Spread and maintenance of a disease in a structured population.

The patterns of interactions among different groups of individuals in a structured population is an important factor affecting the ease of establishment of a disease and the rate of spread of the disease in a population. A model for the spread of a disease in such a population is described. The model considers two levels of interaction: interactions between individuals within a subpopulation because of geographic proximity, and interactions between individuals of the same or different sub-populations because of attendance at common social functions. Analysis of the model leads to sufficient conditions which determine maximum subpopulation sizes which allow the disease to be maintained in the population. These conditions are inequalities relating the removal rate of infectives to the infection rate of susceptibles. Results are discussed for both idealized movement patterns and for the spread of hepatitis A among day care centers in Albuquerque, New Mexico. In addition, the basic structures of the contact matrices necessary to extend the model to deal with vector-borne diseases and with sexually transmitted diseases are discussed.