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Mathematical model seeks to answer anthrax questions
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For an individual to have a 50% chance of becoming infected with anthrax, he would have to inhale 11,000 spores of the bacteria, according to the results from a mathematical model published online this month.
Damon J.A. Toth, PhD, a mathematician and assistant professor of internal medicine at the University of Utah, and colleagues looked at data from animal studies reported in the medical literature and then combined it with data from an accidental exposure at a bioterrorism plant that occurred in Sverdlovsk, Russia, in 1979 to develop the model.
Previous studies at other institutions had provided widely varying estimates of the chance of becoming infected with anthrax with low-dose exposure, according to the researchers.
Damon J.A. Toth
By analyzing the results from a better documented, non-human primate study at another institution, in combination with a carefully constructed mathematical model appropriate for humans, Toth and colleagues estimated that the number of spores required for a 1% chance of infection is 160.
These estimates were derived by developing and refining a competing-risks model in which the inhaled bacteria is trying to set up an infection in the lungs and the human body is trying to expel or control the bacteria. Toth then used available experimental animal data to optimize the working of the model to produce results that matched the timing of cases at Sverdlovsk.
Along with existing animal studies, data gathered from the accident at Sverdlovsk proved invaluable, the researchers said.
Up to 100 people died when a filter was accidently left off a piece of equipment at a plant that was developing anthrax as a bioterrorism weapon. Spores of the bacteria were released into the air near the town of Sverdlovsk. The Soviets eventually let outside experts in to study the accident. From publicly available accounts, despite limited records and a substantial delay before the investigation, it would appear that scientists were able to estimate when the release happened, plot where people were in the surrounding area when it occurred and then look at weather records to identify wind currents. With that information, they plotted how the spores were scattered in relation to people who became infected.
The timing and geographic pattern of the best documented cases from Sverdlovsk were consistent with both the shape of the dose-response curve and the distribution of incubation periods produced by the new model, the researchers said.
The model also sheds light on how long antibiotics should be given after an exposure to decrease the chances of infection, researchers said.
Damon Toth, PhD, can be reached at 295 Chipeta Way, Salt Lake City, UT 84132; email: toth@math.utah.edu.
Disclosure: The researchers report no relevant financial disclosures.
Perspective
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D.A. Henderson, MD, MPH, FRCP
This is an article that deserves attention. I know of no other study that has endeavored to compare experimental monkey exposures with the epidemic curve from Sverdlovsk that we developed and published some time ago (Brookmeyer R. Biostat. 2001;2:233-247.) in comparing experimental studies with the observations from Sverdlovsk and basically confirming a number of the important findings from Sverdlovsk.
In doing so, it should be of help in reining in some of the imaginative flights of fancy that have characterized all too many anthrax modeling studies.
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