The model used to analyze the diffusion of ISO 9000 and ISO 14000 – adapted from the
model used by Franceschini et al. (2004) – is based on the supposition that the growth
of certifications of each standard is proportional to the number of existing certifications
and that this growth rate is also a function of the number of certifications, both for the
general economy as well as for the different economic sectors.
This model was first applied by the Belgian mathematician Verhulst in the
nineteenth century (Boyee and Di Prima, 1992), in the field of Biology, to explain
the growth of a species. According to this model, the growth rate is at its highest in the
beginning, when there are very few individuals of the species and hardly any
competition for the limited resources; it is then reduced to zero when the population
reaches a certain size. This is the population size, at saturation point, that the available
resources allow. This model, represented by the following expression, is developed in
the Appendix.