Diffusion and Social Networks
a Multi-Agent System/Network Theory coupled approach

Nazmun N. Ratna (APSEG, ANU, Australia), Anne Dray, Pascal Perez, David Newth


Coleman et. al. study on adoption of a new drug by doctors is the premier one to focus on social networks as a prime component in the diffusion process. This very well documented study from the late 1950s tried to demonstrate that the new drug is diffused through a snowball or chain reaction process. Far from discarding the influence of individual characteristics or the external role played by the pharmaceutical industry, the authors argue that innovators, in this context, are socially well connected and that late adopters are relatively isolated. The main limitation of the study recognized by the authors is coming from the limited analytical tools available at that time. The authors had to study separately influences from individual characteristics, media of communication, and social networks. The latter was assessed through pair-analysis without any possibility to handle the network structure as a whole entity.

Modelling Framework

Gammanym, an agent-based model, is built with Cormas, according to the information coming from the original study. The medical community is portrayed in a 8x8 spatial grid. The model includes 100 individual doctors located in different types of practices: Private (alone in office), Centre (shared office with two colleagues) and Clinic (working with four colleagues). The doctors may attend local hospitals or medical conferences and exchange information about the new drugs with colleagues. Each doctor is eventually part of a friendship network. The pharmaceutical laboratory can influence the doctors by sending them detail men, flyers, or medical journals. Each doctor makes his decision about adopting the drug according to the number of external influences he has received. Depending on the set of initial conditions, the adoption curves displayed in the original study can be replicated. Furthermore, at each time step, matrices of interactions are exported and analysed from a Network Theory viewpoint. Global characteristics of the different networks are inferred and are used to define critical structures enhancing the chain reaction processes.

Adoption process

Doctors' decisions to adopt a new drug involve interdependent local interactions among different entities. Based on a theory of five cognitive stages of adoption (Coleman, Katz and Menzel, 1966; Van den Bulte and Lilien, 1999), we specify their adoption thresholds or readiness as a step four process. Readiness is decremented when they receive an alert from different sources. At each time step, discussions with friends and colleagues, as well as information from the lab, generates an alert. Discussions with other doctors, either friends or colleagues at practices, conferences, or hospitals generate an alert when the mean adoption rate is 0.50 or above. Doctors' readiness is gradually reduced with alerts from all the aforementioned sources. When the readiness reaches zero, doctors adopt the new drug.


Depending on three sets of initial conditions, cumulative diffusion curves, representing the total number of adopted doctors at each time step are markedly different. As several random functions are included in the algorithm, each scenario is repeated for 100 times in order to estimate output's variability. The three scenarios are specified to evaluate the degree of influences by different factors in the diffusion process: i. Baseline Scenario with one innovator (seed), one detailman and one journal; ii. Heavy Media Scenario with different degrees of external influence, by varying the number of detailman (5) and number of journals (4); and iii. Integration Scenario without any external influence.

Network variables, like clustering coefficient, degree distribution and average shortest path length are calculated to evaluate how and to what extent, network structure influences the diffusion process. All of above indicate that social networks depicted in Gammanym are random graphs. The analysis of network topology reveals that initially the system consisted of a number of disconnected components and quickly saturates after 7-10 time steps to form a giant clusters.

Analysis on evolution of uptake suggests that under heavy media scenario the average size of clusters with agents who have adopted rise much faster than those of the other two scenario. Gammanym therefore shows that though media do not influence the network structure, the speed of diffusion is largely determined by the extent of media influence.


  • Coleman, J. S., Katz, E. and Menzel, H. (1966). Medical Innovation: A Diffusion Study, Inidianapolis, The Bobbs-Merril Company, Inc.
  • Van den Bulte, C. and Lilien, G. (1999). A Two-Stage Model of Innovation Adoption with Partial Observability: Model Development and Application. Pennsylvania, Institute for the Study of Business Markets, The Pennsylvania State University: 1-44.

Download the Cormas model source code and the model documentation (as a set of UML diagrams).

For more information, contact the author.

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