A stochastic two-stage innovation diffusion model on a lattice. (English) Zbl 1356.60164

Coletti, Cristian F.; De Oliveira, Karina B. E.; Rodriguez, Pablo M.

J. Appl. Probab. 53, No. 4, 1019-1030 (2016).

Summary: We propose a stochastic model describing a process of awareness, evaluation, and decision making by agents on the \(d\)-dimensional integer lattice. Each agent may be in any of the three states belonging to the set \(\{0,1,2\}\). In this model \(0\) stands for ignorants, \(1\) for aware, and \(2\) for adopters. Aware and adopters inform its nearest ignorant neighbors about a new product innovation at rate \(\lambda\). At rate \(\alpha\) an agent in aware state becomes an adopter due to the influence of adopters’ neighbors. Finally, aware and adopters forget the information about the new product, thus becoming ignorant, at rate \(1\). Our purpose is to analyze the influence of the parameters on the qualitative behavior of the process. We obtain sufficient conditions under which the innovation diffusion (and adoption) either becomes extinct or propagates through the population with positive probability.

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
60J60	Diffusion processes
60J27	Continuous-time Markov processes on discrete state spaces
60J28	Applications of continuous-time Markov processes on discrete state spaces
60K10	Applications of renewal theory (reliability, demand theory, etc.)

Keywords:

interacting particle system; innovation diffusion model; contact process; oriented percolation