Spreading of innovations and epidemics is a classical problem. Traditionally, they have been analyzed using compartmental models (Bass, SI, …), which implicitly assume that all the individuals are homogeneous and connected to each other. To relax these assumptions, research has gradually shifted to the more fundamental network models, which are particle models for the stochastic adoption/infection by each individual.
In this talk I will present an emerging mathematical theory for the Bass and SI models on networks. I will present analytic tools that enable us to obtain explicit expressions for the expected adoption/infection level on various networks (complete, circular, d-regular, Erdos-Renyi, …), without employing mean-field type approximations. The main focus of the talk will be on the effect of network structure. For example, which networks yield the slowest and fastest spreading? What is the effect of boundaries? Of heterogeneity among individuals? How does the network structure influence the optimal promotional strategy?