Abstract for: Approximating Network Dynamics in Compartmental System Dynamics Models
Over the past few decades, the field of “network science” has exploded in popularity. A fundamental tenant of this research is that network structure – who interacts with whom – matters for individual and collective outcomes (e.g. Watts and Strogatz, 1998; Newman, 2003; Burt, 2005). One criticism of compartmental system dynamics (CSD) models is the lack of an underlying network specifying the topological structure of interactions among individuals. Within compartments, individuals are assumed to be well-mixed, and the effect of this assumption can be substantial. For example, Rahmandad and Sterman (2008) show that for clustered network topologies the predicted dynamics of a standard contagion model differ significantly when simulated using an agent-based model (AB) versus a CSD. Despite this potential shortcoming, CSDs have many advantages over models with fully represented networks including computational efficiency, clarity of exposition, and more tractable analysis. However, as this paper demonstrates, CSDs and networks are not mutually exclusive. We describe a framework developed primarily in theoretical biology, known as a pair approximation or correlation model, that can be readily implemented using standard CSD tools, thus retaining the speed, simplicity, and tractability of the CSD approach, while capturing a substantial portion of the effect of an underlying network structure. We illustrate the approach and its effectiveness using two examples, a standard SIS epidemiological model and a new model of social contagion that we call SIS2.