Population Structure and the Spread of Disease

A model for the spread of disease in a population consisting of several interacting subpopulations is developed and analyzed. The model considers two different types of interactions between individuals; interac- tions between individuals within a subpopulation because of geographic proximity, and interactions between individuals of the same or different subpopulations because of attendance at common social functions. A sta­bility analysis is performed on the equilibria of the model, which shows that there are two possible stable states. One stable state consists of a population composed solely of susceptible individuals with no disease present. The second stable state occurs at an interior point where there are susceptible, infective, and recovered individuals present at all times. The condition for maintenance (or extinction) of the disease is found to be given by a simple inequality relating the removal rate of infectives to the infection rate of susceptibles.Three idealized patterns of social interaction are studied. These in­clude completely random mixing, complete isolation of all groups, and local clustering of some of the groups with others randomly mixing. In addition, results are discussed in relation to a particular type of social interaction, attendance of preschool children at day care centers. The analysis shows that the threshold for disease maintenance is more easily exceeded in cen­ters that are members of a small local cluster than in randomly mixing centers, but that the spread of the disease throughout the population occurs more rapidly when the initial case attends a randomly mixing center. These analytical results are compared with data on the spread of hepatitis A among pre-school children in Albuquerque, New Mexico