Title: Epidemic viruses as Computational Entities

Newly emerging epidemic viruses, including HIV/AIDS, West Nile, SARS, and Influenza, have several important features in common. They (1) are small RNA viruses with genome lengths of approximately 10,000 nucleotides (2) emerged from animal reservoirs,(3) have high mutation rates, and (4) have genome structures that readily permit recombination or re-assortment between parental strains. In this lecture I will review current understanding on the mechanisms of emergence, adaptation, and global spread of viruses, and present an argument that epidemic viruses are best understood as computational entities.

Title: Visualization Experiences with Seer Cancer Data

We will discuss our experiences in using graph theorethical methods for the Analysis of SEER Cancer Data. The fourth main issues that we have been wrestling with are: efficient identification of essential data attributes, data driven partition methods, patient clustering and visual data navigation. The lattice of bicliques, of a graph theorethical interpretation of the data records, plays a central role in our investigations. This lattice is identical to the Concept Lattice. One of the aims is to identify the effect caused in the concept lattice by certain basic semantic operations on the data. We will demo our current prototype for SEER Cancer Data exploration with the objective of promoting healthy discussions about the usefulness of this approach for epidemiological research.

Portions of this work have been done in cooperation with Frank V. Ham, L.Miller, D. Millman and Alex Pogel.

Title: Modelling the ecology and evolution of Influenza A viruses.

Influenza viruses impose a heavy morbidity and mortality burden on the human population. They also provide a remarkable system for evolutionary and ecological study. Influenza A viruses evolve effectively at two different scales: gradual antigenic change due to point mutations allows annual epidemics, while dramatic antigenic change due to reassortment allows occasional global pandemics. Influenza viral evolution shapes and is shaped by the influenza immunity profile of the human population. I will discuss modeling approaches to the evolutionary ecology of influenza, and discuss ongoing investigations into genomic and epidemiological data.

Title: Disease containment by progressive vaccination on trees and grids

We consider a deterministic discrete-time model of disease spread on graphs, where the disease spreads to adjacent vertices at each time step. A limited number of vertices can be vaccinated at each time step. Which vertices should be vaccinated to minimize the total number of infected vertices? This model is equivalent to a model of fire spread introduced by Hartnell, where firefighters fill the role of vaccination. We consider the question of minimizing the number of infected or burnt vertices for finite trees and for infinite d-dimensional square grids.

Title: Networks of groups with homogeneous mixing

I will present two models. The first is an "immunoepidemic" models that analyses the long-term behavior of an epidemic on a network of hosts with varying immune response to the disease. The second is a model of a network of groups with homogeneous mixing. We derive a formula for R0, the basic reproductive number.

If there is time I will briefly discuss our agent-based models of livestock disease.