Communicable Disease Control Health Article

EPIDEMIC THEORY AND MATHEMATICAL MODELS OF INFECTIOUS DISEASES

Based on observed characteristics of infectious diseases, epidemiologists have attempted to construct mathematical models that would make it possible to predict the pattern of spread of a condition within the population. Some diseases have constant features, which make mathematical modeling particularly attractive. Measles, for example, has a predictable incubation period (ten to fourteen days) and limited duration of infectivity of a given patient (four to seven days). In addition, it is highly infectious (nearly every susceptible person who comes in contact with an infectious person will become infected), and nearly everyone who is infected develops clinical illness. Lifelong immunity follows infection. There is no nonhuman reservoir. Given these relatively constant parameters, it is possible to predict the pattern of transmission if measles is introduced into a population, using different estimates for the proportion of susceptible persons in the population, the distribution of these susceptibles (e.g., randomly dispersed, clustered together), and the likelihood of contact between the infectious patient and the susceptibles. Because of the extreme infectiousness of measles, models indicate that it is necessary to reach very high levels of immunity in a population (on the order of 95 percent or greater) in order to prevent sustained transmission of measles. Given the fact that measles vaccine is approximately 95 percent effective, this indicates that, to eradicate measles, it will be necessary to reach 100 percent of the population with a single dose of the vaccine or to reach 90 percent of the population on each of two rounds of vaccination (assuming that the second round will reach 90 percent of those who were not reached by the first round). Since babies are being born all the time, this also must be an ongoing process. The major reason for continuing debate over whether measles eradication is an achievable goal using current vaccines is the necessity to achieve and maintain such high levels of immunity.

ALAN R. HINMAN

(SEE ALSO: Emerging Infectious Diseases; Food-Borne Diseases; Immunizations; Sexually Transmitted Diseases; Vector-Borne Diseases; Waterborne Diseases; Zoonoses; and articles on specific diseases mentioned hereine)