The accelerated development of digital libraries and archives, in tandem with efficient search engines and the computational ability to retrieve and parse massive amounts of information, are making it possible to quantify the time evolution of scientific literatures. These data are but one piece of the tangible recorded evidence of the processes whereby scientists create and exchange information in their journeys towards the generation of knowledge. As such, these tools provide a proxy with which to study our ability to innovate. Innovation has often been linked with prosperity and growth and, consequently, trying to understand what drives scientific innovation is of extreme interest. Identifying sets of population characteristics, factors, and mechanisms that enable scientific communities to remain at the cutting edge, accelerate their growth, or increase their ability to re-organize around new themes or research topics is therefore of special significance. Yet generating a quantitative understanding of the factors that make scientific fields arise and/or become more or less productive is still in its infancy. This is precisely the type of knowledge most needed for promoting and sustaining innovation. Ideally, the efficient and strategic allocation of resources on the part of funding agencies and corporations would be driven primarily by knowledge of this type. Early steps have been taken toward such a quantitative understanding of scientific innovation. Some have focused on characterizing the broad properties of relevant time series, such as numbers of publications and authors in a given field. Others have focused on the structure and evolution of networks of coauthorship and citation. Together these types of studies provide much needed statistical analyses of the structure and evolution of scientific communities. Despite these efforts, however, crucial elements of prediction have remained elusive. Building on many of these earlier insights, we provide here a coarse-grained approach to modeling the time-evolution of scientific fields mathematically, through adaptive models of contagion. That is, our models are inspired by epidemic contact processes, but take into account the social interactions and processes whereby scientific ideas spread - social interactions gleaned from close empirical study of historical cases. Variations in model parameters can increase or hamper the speed at which a field develops. In this way, models for the spread of 'infectious' ideas can be used to identify pressure points in the process of innovation that may allow for the evaluation of possible interventions by those responsible for promoting innovation, such as funding agencies. This report is organized as follows: Section 2 introduces and discusses the population model used here to describe the dynamics behind the establishment of scientific fields. The approach is based on a succinct (coarse) description of contact processes between scientists, and is a simplified version of a general class of models developed in the course of this work. We selected this model based primarily on its ability to treat a wide range of data patterns efficiently, across several different scientific fields. We also describe our methods for estimating parameter values, our optimization techniques used to match the model to data, and our method of generating error estimates. Section 3 presents brief accounts of six case studies of scientific evolution, measured by the growth in number of active authors over time, and shows the results of fitting our model to these data, including extrapolations to the near future. Section 4 discusses these results and provides some perspectives on the values and limitations of the models used. We also discuss topics for further research which should improve our ability to predict (and perhaps influence) the course of future scientific research. Section 5 provides more detail on the broad class of epidemic models developed as part of this project.
