Epidemics in nonrandomly mixing populations: A simulation

Abstract

Two stochastic, discrete-time simulation models for the spread of an epidemic through a population are presented. The models expolore the effects of nonrandom mixing within the population and are based on an SIR epidemic model without vital statistics. They consider a population of preschool children, some of whom attend child care facilities. Disease transmission occurs both within the home neighborhood and at the child care facility used, if any. The two models differ in population size used, population density, the proportions of children using different kinds of care, and the functions used for calculating the probability of disease transmission. Results are presented for seven different variables–length of the epidemic in weeks, number of cases, number of cases in each kind of care (two day care centers, private homes, and children staying at home), and the number of private home providers affected by the epidemic. In addition, the distribution of total epidemic size and the progress of an epidemic are estimated from 25 epidemic trials. The effects of the location of homes of initial cases, the type of care used by initial cases, and the density of the population are discussed. Results from the simulation confirmed the importance of type of care on the risk for disease transmission. Results from all runs of the simulation showed that children who attended a day care center were most likely to become infected, children who went to a private home were intermediate, and children who did not use any day care facility were at the lowest risk. The size and length of the epidemics were related to the presence of the disease in day care centers, regardless of the location of the initial case, and the time at which the disease entered the center(s). The simulations also showed that the geographical distribution of the homes of children attending a particular center was a critical feature involved in the production of epidemics. The center with more widely distributed homes of students was less likely to experience a major epidemic than the center with clustering of student′s homes within a neighborhood. This indicates that it is not simply attendance at a day care center that is critical for disease spread, but that the nature of the population of children attending a center is also of critical importance in the actual risk for disease spread within the center. These results are discussed with reference to the spread of hepatitis A among day care centers in Albuquerque, New Mexico.