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.
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.
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.
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