The Calculus of Transmission

Abstract

Models are used to explain complexity in the real world. Models are useful insofar as they provide some understanding of reality and our collective experience. To illustrate, professionals responsible for the control of nosocomial infections in healthcare institutions employ a variety of barrier techniques to prevent the spread of transmissible pathogens. These techniques are extrapolated from models that describe our understanding of the processes of transmission. The models are based on the empirical observations of experts and often lack explicit, objective evidence to validate the model. Nevertheless, the models provide an understanding of current reality and support a belief system that determines our behavior when confronted with the complex circumstances surrounding transmission of nosocomial pathogens. Models that undergird our beliefs and behaviors may be more or less explicit. One of the early efforts to use explicit mathematical models to describe disease transmission was that described by Sir Ronald Ross in 1911.2 Ross was a parasitologist and epidemilogist who described the malaria life cycle. Based on his careful studies of the life cycle of malaria in humans and mosquitoes, Ross developed a mathematical model of transmission. From that explicit model, he deduced that malaria could be controlled by environmental interventions that eradicate mosquitoes. This idea initially was met with skepticism. Wh n the hypothesis was put to the test, it resulted in the control of a disease that was-and is-a major source of human morbidity and mortality in many parts of the world. Subsequent efforts to generate mathematical models to illumine understanding of disease transmission were received with mixed enthusiasm. Parasitologists were responsible for much of the early work with mathematical models of transmission.3 Because of the complex transmission systems inherent in parasite life cycles (eg, schistosomiasis), mathematical theory often was so disconnected from reality that epidemiologists became disenchanted with efforts to describe diseases with theoretical mathematical models. Sebille Chevret, and Valleron4 describe an explicit mathematical model of the transmission of a resistant nosocomial pathogen in this issue of Infection Control and Hospital Epidemiology. Based on assumptions derived from the medical literature regarding probabilities of transmission and coloniza-