A discrete-time communicable disease model with a stochastic contact rate for nonhomogeneous populations.

A discrete-time communicable disease model with a stochastic contact rate for nonhomogeneous populations is described which is capable of simulating the irregular incidence patterns seen in many communicable diseases. The epidemic curve for these contagious diseases is typically characterized by epidemics of varying intensity separated by variable time intervals. The compartmental model is an extension to the Reed-Frost theory with age-specific stochastic contact rates. The population is partitioned into age constant groups and is closed; the births flowing into the first age group equals the deaths from all age groups. The population in each age group is subdivided into four states that characterize the course of an infection: susceptible, incubation, infectious, and immune. The incubation and infectious states are divided further depending on the length of the time period and the statistics of the condition. The age specific contact rates are random variables with a seasonal variation and a population specified density function. An example is presented in which all parameters and distributions of the model are estimated for measles in the city of Baltimore, Maryland for the years 1900 through 1917. The computer calculated epidemic curves adequately describe the incidence pattern of the data with no significant differences noted.