Can epidemic models describe the diffusion of topics across disciplines?

Abstract

This paper introduces a new approach to describe the spread of research topics across disciplines using epidemic models. The approach is based on applying individual-based models from mathematical epidemiology to the diffusion of a research topic over a contact network that represents knowledge flows over the map of science—as obtained from citations between ISI Subject Categories. Using research publications on the protein class kinesin as a case study, we report a better fit between model and empirical data when using the citation-based contact network. Incubation periods on the order of 4–15.5 years support the view that, whilst research topics may grow very quickly, they face difficulties to overcome disciplinary boundaries.

Introduction

How concepts, ideas, technologies and/or innovations spread across heterogeneous communities has long been one of the central questions of the sociology of science and technology (Mulkay, 1974, Rogers, 1962). In recent years, studying the diffusion of scientific topics has become much more feasible due to the wider availability of a variety of databases, fast and cheap computing power and efficient search and model-fitting algorithms. There are a number of ways in which the diffusion of topics can be tracked (e.g., Chen & Hicks, 2004). In terms of transmission dynamics, the similarities between the spread of research topics and the spread of infectious diseases have not gone unnoticed (Bettencourt, Cinrón-Arias, Kaiser, & Castillo-Chávez, 2006). In the spread of a disease through a population, contact between an infectious and a susceptible individual can lead to the transmission of infection. In a similar way, individuals or groups working on a particular research topic or topics can motivate other individuals or groups to start work based on the same or similar research topics with citation being evidence of motivation.

Though models of social contagion date back to the mid 20th century¹, the use of epidemiological models to capture the diffusion of research topics through scientific publications was recently discussed by Bettencourt et al. (2006), who found a good fit between suitably adapted epidemic models and data for the spread of a specific research topic (Feynman diagrams in theoretical physics). They further showed that this good fit is not dependent on the particular topic chosen and that epidemic models provide good descriptions of the spread of other topics in both theoretical and experimental physics (Bettencourt, Kaiser, Kaur, Castillo-Chávez, & Wojick, 2008).

However, the epidemiological models investigated so far have been of the simple differential-equation-based compartmental type. While compartmental models are transparent and allow the derivation of some analytical results, they are limited in their capability to capture heterogeneities at the individual level and in the interaction between individual epidemiological units, both of which we expect to see in citation networks (see model description below). As a potentially useful alternative method, we have developed an individual-based directed and weighted network model.

The second novelty of the approach we present here is that, whereas previous studies have investigated the growth of a topic in terms of number of published papers or publishing authors, we inquire here into how a research topic spreads over an existing network of disciplines. In other words, whereas previous studies had focused on growth dynamics, this novel perspective captures the diffusion of topics over the network of connections between scientific disciplines, as assigned by the ISI Web of Science's classification in terms of Subject Categories (SCs), following Leydesdorff and Rafols’ approach (2009). This underlying network of citations among SCs represents the knowledge flows over the “backbone” of the map of science (Boyack, Klavans, & Börner, 2005). The weight of a link (i.e., the normalised number of citations between SCs) in this network is taken to be a good indicator of the likelihood of a SC becoming research-active in a certain area given that some other related SCs are already research-active in this specific area. We can then ask whether a novel topic (a newly discovered phenomenon, material, method or piece of instrumentation) seeded at one particular node or vertex in the network will diffuse through it following to some extent the weighted connections between SCs.

In this exploratory study we examined the spread of research on kinesin. Kinesin represents a class of eukaryotic motor proteins (often referred to as a molecular motor or “nano-engine”) that functions by moving actively along microtubules (Block, 1998). Kinesin research first emerged in 1985, with the report of its discovery published in the areas of Biochemistry and Cell Biology. In the 1990s, research on kinesin spread broadly to other fields in the biological sciences and in the 2000s it reached other biomedical research, on the one hand, and chemistry, physics and materials sciences, on the other, as illustrated in Fig. 1. This later development is associated with potential bionanotechnology applications, which made kinesin an interesting case for the study of interdisciplinary research (Rafols, 2007, Rafols and Meyer, 2009).

Here, we show that the spread of kinesin-related research over a network of disciplines can be well approximated by models used in the context of the transmission of infectious diseases (Anderson and May, 1991, Diekmann and Heesterbeek, 2000, Keeling and Rohani, 2008). Similar network models have been successfully used to explain and predict the pattern of infectious disease transmission (Green et al., 2008, Keeling et al., 2001, Kiss et al., 2005, Kiss et al., 2006a, Kiss et al., 2006b, Eames and Keeling, 2002), and such models are well researched in the context of mathematical epidemiology (Keeling & Eames, 2005).

The paper is organised as follows: we first introduce the data and methods; second, we describe the model; then we present the results of the quality of fit for two different disease transmission models (i.e., Susceptible-Infected or SI, and Susceptible-Exposed-Infected or SEI). Results based on the directed and weighted empirical network are compared to the case of homogeneous disciplinary spread (i.e., equal weights) on the same network. The discussion and conclusions briefly explore possible future improvements of the model and its applications in science policy.