**D**iseases seem to be in the news almost every day lately, with breaking stories about SARS, "mad cow" disease, and avian influenza. Interest in infectious diseases has increased greatly in recent years as new diseases such as West Nile virus, HIV/AIDS, hepatitis C, hantavirus, and Lyme disease have emerged, and antibiotic-resistant strains of tuberculosis, pneumonia, and gonorrhea have evolved.

Methods of mathematics and computer science have become important tools in analyzing the spread and control of infectious diseases. Partnerships among computer scientists, mathematicians, epidemiologists, public health experts, and biologists are increasingly important in the defense against disease. The field of computational and mathematical epidemiology is giving rise to many new and interesting career opportunities. This article will discuss the field, relevant mathematical methods, career opportunities, and related programs at the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) at Rutgers University.

DIMACS is a consortium of Rutgers and Princeton Universities, AT&T Labs, Bell Labs, NEC Research, and Telcordia Technologies, with affiliated partners at Avaya Labs, HP Labs, IBM Research, and Microsoft Research. The center was founded in 1989 as a National Science Foundation "science and technology center." Researchers affiliated with DIMACS and their partners nationally and internationally are interested in ways that fundamental methods of computer science and mathematics can be applied to important problems of society. The center was one of the pioneers in the field of computational biology through its tutorials, workshops, and graduate student and postdoctoral training programs, focusing the talents of some of the computer science community's strongest researchers on problems arising from molecular biology.

**Modeling the Spread of Diseases**

Epidemic models of infectious diseases go back to Daniel Bernoulli's mathematical analysis of smallpox in 1760, and they have been developed extensively since the early 1900s. Hundreds of mathematical models have been published since, exploring the effects of bacterial, parasitic, and viral pathogens on human populations. The results have highlighted and formalized concepts such as the core population in sexually transmitted diseases, and they have made explicit other concepts such as herd immunity for vaccination policies. Mathematical modeling, with the help of computational tools, has provided new insights into important issues such as drug resistance, rate of spread of infection, epidemic trends, and effects of treatment and vaccination. Yet, for many diseases, we are far from understanding disease dynamics; there is much important work to be done.

Mathematical models, with the aid of computer simulations, are useful for building and testing theories about complex biological systems involving disease, assessing quantitative conjectures, determining sensitivities to changes in parameter values, and estimating key parameters from data. Modeling is especially crucial in epidemiology since in most cases we cannot do experiments.

Statistical methods have long been used in epidemiology for evaluating the role of chance and confounding associations. Yet the role of statistical methods in epidemiology is changing due to the increasingly huge data sets involved. The size of modern epidemiological problems and the large data sets that arise call out for the development of new, powerful computational methods.

A smaller but still venerable tradition within epidemiology is the application of difference and differential equations to understanding infectious disease as a dynamical system. Yet today's powerful computational methods have not yet been systematically applied to these systems, and few computer scientists or computational mathematicians have been involved. Moreover, new computational methods are needed to elucidate the dynamics of multiple interacting strains of viruses and the spatial spread of disease, and to facilitate the early detection of emerging diseases and bioterrorist acts.

Probabilistic methods, in particular stochastic processes, have also played an important role in epidemiological modeling. Computational methods for simulating stochastic processes in complex spatial environments, or on large networks, have increased the complexity of the biological interactions that we can simulate successfully. However, here again, few computer scientists or computational mathematicians have been involved in efforts to bring the power of modern computational methods to bear, and there are important opportunities for those who would try.

**Untapped Resources in Computer Science**

A variety of other potentially useful approaches to epidemiological issues have not yet attracted the attention of many in the mathematics and computer science community, and some relevant methods of computer science and mathematics are not widely known among epidemiologists. For example, many fields of science, especially molecular biology, have made extensive use of the methods of discrete mathematics, broadly defined. Yet, these methods, closely related to theoretical computer science, remain largely unused in epidemiology. The increasing uses in epidemiology of geographical information systems and data mining open up significant opportunities to apply methods of discrete mathematics.

Epidemiology's expanding emphasis on an evolutionary point of view lends itself especially well to the application of methods of discrete mathematics. To fully understand issues such as immune responses of hosts; co-evolution of hosts, parasites, and vectors; drug response; and antibiotic resistance, biologists are increasingly taking approaches that model the impact of mutation, selection, population structure, selective breeding, and genetic drift on the evolution of infectious organisms and their various hosts.

Many current phylogenetic techniques were developed for well-behaved evolutionary problems. But the traditional model of a binary tree with a small number of species as leaves is insufficient to capture the "quasi-species" nature of many viruses and the very high substitution rates of retroviruses. Collaboration between mathematical scientists and epidemiologists in developing and applying new phylogenetic methods is likely to take both epidemiology and mathematical science in new and fruitful directions.

At DIMACS, we are investigating all these types of methodological and modeling issues. In winter 2001 a group of DIMACS researchers started to discuss whether the tools of math and computer science could shed light on mad cow disease or BSE. The discussion quickly broadened to whether math and computer science could illuminate defense against disease of all kinds, and the DIMACS "Special Focus on Computational and Mathematical Epidemiology" was born. The terrorist attacks of 11 September 2001 and the subsequent anthrax attacks focused our attention beyond naturally occurring disease and onto diseases that could be triggered by bioterrorists.

**DIMACS Special Focus on Epidemiology**

This DIMACS special focus aims to introduce outstanding junior people (including students) from the mathematical/computer science and biological science communities to the issues, problems, and challenges of computational and mathematical epidemiology. We aim to develop and strengthen collaborations and partnerships between mathematical scientists and biological scientists; identify and explore methods of mathematical science not yet widely used in epidemiology; and involve biological and mathematical scientists together to help set the agenda and develop the tools of computational and mathematical epidemiology.

This is done, in part, through a series of tutorials, workshops, and training programs for postdoctoral fellows, graduate students, and undergraduates. These tutorials and workshops are open to outside participation for a modest registration fee, and financial support for attendance is sometimes available.

DIMACS has several postdoctoral fellowships available for work in computational and mathematical epidemiology. Graduate students can apply for funds to visit the center and interact with some of the center's researchers during their stay. An NSF-sponsored summer Research Experiences for Undergraduates program is open to students from all over the U.S.

Career opportunities for mathematical and computational epidemiologists are not limited to academic research. Increasingly, epidemiological problems are of interest to government agencies of all kinds, whether they deal with emergency preparedness, spread and control of disease (such as the Centers for Disease Control and Prevention or state or local health departments), homeland security, or agriculture (with the increasing concern about agroterrorism and diseases of animals or plants). Many companies now have emergency-preparedness plans and need experts in modeling to help develop them.

Dealing with data that might be relevant to the spread of disease is big business. Mathematical epidemiologists deal with large data sets, looking to find patterns; increasingly, large epidemiological data sets are of interest not only to health departments, but also to hospitals, insurance companies, and other private-sector organizations. Organizing, sorting, and analyzing health data are increasingly "outsourced" by government agencies, HMOs, and insurance companies. Pharmaceutical companies, of course, deal with disease, and they have departments of epidemiology that are central to their business.

**Math, Biology Skills, and Collaborations Needed**

What kind of background do you need to work in computational and mathematical epidemiology? It's important to have a strong background in the mathematical sciences, especially statistics, probability, dynamical systems, and discrete mathematics. Those with mathematical background can readily learn the appropriate tools. If you are a biological scientist with interest in this work, you may find the move into mathematical and computational epidemiology a bit more difficult; the best advice is to collaborate with someone who has a strong mathematical background.

Similarly, the best advice for those with mathematical credentials is to involve themselves with epidemiology collaborations. Problems of epidemiology and public health are increasingly interdisciplinary, including not only mathematical and biological science aspects, but also aspects of the social sciences. Those interested in going into this field need to feel comfortable working with mixed, interdisciplinary groups. Furthermore, while it isn't possible to be an expert on all the relevant disciplines, a level of comfort and increasingly a level of involvement with such groups is a key to success.

At DIMACS, we have working groups on a wide variety of epidemiology problems, such as vaccination strategies, adverse event detection, health data privacy and confidentiality, and models of social disruptions caused by bioterrorist events. Members of these groups have diverse backgrounds and sometimes are open to others who would like to participate. More information about DIMACS and its epidemiology special focus is available.

Will mathematics and computer science help control the spread of SARS or HIV/AIDS? Not alone. But in conjunction with epidemiology, public health, and the social sciences, it can play an important role. We need more people to take an interest in making this happen.