Modeling the spread of infectious disease in human populations

Abstract

For the past 20 years, there has been an epidemic associated with the development of mathematical models to describe the spread of disease. This epidemic shows no signs yet of dying out. Four major topics related to this discipline are discussed here, including the following: 1) a n introduction to the basic assumptions and general framework common to most epidemic models; 2 ) a discussion of the major questions addressed by epidemic modelers; 3) a brief outline of several of the approaches used in the development of disease models; and 4) reviews of models that have been developed for influenza, malaria, and AIDS. The utility of these models and suggestions for contributions that anthropologists can make to this field are also discussed.Over the last few decades, the number of models developed to describe the spread of disease has been rapidly increasing. In 1975 Norman T. J. Bailey published the second edition of his classic review, The Mathematical Theory of Infectious Diseases. The bibliography of this book documents 539 articles on mathematical epidemiology written between 1900 and 1973. Of these 539 papers, 336 (62%) were published between 1964 and 1973. The distribution of these papers by year is given in Figure 1 and looks remarkably like the beginning of an epidemic curve for a disease that is not transmitted easily, but that spreads rapidly once there is a critical number of infected individuals, Extrapolating this curve to include the years from 1974 to 1989 gives one an idea of the quantity of papers now to be found that incorporate some aspect of the development or analysis of mathematical models for disease spread.To avoid updating and expanding Bailey's 1975 monograph, this paper will review only models addressing the spread of human disease. However, because of the volume of these papers, only a select portion of the literature on human epidemic models will be included. First, there will be a discussion of the important biological and social factors that may be incorporated into epidemic models. Second, there will be a n overview of the major questions leading to the development of epidemic models. This will be followed by a review of the major approaches to the modeling of infectious diseases. Finally, applications of these approaches to three diseases-malaria, influenza, and AIDS-will be considered. The models developed for these diseases and the application of these models to actual populations contain much of interest to anthropologists. INTRODUCTlON TO EPIIIEMIC MODELSInfectious diseases are transmitted as a result of direct or indirect contact between a n infectious person and a susceptible person. Consequently, models for the transmission of infectious diseases in human populations must consider a t least these two types of individuals. The population size is usually assumed to be a constant, N , so that S + I = N , where S is the number of susceptible individuals and I is the number of infective individuals. Many models also assume that there is no migration and that there are no b...

Prehistoric demography of North America inferred from radiocarbon data

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