"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", stated 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 February 17, 2008 in Boston.
"According to our analysis, the most effective way to combat this growing problem is to minimize the use of antibiotics", he stated. "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 Glenn F. 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 "Modelling antibiotic resistance in hospitals: The impact of minimizing treatment duration" published in the Journal of Theoretical Biology in December 2007.
The researchers constructed a two-level model: (1) the bacterial level where non-resistant and resistant strains are produced in the bodies of individual patients and (2) the patient level where susceptible patients are cross-infected by health care workers who have become contaminated by contact with infected 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, non-resistant bacteria have a competitive advantage over the resistant strains that keeps the numbers of resistant bacteria extremely low. During treatment, however, the antibiotics kill off the normal bacteria and that allows the resistant strain to take over. As a result, a patient on antibiotics becomes a potential source of infection with resistant bacteria. This continues as long as the treatment lasts. After the treatment is ended, the population of non-resistant bacteria of all types rebounds and the population of resistant bacteria begins to drop until the patient ceases acting as a source.
What is going on at the bacteria level is linked with the second level which models the interactions between patients and hospital care workers who carry the bacteria from patient to patient. In order to account for individual variations in behaviour, the researchers developed an "individual based model" that views patients and workers as independent agents. They then used a method called a Monte Carlo simulation to simulate the spread of the different strains of bacteria under various conditions by generating thousands of probable scenarios using random values for uncertain quantities.
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.
Currently, hospitals are concentrating on improving hygiene to combat this problem. The model confirms that improvements in hygiene can substantial reduce the frequency of cross-infections. The model also demonstrates that hygiene alone may not be sufficient and improving the way antibiotics are administered will be necessary to eliminate the problem of resistant bacteria. "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", stated Glenn F. Webb.
Yet another mathematical model that looks at different strategies for curbing hospital-acquired infections suggests that antimicrobial cycling and patient isolation may be effective approaches when patients are harbouring dual-resistant bacteria.
In an era of "superbugs", such as methicillin-resistant Staphylococcus aureas (MRSA), and an increasing public awareness and concern over bacterial infections, this type of modelling, if used to develop policies and treatment protocols, may reduce dual drug-resistant infections in hospitals.
The model's results were presented by Carlos Castillo-Chavez, an Arizona State University (ASU) Regents' Professor, also on February 17 at the American Association for the Advancement of Science annual meeting. Carlos Castillo-Chavez was honoured at the meeting with the 2007 AAAS Mentor Award for his efforts to help underrepresented students earn doctoral degrees in the sciences.
In discussing the mathematical models, he noted that the research is an outgrowth of an undergraduate honours thesis by Karen C. Chow, now a graduate student at ASU, in collaboration with his postdoctoral research associate Xiaohong Wang.
"We deal primarily with the issue of finding ways of slowing down the growing levels of dual resistance to antimicrobials that are the result of their intense use in the treatment of nosocomial or hospital-acquired infections", stated Carlos Castillo-Chavez, a mathematical epidemiologist in ASU's College of Liberal Arts and Sciences.
"Model simulations were used to compare the effects of antimicrobial cycling, in which antibiotic classes are alternated over time, with mixing programmes - random allocation of treatment drugs - in a setting where the goal is that of reducing the prevalence of dual resistance", Carlos Castillo-Chavez stated.
"Resistance to multiple drugs cannot be ignored and cycling programmes appear more useful in reducing dual resistance than the random mixing regime", he stated. "The early diagnosis and isolation of colonized patients with dual-resistant bacteria turns out to be quite effective at maintaining lower levels of dual resistance in hospitals."
He noted: "This seems to be the first time that models are used to deal with the evaluation of two distinct methods of reducing the impact of dual resistance in hospitals. Models that focus on reducing the prevalence of pathogens resistant to two types of drugs, excluding the possibility of dual resistance, have been studied in the past. Models were used to show that random allocation treatment regimes might be better than cycling. Here, we show that cycling may be useful when dealing with dual resistance - the most worrisome hospital situation."
"Our theoretical work shows that cycling is better if the goal is to reduce dual antimicrobial resistance. We explore the impact of isolating individuals who have developed dual resistance and found out that isolation, in fact, dramatically reduces the persistence of dual resistance. However, we never win the battle against antimicrobial resistance through the exclusive use of integrated microbial management approaches that focus entirely on the prescription of antibiotics", he stated.
"Focusing on reducing dual resistance results in increases in the levels of individuals experiencing single resistance. In other words, at the end of the day, drugs provide no silver bullet and only policies that reward their judicious use have a shot at slowing down what appears to be a loosing battle", he stated. "If we insist in the exclusive use of antimicrobials to fight nosocomial infections, then it is only a matter of time before we begin to run out of effective antibiotics."
The next step, according to Carlos Castillo-Chavez, is to connect these models more explicitly to specific studies, and to collaborate with others who are treating patients in hospitals.