Modeling Use Diffusion

Two differential equations modeling the diffusion of use of cultural forms are developed as alternatives to an earlier model based on exponential epochs of diffusion. Both new models are similar in that they incorporate imitation and desertion effects, but differ in the manner in which these effects operate over the course of the diffusion of use. The model which has a Gompertz curve as its integrated form fits data from 17 instances of use diffusion better than the model which has a logistic curve as its integrated form and, in addition, is more parsimonious than the original exponential epoch model. The relationship between the observed values of the parameters representing imitation and desertion is discussed in the context of the process of use diffusion. Cultural diffusion has usually been thought of as the gradual spread of a cultural form among a population. Cultural forms can mean many thingsinformation, a custom, a role, a technical or social invention, a type of violence, even a psychiatric disorder. Their cumulative spread, adoption, or incorporation into the lifeways of a people is a much studied, well documented social process (see Chapin; Coleman et al.; Davis, a,b; Dodd, a,b; Griliches; Hamblin and Miller; Hamblin et al.; Hernes; Ogburn, c; Pemberton, a,b; Rogers, a,b; Ryan and Gross). While many feel that cultural diffusion is one of the most theoretically and methodologically developed lines of research in sociology, progress comes by successive approximations as important issues emerge from the collective effort and are resolved through further theoretical analysis and empirical investigation. The issue here is whether diffusion as a quantitative use process is better modeled by Gompertz or logistic equations or as exponential epochs. *The first author worked out the Gompertz model, including the imitation law.