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Bioterrorism: Mathematical Modeling Applications in Homeland Security

H. T. Banks and Carlos Castillo-Chavez, editors
Publication Date: 
Number of Pages: 
Frontiers in Applied Mathematics 28
[Reviewed by
Raymond N. Greenwell
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This book is a spinoff from a workshop in 2002 sponsored by the Center for Discrete Mathematics & Theoretical Computer Science (DIMACS) and the National Science Foundation (NSF). It consists of ten independent chapters, each describing a mathematical model related to bioterrorism, a topic of intense interest in the United States after the anthrax scare of fall 2001.

The audience for this book is narrower than that of most books reviewed in Read This! Certainly anyone doing research on mathematical models related to bioterrorism would want to study this collection of recent models, trends, and results. More generally, mathematicians or biologists doing any type of mathematical modeling may consider this a valuable direction for their efforts, under the suspicion that funding is available for anything related to homeland security. Some, but not all, of the chapters are straightforward and basic enough to interest an undergraduate student of mathematical modeling. Those are also the chapters that I found most interesting. I'm not sure that the typical reader of this review would find this book worth reading unless they have a particular interest in such models. This is not so much a fault of the book as an inherent property of conference proceedings consisting of technical papers.

The book starts out emphasizing discrete math; Chapter 1, by Fred S. Roberts, DIMACS Director, is entitled "Challenges for Discrete Mathematics and Theoretical Computer Science in the Defense against Bioterrorism." It is an overview of the field, with a list of 250 references that is almost as long as the chapter itself.

Chapter 2, "Worst-Case Scenarios and Epidemics" by Gerardo Chowell and Carlos Castillo-Chavez, is the only other chapter emphasizing discrete math, using network theory to model how an epidemic can rapidly spread through a city.

With Chapter 3, "Chemical and Biological Sensing: Modeling and Analysis from the Real World" by Ira B. Schwartz et al., the book switches to continuous models, where it stays. Systems of differential equations are used to study detectors of explosives known as continuous flow displacement immunosensor (CFI sensors). In what is either a joke or a very poor choice of words, the authors state that "The CFI sensors have exploded on the scene."

Chapter 4, "The Distribution of Interpoint Distances" by Marco Bonetti et al., shows how statistics can give an early detection of a bioterrorism attack.

Chapter 5, "Epidemiologic Information for Modeling Foot-and-Mouth Disease" by Thomas W. Bates et al., discusses some of the models of this disease without going into any mathematical details. The author suggests that the disease could be intentionally introduced into this country as a means of economic bioterrorism.

Chapter 6 by H. T. Banks et al. is entitled "Modeling and Imaging Techniques with Potential for Application in Bioterrorism." This chapter discusses two rather complex models. "The first focuses on physiologically based pharmacokinetic (PBPK)-type models and the effects of drugs, toxins, and viruses on tissue, organs, individuals, and populations wherein both intra- and interindividual variability are present when one attempts to determine kinetic rates, susceptibility, efficacy of toxins, antitoxins, etc. in aggregate populations... A second effort concerns the use of remote electromagnetic interrogation pulses linked to dielectric properties of materials to carry out macroscopic structural imaging of bulk packages..."

Chapter 7, "Models for the Transmission Dynamics of Fanatic Behaviors" by Carlos Castillo-Chavez and Baojun Song, uses systems of differential equations to study how fanaticism might spread. The same authors, plus Juan Zhang, wrote Chapter 8 on "An Epidemic Model with Virtual Mass Transportation: The Case of Smallpox in a Large City," which uses a system of ordinary differential equations to study the minimum vaccination rate needed to prevent an epidemic. Chapter 9, "The Role of Migration and Contact Distributions in Epidemic Spread" by K. P. Hadeler, also uses differential equations to study epidemics.

Chapter 10, by James M. Hyman and Tara LaForce, is entitled "Modeling the Spread of Influenza among Cities." Rather than discuss how terrorists might spread the flu, the authors use a system of differential equations to model how the flu currently spreads through a network of 33 U.S. cities, and then compare the results of the model with actual data.

Each chapter has its own list of references. There is an index for the entire book.

Raymond N. Greenwell ( is Professor of Mathematics at Hofstra University in Hempstead, New York. His research interests include applied mathematics and statistics, and he is coauthor of the texts Finite Mathematics and Calculus with Applications, both published by Addison Wesley.

Preface; Chapter 1: Challenges for Discrete Mathematics and Theoretical Computer Science in the
Defense against Bioterrorism, Fred S. Roberts; Chapter 2: Worst-Case Scenarios and Epidemics, Gerardo Chowell and Carlos Castillo-Chavez; Chapter 3: Chemical and Biological Sensing: Modeling and Analysis from the Real World, Ira B. Schwartz, Lora Billings, David Holt, Anne W. Kusterbeck, and Ioana Triandaf; Chapter 4: The Distribution of Interpoint Distances, Marco Bonetti, Laura Forsberg, Al Ozonoff, and Marcello Pagano; Chapter 5: Epidemiologic Information for Modeling Foot-and-Mouth Disease, Thomas W. Bates, Mark C. Thurmond, and Tim E. Carpenter; Chapter 6: Modeling and Imaging Techniques with Potential for Application in Bioterrorism, H. T. Banks, David Bortz, Gabriella Pinter, and Laura Potter; Chapter 7: Models for the Transmission Dynamics of Fanatic Behaviors, Carlos Castillo-Chavez and Baojun Song; Chapter 8: An Epidemic Model with Virtual Mass Transportation: The Case of Smallpox in a Large City, Carlos Castillo-Chavez, Baojun Song, and Juan Zhang; Chapter 9: The Role of Migration and Contact Distributions in Epidemic Spread, K. P. Hadeler; Chapter 10: Modeling the Spread of Influenza among Cities, James M. Hyman and Tara LaForce; Index.