A Mathematical Model for the Epidemiologic Study of Infectious Diseases

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Abstract
Hillis A [Department of Ophthalmology, Johns Hopkins School of Medicine and the Departments of Biostatistics and Pathobiology, Johns Hopkins School of Hygiene and Public Health, 550 N. Broadway, Suite 302, Baltimore, Maryland 21205 USA]. A mathematical model for the epidemiologic study of infectious diseases. International Journal of Epidemiology 1979, 8: 167–176. Many infectious diseases have been hypothesized to represent common virus infections in which only small proportions of cases result in clinically recognizable disease. In order to find a method of studying this class of diseases, a mathematical model of the age distribution of clinical disease was developed using poliomyelitis as a prototype. The model is shown to fit the age distribution of reported poliomyelitis in a variety of localities before the use of artificial immunization. The true yearly rate of infection is easily estimated and ranges from .11 in rural Sweden to 1.20 in Chile. The model accounts for several major features of poliomyelitis epidemiology, including the shift to older ages and the high rate of clinically apparent disease which were frequently observed in populations which could be expected to have a comparatively low rate of spread. An examination of the age distribution of other diseases by these methods may provide a method of identifying other common infections which only occasionally result in clinically apparent disease.