Mariangela Guidolin

Cellular automata and Riccati equation models for diffusion of innovations

Innovation diffusion represents a central topic both for researchers and for managers and policy makers. Traditionally, it has been examined using the successful Bass models (BM, GBM), based on an aggregate differential approach, which assures flexibility and reliable forecasts. More recently, the rising interest towards adoptions at the individual level has suggested the use of agent based models, like Cellular Automata models (CA), that are generally implemented through computer simulations. In this paper we present a link between a particular kind of CA and a separable non autonomous Riccati equation, whose general structure includes the Bass models as a special case. Through this link we propose an alternative to direct computer simulations, based on real data, and a new aggregate model, which simultaneously considers birth and death processes within the diffusion. The main results, referred to the closed form solution, the identification and the statistical analysis of our new model, may be both of theoretical and empirical interest. In particular, we examine two applied case studies, illustrating some forecasting improvements obtained.

Pre-launch forecasting of a pharmaceutical drug

Purpose The emergence of a pharmaceutical drug as a late entrant in a homogeneous category is a relevant issue for strategy implementation in the pharmaceutical industry. This paper aims to suggest a methodology for making pre-launch forecasts with a complete lack of information for a late entrant. Design/methodology/approach The diffusion process of the emerging entrant is estimated using the diffusion dynamics of pre-existing drugs, after an appropriate assessment of the drug’s entrance point. The authors’ methodology is applied to study the late introduction of a pharmaceutical drug in Italy within the category of ranitidine. Historical data of seven already active drugs in the category are used to assess and estimate ex ante the dynamics of a late entrant (Ulkobrin). Findings The results of applying the procedure to the ranitidine market reveal a high degree of accuracy between the ex post observed values of the late entrant and its ex ante mean predicted trajectory. Moreover, the assessed launch date corresponds to the actual date. Research limitations/implications The category has to be homogeneous to ensure a high degree of similarity among the existing drugs and the late entrant. For this reason, radical innovations cannot be forecast with this methodology. Originality/value The proposed approach contributes to the still challenging research field of pre-launch forecasting by estimating the dynamic features of a homogeneous category and exploiting them for forecasting purposes.