reproductive rate is strictly declining. Those occur, however, if reproduction is size specific and limited to individuals of large enough size. In conclusion, we pose an open hypothesis that size-specific predation can destabilize the predator-prey equilibrium in the PDE model.
Jan. 25. Little Hall 368, 12:50-1:40 pm

Bryan Kolaczkowski, Department of Microbiology and Cell Science
Detecting the Action of Natural Selection on the Genome
One of the central tenants of Darwin's evolutionary theory is that mutations conferring a selective advantage - "adaptive mutations" - will lead to differences among species as different species adapt to different environments. But differences between species can also arise due to random chance or historical accident, even if they confer no fitness advantage. Determining which differences were driven by natural selection and which were neutrally acquired is therefore one of the chief goals of evolutionary biology. With the recent ability to sequence multiple genomes from individuals within a single species, we are now in the position to directly ask the question: "Where is selection acting in the genome?" If we can answer this question, we can essentially provide a catalog of all the adaptive mutations that have accrued within a given species, giving a complete molecular description of how this species has adapted to its environment. Here I outline our understanding of what adaptive evolution looks like at the molecular level and the statistical techniques available to identify molecular adaptation. I highlight how biological reality makes it tricky to detect the action of natural selection on the genome.
Feb. 1, Little Hall 368, 12:50-1:40 pm

Biomathematics Seminar, Fall 2010

Maia Martcheva
"Avian Influenza: Modeling and Implications for Control."
August 31, Sept 7. Little Hall 368, 12:50-1:40 pm

Swati DebRoy
"Within-host models for Hepatitis C infection, treatment and related side-effects"
Sept. 21. Little Hall 368, 12:50-1:40 pm

Scott McKinley
"First thoughts on modeling with Stochastic Differential Equations"
In the first of these two lectures we will focus on introducing key qualitative properties of SDEs that help in developing mathematical models. In particular, we will have the development of population and epidemiology models in mind when we discuss Ito's formula, additive vs multiplicative noise, stationary vs. nonstationary processes, tests for explosion and techniques for determining the probability of hitting points.

In the second lecture, we will survey recent work on stochastic SIR (susceptible-infected-recovery) models, making note of open problems along the way.
Sept. 28, Oct. 5. Little Hall 368, 12:50-1:40 pm

Karli Jacobson, Jillian Stupiansky
"Citrus Greening: Motivation and Modeling"
Discovered in Florida in 2005, Citrus Greening (Huanglongbing) has caused a major decline in citrus production in the state and now threatens Texas and California as well. We will provide a brief history of this vector-transmitted disease in Florida and describe the challenges facing the citrus industry and researchers. We will introduce a grove-scale population model for citrus trees, calculate the basic reproduction number under various modifications, and discuss our current efforts towards modeling the psyllid vector population.
Oct. 19. Little Hall 368, 12:50-1:40 pm

Swati Patel
Introduction to the use of coalescent theory in genetic population models.
Population genetics is built on the idea of thinking of a population as a mixing pool of alleles. Thus, we can predict how this gene pool will react to demographic changes in the population. Coalescent theory is a subfield of population genetics, which, like population genetics, aims to extract information about a population based on genetic data. I will introduce basic coalescent theory and explain one simple application of how to use genetic data from a small sample of a population to estimate parameters that describe a population.
Nov. 2. Little Hall 368, 12:50-1:40 pm

Craig Osenberg, Jessica Langebrake
Differential movement and movement bias models for Marine Protected Areas
Marine protected areas (MPAs) are promoted as a tool to protect overfished stocks and increase fishery yields. Previous models suggested that adult mobility modified effects of MPAs by reducing densities of fish inside reserves but increasing yields (i.e., increasing densities outside of MPAs). Empirical studies contradicted this prediction: as mobility increased, the relative density of fishes inside MPAs (relative to outside) increased. We hypothesized that this disparity between theoretical and empirical results was the result of differential movement of fish inside vs. outside the MPA. We therefore developed a model with unequal and discontinuous diffusion, and analyzed its steady state and stability. We determined the Abundance in the Fishing Grounds, the Yield, the Total Abundance and the Log Ratio at steady-state and examined their response to adult mobility (while keeping the relative inequity in the diffusion constant). Abundance in the Fishing Grounds and Yield increased, while Total Abundance and Log-Ratio decreased, as mobility increased. These results were all qualitatively consistent with previous models assuming uniform diffusivity. Thus, the mismatch between empirical and theoretical results must result from other processes or other forms of differential movement.
Nov. 23. Little Hall 368, 12:50-1:40 pm

Samares Pal
Algal bloom dynamics modeled in presence of nutrient and toxic substances and its effects on Zooplankton species
We have studied a model consisting of nutrient, non-toxic phytoplankton, toxin producing phytoplankton and their predator zooplankton population in open marine system. It is observed that nutrient- phytoplankton-zooplankton interactions are very complex and situation specific. Different exciting results, ranging from stable situation to cyclic blooms may occur under different favorable conditions.
Nov. 30. Little Hall 368, 12:50-1:40 pm

Andrew Hein
"Biological search in a low signal environment: a strategy for locating targets with sparse information."
Locating a target whose location is unknown is a common problem faced by biological organisms. Many such targets emit signals (e.g. a prey item emitting a scent) that contain information that can be used by the searcher to locate the target. Traditionally, biologists have assumed that searching organisms use chemotaxis--a strategy that involves moving up the gradient in signal strength-- to locate targets. However, chemotaxis performs poorly in many realistic situations (e.g. advected flows, sparse signals). I will discuss an alternative way to think about how organisms search for resources that is based on probability maps of the target's location. I'll provide an intuition for how these searches work and show results of simulations that allow for comparison among a suite of strategies that use probability maps to find targets.
Dec. 7. Little Hall 368, 12:50-1:40 pm