Comparing an Individual-Based Model of Behaviour Diffusion with Its Mean Field Aggregate Approximation

In this paper we compare a version of the individual-based “threshold model†of innovation diffusion (Valente 95) with an aggregate deterministic model that we constructed from it. The classical threshold model supposes that an individual adopts a behaviour according to a trade-off between a social pressure (the number of his neighbours adopting the behaviour) and a personal interest or resistance to change (the threshold). The aggregate model makes approximations in order to estimate the evolution of groups of individuals with the same number of neighbours of similar behaviour. We compare both models at different points of the parameter space. We find that the aggregate model gives a good approximation of the individual in some cases ; however in other cases the behaviour of the aggregate approximation differs. Using theoretical interpretation of this difference based on a study of the attractors of the aggregate model, we hypothesise that the two models have the same behaviour when the aggregate model has only one attractor and that differences can occur when it has two.