Mathematical models can help prepare for and respond to bioterrorism attacks, provided that their strengths and weaknesses are clearly understood. A series of initiatives within the Department of Health and Human Services brought modelers together with biologists and epidemiologists who specialize in smallpox and experts in bioterrorism response and health policy and has led to the parallel development of models with different technical approaches but standardized scenarios, parameter ranges, and outcome measures. Cross-disciplinary interactions throughout the process supported the development of models focused on systematically comparing alternate intervention strategies, determining the most important issues in decision-making, and identifying gaps in current knowledge.

The man who demonstrated that malaria is transmitted by mosquitoes, Sir Ronald Ross, developed the first mathematical model of malaria transmission in 1911. In presenting his model, Ross made the crucial point that "the mathematical method of treatment is really nothing but the application of careful reasoning to the problems at issue" (1). In short, mathematical modeling is no more and no less than a tool to support clear thinking.

In the United States, mathematical models are familiar, everyday tools in engineering, business, and military applications and in most sciences. They represent hypotheses about underlying mechanisms that generate observed phenomena or the options for action and potential consequences. However, those models are rare in the biomedical-research and public health communities.

The events of September 11,2001, emphasized that the United States should use every tool available to help prepare for, and respond to, bioterrorism. With that understanding in mind, a series of National Institutes of Health (NIH) consultations was organized to address the potential of mathematical models to help with bioterrorism preparedness and response.

The first of those, in December 2001, brought together a small group of modelers and a small group of health-policy experts. The basic idea of this meeting was to see if a productive dialogue would emerge, and one did, despite the language and culture barriers. This dialogue led to a much better understanding of what modeling could and could not do to help.

The overall conclusion of the meeting was that models can be of great value, provided that their strengths and weaknesses are clearly understood. Modelers and nonmodelers should develop realistic expectations. For instance, models will not provide accurate numerical predictions of outcomes in this context; models can be used to forecast only in fairly gross terms. The key is to look not for absolute numbers but for differences in outcomes between different strategies and between different models. The consensus from that first consultation was that models can provide a means to systematically compare alternative intervention strategies, determine the most important issues in decision-making, and identify critical gaps in current knowledge.

Those three points are not as simple and straightforward as they may seem. For instance, if modeling is going to help identify and focus on the decisions likely to have the largest effects on outcomes, the models must address actual decisions to be made in actual bioterrorism events. That first consultation highlighted the need for active engagement and creative tension between modelers and policy experts. Modelers may focus on areas that interest them but seem tangential to decision-makers. On the other hand, if only policy experts are engaged, they may concentrate on information that fits their opinions and interests. The modeling most likely to help with bioterrorism preparedness and response will emerge from scientific, operational, and policy professionals who listen to and engage each other, with real respect and candor, on a continuing basis.

A corollary conclusion from that first consultation was that modeling can provide a comprehensive, explicit examination of the assumptions and logic that enter into a decision, in a way that purely verbal reasoning and debate cannot. In that sense, even if the results of a model were discarded, the modeling process alone, properly conducted, would more than return the investment.

Another way of looking at this same set of issues is the observation that many people, modelers and nonmodelers alike, seem to believe that one "right" model exists. In this context, at least, that is not likely to be the case. However, a great deal can be learned from examining circumstances in which several models disagree, whether or not they agree on some overall, qualitative result.

For example, the Figure shows output from two hypothetical models. The horizontal axis gives the fraction of a population covered by some intervention, e.g., a vaccine, and the vertical axis shows the resulting percentage reduction in death rate. At 0% coverage, the number of deaths does not change. Approaching 100% coverage, deaths are reduced nearly 100%. Both models agree that fewer deaths occur when more people are covered, but obvious differences also exist between the model results. According to model A, slightly less than 30% coverage would reduce deaths by half; according to model B, almost 70% coverage is needed to reduce deaths by the same amount.