Math model identifies key to controlling epidemic

The graph on the left shows the percentage of patients who are infected with antibiotic-resistant bacteria (red) and nonresistant bacteria (green) when antibiotics are administered three days after diagnosis for... Click here for more information.

When you check into a hospital, the odds are one in ten that you will become infected with a strain of antibiotic-resistant bacteria as a result of your stay. That is because the problem of drug-resistance has become endemic in today’s hospitals despite the best efforts of the medical profession. In the United States alone this currently causes about 100,000 deaths per year.

Now, a sophisticated new mathematical model has identified what may be the key to getting this growing health problem under control: Changing 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 in Boston.

“According to our analysis, the most effective way to combat this growing problem is to minimize the use of antibiotics,” he said. “It is no secret that antibiotics are overused in hospitals. How to optimize its administration is a difficult issue. But the excessive use of antibiotics, which may benefit individual patients, is creating a serious problem for the general patient community.”

For example, the model calculates that in a hospital where antibiotic treatments are begun on average three days after diagnosis and continued for 18 days, the number of cross-infection by resistant bacteria (that is, cases where patients are accidentally infected by health care workers who have been exposed to these bacteria while treating other patients) waxes and wanes but never disappears completely. However, when antibiotic treatments are begun on the day of diagnosis and continued for eight days, the cross-infection rate drops to nearly zero within 250 days.

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 Université 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 in December 2007.