We developed a mathematical model of a cows-to-consumers supply chain associated with a single milk-processing facility that is the victim of a deliberate release of botulinum toxin. Because centralized storage and processing lead to substantial dilution of the toxin, a minimum amount of toxin is required for the release to do damage. Irreducible uncertainties regarding the dose-response curve prevent us from quantifying the minimum effective release. However, if terrorists can obtain enough toxin, and this may well be possible, then rapid distribution and consumption result in several hundred thousand poisoned individuals if detection from early symptomatics is not timely. Timely and specific in-process testing has the potential to eliminate the threat of this scenario at a cost of <1 cent per gallon and should be pursued aggressively. Investigation of improving the toxin inactivation rate of heat pasteurization without sacrificing taste or nutrition is warranted. bioterrorism ͉ mathematical modeling A mong bioterror attacks not involving genetic engineering, the three scenarios that arguably pose the greatest threats to humans are a smallpox attack, an airborne anthrax attack, and a release of botulinum toxin in cold drinks (1). The methods of dissemination in these three scenarios are, respectively, the person-to-person spread of a contagious disease, the outdoor dispersal of a highly durable and lethal agent, and the large-scale storage and production and rapid widespread distribution and consumption of beverages containing the most poisonous substance known. The first two scenarios have been the subject of recent systems modeling studies (2-5), and here we present a detailed systems analysis of the third scenario. For concreteness, we consider a release in the milk supply, which, in addition to its symbolic value as a target, is characterized by the rapid distribution of 20 billion gallons per year in the U.S.; indeed, two natural Salmonella outbreaks in the dairy industry each infected Ϸ200,000 people (6). Nonetheless, our methods are applicable to similar food products, such as fruit and vegetable juices, canned foods (e.g., processed tomato products), and perhaps grainbased and other foods possessing the bow-tie-shaped supply chain pictured in Fig. 1 . The mathematical model considers the flow of milk through a nine-stage cows-to-consumers supply chain associated with a single milk-processing facility (Fig. 1) . Supporting Appendix, which is published as supporting information on the PNAS web site, contains a detailed mathematical formulation of the model, a discussion of the modeling assumptions, and the specification of parameter values, some of which are listed in Table 1 . The supply-chain parameter values are representative of the California dairy industry, which produces Ͼ20% of the nation's milk (California dairy facts, www.dairyforum.org͞cdf.html, accessed on May 18, 2004). In our model, cows are milked twice daily, and the milk from each farm is picked up once per day by a 5,500-gallon truck, which makes two round trips daily between various farms and the processing plant. Upon a truck's arrival at the processing plant, the milk is piped into one of several raw milk silos, each capable of holding Ϸ50,000 gallons. Raw milk is piped into the processing facility, goes through a sequence of processes (e.g., separation, pasteurization, homogenization, and vitamin fortification), where each processing line may simultaneously receive milk from several silos, and is held in 10,000-gallon postpasteurization tanks before being bottled. In our base case, we assume that milk from different silos does not mix during downstream processing and relax this assumption later; although downstream mixing is physically possible at many facilities, it is not always done. Bottled milk is stored as finishedgoods inventory before traveling through the downstream distribution channel, eventually being purchased and consumed. We assume that botulinum toxin is deliberately released in either a holding tank at a dairy farm, a tanker truck transporting milk from a farm to the processing plant, or a raw milk silo at the processing facility. Each of these release locations leads to identical consequences, because the toxin is eventually well mixed throughout the contents of a raw milk silo. The crux of our analysis is to calculate the amount and toxin concentration of contaminated milk (see Fig. 4 , which is published as supporting information on the PNAS web site). By California state law, a raw milk silo must be cleaned after 72 h of operation. During these 72 h, the silo is initially filled up, then replenished (i.e., simultaneously filled and drained) for most of the 72-h period, and finally drained empty by 72 h. Because the toxin concentration in the silo drops exponentially during the replenishment interval, each postpasteurization holding tank has a different concentration level. Moreover, the amount of contaminated milk and the concentration distribution are themselves random quantities, depending upon when in the 72-h silo operation cycle the deliberate release occurs. Because of the difficulty of a terrorist in scheduling the release for maximum impact, we assume the release occurs randomly throughout the filling and replenishment intervals and report the mean number of poisoned people averaged over the random release time within the cycle. Using heat-inactivation data for foods with similar pH (7), we estimate that the heat-pasteurization process [170°F (77°C) for 15 min] inactivates 68.4% of the toxin. Each gallon of purchased milk is continuously consumed by four people (one child and three adults) over a 3.5-day period. Children aged 2-11 and adults have differential milk consumption rates and dose-response curves in our model. A probit dose-response model dictates the precise timing of each poisoning. Our dose-response relationship is based on scant human data (ID 50 ϭ 1 g for adults, ID 50 ϭ 0.43 g for children) (8, 9). The attack can be detected via either early symptomatics or in-process testing results, whichever occurs first. We assume the outbreak is detected when the 100th person develops symptoms [the incubation period, which is the interval between the time of poisoning and the onset of symptoms, is log normal with a median of 48 h and a dispersal factor of 1.5 (10)], and an
Wein and Liu REF developed a mathematical model of a cows-to-consumers supply chain associated with a single milk-processing facility that is the victim of a deliberate release of botulinum toxin.
Analyzing a bioterror attack on the food supply: the case of botulinum toxin in milk.
Proceedings of the National Academy of Sciences of the United States of America
Proceedings of the National Academy of Sciences of the United States of America
Medicine