1. Challenges for Discrete Mathematics and Theoretical Computer Science in the Defense against Bioterrorism

Abstract

The recent acts of bioterrorism using anthrax have raised great concern about the use of biological agents as weapons of mass destruction. This has led to major national debate and discussion—for example, about the possible impact of viruses such as smallpox as a biological weapon and about the possibility that bioterrorists would take advantage of genetic manipulation of highly variable viruses such as influenza. The great concern about the deliberate introduction of diseases by bioterrorists has raised new challenges for mathematical scientists. Dealing with bioterrorism requires detailed planning of preventive measures and responses: vaccination; vaccine dilution; vaccine stockpiling; quarantine of individuals, buildings, or regions; and systematic surveillance of emergency rooms, food supply, and water supply, to name just a few examples. Both planning and response require precise reasoning and extensive analysis of the type that mathematical scientists are very good at. Discrete mathematics and theoretical computer science, broadly defined, seem very relevant. In this chapter, we describe challenges for discrete mathematics and theoretical computer science raised by the need to plan for and defend against bioterrorist attacks. To begin, however, we talk briefly about a variety of mathematical sciences approaches to the defense against bioterrorism. Understanding infectious systems consisting of parasites, vectors, and hosts requires being able to reason about highly complex biological systems, sometimes with hundreds of demographic and epidemiological variables. Obtaining such understanding is crucial in the defense against bioterrorism. Components of host-pathogen systems are sufficiently numerous and their interactions sufficiently complex that intuition alone is insufficient to fully understand the dynamics of such interactions. Yet experimentation or field trials are often prohibitively expensive or unethical and do not always lead to understanding at a fundamental level. Therefore, mathematical modeling becomes an important experimental and analytical tool. Mathematical models have become important tools in analyzing the spread