Power Law Could be Used to Predict Size, Scope of Food-Borne Outbreaks

Could a power law be used to predict food-borne outbreaks and thus help public health agencies better prepare?

Food-borne outbreaks often reach greater portions of the population than expected because of a lack of an effective, expedient identification of the outbreak. In the case of large outbreaks, often the necessary resources to deal with outbreaks of this scale are not available because local public health services were unable to gather them in time. However, regardless of whether public health entities are dealing with large food-borne outbreaks or small ones, there is a need for a “useful tool to estimate how many small outbreaks are missed,” argued Julie Self, PhD, a member of the Epidemic Intelligence Service (EIS) Division of Scientific Education and Professional Development at the Center for Surveillance, Epidemiology, and Laboratory Services at the Centers for Disease Control and Prevention (CDC), in an oral presentation on April 24, 2017, at the EIS Annual Conference, on the use of the “power law” to predict size and frequency of such outbreaks.

“More than 800 outbreaks are reported per year, which translates to 15,000 illnesses and 9,000 hospitalizations,” Dr. Self stated, noting, “Some outbreaks are never detected or reported. We believe that [the] size [of the outbreaks] may affect detections, investigations, public health interventions, and reporting.” By applying the power law to food-borne outbreaks, Dr. Self and her team hoped to define a mathematical relationship between the size of outbreaks and frequency, which could assist public health organizations in establishing the actual frequency of smaller, less-likely-to-be-reported outbreaks and predict when an area is primed for a larger outbreak.

According to the New England Complex Systems Institute (NECSI), a power law is “a relationship in which a relative change in one quantity gives rise to a proportional relative change in the other quantity, independent of the initial size of those quantities.”

Because “outbreaks can be considered natural occurrences and natural occurrences often have mathematical relationships, we hoped to define a mathematical relationship between outbreaks and size, with ‘magnitude’ being outbreak size and ‘frequency’ being the number of outbreaks,” explained Dr. Self.

The team used the Foodborne Disease Outbreak Surveillance System to pull data on food-borne outbreaks that occurred between 1998 and 2015, and then bootstrapped 5000 samples (they reached the threshold at 3000) to assess whether the outbreaks fit a power law.

Although the mathematical model was not disclosed, Dr. Self stated that the data fit the projections overall. However, she said that “every year we see 800 fewer-than-expected small outbreaks, and every 3 years we see 1 fewer than expected large outbreak.” Not surprisingly, there tend to be more small food-borne outbreaks, which are also much easier to “miss” than large-scale ones, and therefore there are likely many small outbreaks that are either not documented or not officially identified and reported.

Large-scale outbreaks, on the other hand, which happen less frequently than smaller ones, are easier to spot but may not actually swell to their full “potential” before intervention stalls them. This may lead to outbreaks that the model would predict to be “large” being classified somewhere lower on the relative scale.

There are several possible limitations on larger outbreaks’ size, including public health interventions, food-safety policies, outbreak investigation and response protocols that may terminate large outbreaks before they reach their natural limitations, as well as some natural limitations on large outbreak size, the team observed. Dr. Self also noted in response to an audience question that since outbreak response tends to improve over time, it is possible that this could have played a role in the results particularly toward the end of the study time frame.

“We would like to look at outbreaks by pathogen,” she concluded, adding that the team hypothesized that they would see similar relationships in this study, albeit possibly with “different slopes.” She also noted that the power law tool might be particularly useful in the allocation of resources and outbreak planning. “In some of the largest outbreaks we’ve observed, the resources to subtype have been lacking. They [public health organizations] have run out of reagents at times in order to subtype a large outbreak. This [model] gives us a better estimate of what is needed,” she said.