  Graph models are widely used to study diffusion processes in contact
networks. Recent data-driven research has highlighted the significance of
indirect links, where interactions are possible when two nodes visit the same
place at different times (SPDT), in determining network structure and diffusion
dynamics. However, how to generate dynamic graphs with indirect links for
modeling diffusion remains an unsolved challenge. Here, we present a dynamic
contact graph model for generating contact networks with direct and indirect
links. Our model introduces the concept of multiple concurrently active copies
of a node for capturing indirect transmission links. The SPDT graph model
builds on activity driven time-varying network modelling for generating dynamic
contact networks using simple statistical distributions. This model is fitted
with a large city-scale empirical dataset using maximum likelihood estimation
methods. Finally, the performance of the model is evaluated by analysing the
capability of capturing the network properties observed in empirical graphs
constructed using the location updates of a social networking app and
simulating SPDT diffusion processes. Our results show that, in comparison to
current graph models that only include direct links, our graph model with
indirect links match empirical network properties and diffusion dynamics much
more closely.
