Modelling innovation adoption spreading in complex networks

Innovation adoption pattern has been found to be influenced by the underlying social network structure and its constituent entities. In this paper, we model innovation diffusion considering (1) the role of network structures in dictating the spread of adoption and (2) how individual's characteristic/capability influences the path of diffusion (e.g. an individual may have different attitude or ability towards adopting a new innovation). We consider that each individual is unique and his/her position in the network is important. We draw on the epidemic theory and model the diffusion dynamics via a continuous-time Markov chain which offers strong analytical tractability while retaining a high-level of generality. Our model allows derivation of individual's adoption probability and the aggregate adoption behavior of the network as a whole. Precise computation of individual adoption decision conditioned by the population's behavior is of exponential complexity (i.e., the state space exponentially increases with the size of the network). By applying a mean field approximation, the analysis complexity of the spreading mechanics is reduced from exponential (O(5N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(5<^>N)$$\end{document}) to polynomial (O(N)) and thus allowing our approach to scale for large networks. We offer insights into how the network spectrum affects the innovation exposure rate and spreading of innovation individually and across communities with different adoption behaviors. We compare our model against a wide-range of Monte-Carlo experiments and show close agreements in different settings (including both homogeneous and heterogeneous population cases). Finally, we illustrate the effects of the embedded social structure and the characteristics of individuals in the network on the path of innovation diffusion via two use cases: (i) innovation adoption of EU countries in a Single Market Programme and (ii) innovation adoption of specific class of technology (specifically financial technologies (FinTech)).