Mathematical Model for Prescribing Antibiotics May Help Control Antibiotic Resistant Bacteria

In the United States some 100,000 people die every year because they become infected in hospital with a strain of antibiotic-resistant bacteria. To combat this problem, a sophisticated mathematical model has been developed that changes the way that antibiotics are prescribed and administered.

"We have developed the mathematical model in order to identify the key factors that contribute to this problem and to estimate the effectiveness of different types of preventative measures in typical hospital settings," said Vanderbilt mathematician Glenn F. Webb, who described the results at a presentation at the annual meeting of the American Association for the Advancement of Science on Feb. 17, 2008 in Boston, Massachusetts.

The most effective way to combat this growing problem, said Mr. Webb, was to minimize the use of antibiotics. It was no secret, he continued, that antibiotics were overused in hospitals. How to optimize its administration was a difficult issue. But the excessive use of antibiotics, which may benefit individual patients, was creating a serious problem for the general patient community.

The model, developed by an inter-disciplinary team of researchers, showed that in a hospital where antibiotic treatments were begun 3 days after diagnosis and continued for 18 days, the number of cross-infections by resistant bacteria increased and decreased but never disappeared completely. When antibiotic treatments started the day of diagnosis and continued for 8 days, however, the cross-infection rate fell to nearly zero within 20 days.

. The mathematical analysis reveals that the "optimal strategy" for controlling hospital epidemics is to start antibiotic treatments as soon as possible and administer the drugs for the shortest possible time. Beginning treatment as early as possible is the most effective in knocking down the population of the non-resistant bacteria that is causing a patient’s initial illness and minimizing the length of treatment shortens the length of time when each patient acts as a source of infection. "Our results point out an urgent need for more research into the issue of the best timing for the administration of antibiotics and how to reduce its misuse and overuse," said Webb.

The model was developed by an interdisciplinary team of researchers. In addition to Webb, the contributors are Erika M.C. D’Agata at Harvard University’s Beth Israel Deaconess Medical Center, Pierre Magal and Damien Olivier at the Universit√© du Havre in France and Shigui Ruan at the University of Miami, Coral Gables. It is described in the paper "Modeling antibiotic resistance in hospitals: The impact of minimizing treatment duration" published in the Journal of Theoretical Biology.

Source: Journal of Theoretical Biology, December, 2007.

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