# UW-Eau Claire Students Demonstrate Practical Applications of Mathematical Models

RELEASED: July 6, 2009

EAU CLAIRE — A number of University of Wisconsin-Eau Claire mathematics students are using what they learn through research to help Eau Claire and other communities in practical, measurable ways.

 Dr. Simei Tong

Kaitlyn Hellenbrand, Middleton, Mark Bauer, Spencer, and Emily Klungtvedt, Moorhead, Minn., recently worked with Dr. Simei Tong, associate professor of mathematics, to design a mathematical model that can predict the most efficient method for evacuating a hospital in an emergency situation. When they applied their model to Luther Hospital in Eau Claire, which has five floors and seven departments that include bedridden patients, they identified a procedure that would evacuate the hospital 23 percent faster than by simply taking patients to the nearest available elevators.

The plan focused primarily on bedridden patients since they require the most time and resources during an emergency evacuation. The students needed to consider information gathered from hospital staff about which elevators could accommodate beds; transport time from each department to the elevators; time required for nurses to prepare patients for transport; travel time from each floor to the first floor; and other factors. They used the Simplex model in Excel to make their calculations.

"Once we calculated the optimal way to evacuate the hospital, we were surprised by the method of evacuation," Hellenbrand said. "For example, 11 patients from medical/surgical were sent to one elevator, while 14 patients from the same department were sent to an elevator on the other side of the building. Most people think that it would be most efficient to just send people to the closest elevator, but this research project showed that we may need to plan differently during an emergency situation in order to evacuate people most efficiently."

In addition, the students demonstrated that the model can be modified to suit different situations, so, for example, if one of the elevators was not functional during the evacuation, the model could produce a revised plan and predict the amount of additional time needed for evacuation.

"Producing an evacuation plan for a local hospital is another great example of how mathematics can give back to the community," said Bauer, who described the project as "a great experience."

The mathematical model they used was essentially the same as one developed earlier through work Tong did with recent UW-Eau Claire graduate Mitch Phillipson, Chippewa Falls, who is now on his way to do graduate work in mathematics at Texas A&M University. Phillipson and Tong designed the model while developing an emergency flood evacuation plan for the city of Owen. They began a similar project for Eau Claire County, and that project was later completed by students in Dr. Daniel Ernst's computer science class. Tong and Phillipson wrote an abstract about their model, "Shortest Paths and Optimal Solutions for Evacuation in Emergency Situations," which was published in 2008 by the American Mathematical Society.

The students working on the current project presented their work, "Optimal Evacuation Plan for Hospitals," at the annual Joint Mathematics Meet in Washington, D.C., in January, and also presented it at a meeting of the west-central Wisconsin regional emergency management officers in May.

Klungtvedt said presenting to the local officers was her favorite part of the project because the officers told them what they found to be applicable to their situations.

"Hearing their opinions allowed us to get a new perspective on what we have done well and how we can expand the project," Klungtvedt said.

In the meantime, Bauer and Klungtvedt have moved on to conducting a similar project for a larger hospital/clinic with 10 floors, which Dr. Tong describes as "a major U.S. hospital." For security reasons, they may not currently disclose the name of the clinic. For this project, the model will be revised to include a plan in which no elevators are functional and patients must be transported by sliding down to safety through windows.

"We are very fortunate to have received the support of the hospitals that let us work with them, as well as the grant support from UW-Eau Claire's Office of Research and Sponsored Programs," Tong said.

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