Globalization and electronic communications have made the concept of national borders obsolete. We are closer to each other than ever before! "Six degrees of separation" is not a myth. The Internet and massive air travel are two of the most powerful "connecting" technologies, bringing multiple communities together into a single global family. As economic interdependence between nations becomes the norm, the financial difficulties of country X will ultimately affect the world. Similarly, political unrest such as a military coup or domestic disturbance such as an act of terrorism becomes everyone's problem. In this month's edition of Beyond Numbers and Proofs, I will address a few issues on the impact of global change with respect to the role of mathematics.

Viral Infections

Influenza or flu epidemics typically spread from Asia to the rest of the world. A few decades ago when air travel was minimal, scientists had plenty of time to assess the danger posed to populations and develop vaccines for new emerging flu strains. However, we do not have all the answers. Typically, vaccine development focuses on strains believed to be most virulent, but the virus' high mutation rate makes battling this foe very complex. Researchers are working overtime to produce vaccines that will minimize (with some probability) the impact of new strains affecting humans.

Due to air travel, the recent SARS epidemic spread almost simultaneously throughout China, Hong Kong, Vietnam, Taiwan, and Canada. Because there was no epidemiological understanding of this "new" virus, there was no available vaccine. Drastic efforts had to be implemented to contain it and mathematical models were used to validate the effectiveness of the approaches taken by the Canadians.

A technical article was published last May which discussed the outbreak [G. Chowell, P. W. Fenimore, M. A. Castillo-Garsow, and C. Castillo-Chavez, "SARS Outbreaks in Ontario, Hong Kong and Singapore: the role of diagnosis and isolation as a control mechanism," J. Theor. Biology 224, 1 (2003)]. Challenges posed by SARS may become the norm in the future. Hence, the collaboration of interdisciplinary groups of researchers, including mathematical scientists, is essential to minimize, prevent, and respond to the threats posed by natural or deliberate releases of biological agents.

Bioterrorism and Biological Mathematics

A recent paper highlighted the criticality of involving mathematical scientists in the study and assessment of biological agents. Discussions of potential scenarios associated with deliberate releases at various scales (communities, regions, countries, and the world) were published in a report spearheaded by Fred Roberts and myself. It included contributions of over 50 mathematical experts with positions at schools of public health at colleges and universities, the Centers for Disease Control and Prevention, and the National Institutes of Health. The report focused on issues that ranged from the use of models to assess and predict the dangers associated with acts of agroterrorism to the development of mathematical frameworks that may help understand the mechanisms behind the spread of fanatic behaviors.

Bioterrorism: Mathematical Modeling Applications in Homeland Security

Many mathematical applications may be found in this volume. Baojun Song of Montclair State University, Juan Zhang of Xian Jiaotong University, and I wrote a chapter that looked at the impact of deliberate releases of biological agents on mass transportation systems such as subways in cities with large transient populations. A test-bed experiment was carried out using New York City data. This city of 8 million people welcomes over 200,000 visitors per day--a large transient population. The challenges associated with the development of dynamic epidemiological models (differential equations) capable of incorporating transient populations were complex. Prior published work on epidemics in cities did not include possible secondary infections generated by the movements of infected individuals from transient populations (tourists, for example).

We found that epidemic "control" or containment was only possible under contingency plans that included a vaccination policy which included a significant percentage of tourists. Estimates on the critical proportion of city dwellers and tourists to be vaccinated were calculated using various scenarios. As is customary with this type of work (since all the data were not available), few answers were provided. However, a wealth of questions was generated.

One of these questions has motivated Sara Del Valle, a graduate student in the mathematics department at the University of Iowa and a former alum of the Mathematical and Theoretical Biology Institute. She has focused on the impact of timely and accurate government information on a biological agent like smallpox. Her model takes into account behavioral changes that are likely to occur when such catastrophes happen, such as people not showing up for work and most individuals avoiding crowds. All evidence, including the events of 11 September, point to the fact that individuals who face tragic events behave quite rationally; the release of accurate and timely information to affected populations may significantly reduce the impact of the deliberate release of a biological agent.

The importance of bioterrorism has prompted many experts to address it at national meetings. Special sessions on bioterrorism and mathematics were organized for the first time at the 50th annual meeting of the Society for Industrial and Applied Mathematics (SIAM) in Philadelphia, June 2002. Discussions and exchanges at this meeting were collected in the volume entitled "Bioterrorism: Mathematical Modeling Applications in Homeland Security," SIAM Series Frontiers in Applied Mathematics. The essence of the volume is captured in its introduction, which states, "Globalization and the possibility of bioterrorist acts have highlighted the pressing need for the development of theoretical and practical mathematical frameworks that may be useful in our systemic efforts to anticipate, prevent and respond to acts of destabilization." See the text box below for more information on this important compilation.

Final Thoughts

The advent of faster computers and the development of computational methods and tools have opened new frontiers for the application of mathematics. Mathematicians who want to be part of the scientific revolution in this current "biological era" can now find a large cadre of scientists in the biological and social sciences who either appreciate or who possess great quantitative and computational skills. There is now room for "math types" in almost every university department, national laboratory, government agency, or private corporation. It is a good time to be a mathematician particularly if you are interested in real-life applications.

Editor's note: Carlos Castillo-Chavez is a Joaquin Bustoz Jr. Professor of Mathematical Biology at Arizona State University and may be reached at Dr. Castillo-Chavez is the guest editor of Next Wave's February 2004 feature, Math and Biology: Careers at the Interface. That collection includes an article by Fred Roberts, also cited in this article.