In 1993, 50 Americans died in Milwaukee, Wisconsin, and a quarter of the citys population had severe cases of diarrhea. Scientists later discovered that at the same time, there was a failure in the municipal water treatment plant, and as a result, the towns drinking water contained a high level of a certain microbe called "crypto."
Outbreaks from bugs in tap water are rare, in part because water treatment policy is made to prevent major health hazards. But even though a large group of people may not fall sick simultaneously, the murky reality is that countless endemic cases of illness go unreported in the general population.
Currently in the US, the Environmental Protection Agency (EPA) monitors and establishes treatment policy. It conducts a four-step risk assessment: count the microbes in the water, assess the percentage of microbes removed by treatment, determine the probability of infection from the microbe, and determine the probability of deleterious outcome or infection. Outcomes for each individual at risk are assumed to be independent of the risk to others. Then, policies for water treatments (like chlorine treatment or filtration systems) help achieve safe levels of chemicals and microbes in the drinking water.
But consider that people who are already ill can experience more drastic consequences of specific microbes than the rest of the population. For example, individuals with HIV can die if they are exposed to crypto, even though that microbe might give someone else an upset stomach or have no effect at all. How can sub-populations with higher risk of infection be protected?
Based on standard risk analysis, a person with HIV would have an individual filtration system that cuts out 100% of crypto in the water in her home. But what about other health factors in the environment? Perhaps a person without a personal filter drinks his tap water and becomes a crypto carrier; although he does not get ill, he might sneeze on someone with HIV. There are millions of microbial agents that may circulate through secondary routes such as human-to-human contact, and these are not appraised nor reflected in standard risk assessment approaches.
Motivated by the devastation of the Milwaukee outbreak and the current legislation and water purification policies in the US, Stephen E. Chick (Associate Professor of Technology Management, INSEAD), Dr. James S. Koopman (Department of Epidemiology, Center for the Study of Complex Systems, the University of Michigan) and Sada Soorapanth (PhD candidate, Department of Industrial Operations and Engineering, the University of Michigan) discover a way to account for key infection transmission parameters that might influence water policy. They incorporate risk analysis and dynamical systems, and come up with a more comprehensive way to determine the key parameters.
The authors develop inference methods to assess secondary transmission parameters, based on water contamination and disease data. They draw upon several operations research tools, including stochastic processes, Bayesian inference, and dynamic systems models. They use a mixed stochastic/deterministic infection transmission system model, which first uses a differential equation to determine the role of water in infection transmission. Then to account for the unknown parameters, they employ the stochastic equation, using examples in nature to account for randomness.
By running simulations, they find that implementing a centralized municipal treatment system can be effective at protecting susceptible sub-populations from secondary transmission. Their conclusion demonstrates that dynamic system models can inform risk assessments for microbial infections transmitted through the water system. While the authors acknowledge that their work does not account for some complications and fluctuations of parameters, they suggest that its techniques provide a foundation for future work in the field.