Heterogeneity and Network Structure in the Dynamics of Diffusion: Comparing Agent-Based and Differential Equation Models

By Hazhir Rahmandad, John D. Sterman. Management Sciences, 2008

790 citations recorded by the source corpus.

When is it better to use agent-based (AB) models, and when should differential equation (DE) models be used? Whereas DE models assume homogeneity and perfect mixing within compartments, AB models can capture heterogeneity across individuals and in the network of interactions among them. AB models relax aggregation assumptions, but entail computational and cognitive costs that may limit sensitivity analysis and model scope. Because resources are limited, the costs and benefits of such disaggregation should guide the choice of models for policy analysis. Using contagious disease as an example, we contrast the dynamics of a stochastic AB model with those of the analogous deterministic compartment DE model. We examine the impact of individual heterogeneity and different network topologies, including fully connected, random, Watts-Strogatz small world, scale-free, and lattice networks. Obviously, deterministic models yield a single trajectory for each parameter set, while stochastic models yield a distribution of outcomes. More interestingly, the DE and mean AB dynamics differ for several metrics relevant to public health, including diffusion speed, peak load on health services infrastructure, and total disease burden. The response of the models to policies can also differ even when their base case behavior is similar. In some conditions, however, these differences in means are small compared to variability caused by stochastic events, parameter uncertainty, and model boundary. We discuss implications for the choice among model types, focusing on policy design. The results apply beyond epidemiology: from innovation adoption to financial panics, many important social phenomena involve analogous processes of diffusion and social contagion.

Subfields: Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a0fe177a49b9c465065373cf76b949d13e6fccc2

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In Statistical and Nonlinear Physics

Citations in the corpus

A bibliometric review of the innovation adoption literature (2018, neutral): “For example, Rahmandad and Sterman [221] discussed when to apply agent-based (AB) models and when to opt for differential equation models (DE) while modelling dynamic diffusion processes, taking into account network structure and heterogeneity (examples of both can be found in Cluster 4).”
Agent-Based Modeling in Marketing: Guidelines for Rigor (2011, background): “For instance, several researchers (Goldenberg, Han, Lehmann, & Hong, 2009; Rahmandad & Sterman, 2008; Stephen, Dover, & Goldenberg, 2010; Watts, 2002; Watts & Dodds, 2007) have used an agent-based approach integrated with network science to model the role of influentials in diffusion.”
Systems Science Methods in Public Health (2012, neutral): “, include a larger number of relevant explanatory variables) and be more amenable to including variables for which strong empirical data may not be available (68, 115).”
Agent-based simulation of innovation diffusion: a review (2011, background): “Rahmandad and Sterman (2008), while primarily concerned with comparing stochastic agent-based and deterministic differential equation models, also study the impact of different network structures.”