New Math Model May Help Contain Hospital Infection Rates

March 10, 2008

A mathematical model has apparently identified critical ways of reducing hospital infection rates: cutting back the amount of antibiotics prescribed but administering the medication quickly.

Hospital-related drug-resistance is said to account for 100,000 deaths per year in the U.S.

“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 mathematician Glenn F. Webb (Vanderbilt University). He presented the findings at this year's meeting of the AAAS, in Boston, in mid-February.

According to analysis, "The most effective way to combat this growing problem is to minimize the use of antibiotics,” Webb 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.”

Webb's model demonstrates that when antibiotic treatment begins on the day of diagnosis and continues for eight days, the cross-infection rate vanishes within 250 days. At present, when treatment starts three days after diagnosis and continues for 18 days, the number of cases of cross-infections only waxes and wanes.

The researchers constructed a two-level mathematical model: at the bacterial level where non-resistant and resistant strains are produced in the bodies of individual patients; and at the patient level where susceptible patients are cross-infected by health care workers who have become contaminated by patients.

At the bacterial level, the model takes an ecological approach that describes the competition between non-resistant and resistant strains of infectious bacteria. In untreated patients, nonresistant bacteria have a competitive advantage over the resistant strains that keeps the numbers of resistant bacteria low. During treatment, however, antibiotics kill off the normal bacteria, allowing the resistant strain to take over. As a result, a patient on antibiotics becomes a potential source of infection for resistant bacteria. This continues as long as the treatment lasts. After the treatment has ended, the population of nonresistant bacteria rebounds and the population of resistant bacteria begins to drop until the patient is no longer a source.

What is going on at the bacteria level is linked with the second level that models the interactions between patients and hospital care workers who carry the bacteria from patient to patient. In order to account for variations in behavior, the researchers developed an “individual based model””that views patients and workers as independent agents. They then used the mathematical method called a “Monte Carlo simulation” to reproduce the spread of the different strains of bacteria under various conditions.

The mathematical analysis then revealed the “optimal strategy” for controlling hospital epidemics. The model was developed by an interdisciplinary team of researchers. In addition to Webb, the contributors are Erika M.C. D’Agata (Harvard University), Pierre Magal and Damien Olivier (Université du Havre, in France) and Shigui Ruan (University of Miami, Coral Gables). Their paper, “Modeling Antibiotic Resistance in Hospitals: The impact of Minimizing Treatment Duration,” appeared in the Journal of Theoretical Biology (December, 2007).

Source: EurekAlert