Modelling diffusion processes on dynamic contact networks is an important research area for epidemiology, marketing, cybersecurity, and ecology. However, current diffusion models cannot capture transmissions occurring for indirect interactions. For example, an airborne infected individual releases infectious particles at locations that can suspend in the air and infect susceptible individuals arriving even after the infected individual left. Thus, current diffusion models miss transmissions during indirect interactions. In this thesis, a novel diffusion model called the same place different time transmission based diffusion (SPDT) is introduced to take into account the transmissions through indirect interactions. The behaviour of SPDT diffusion is analysed on real dynamic contact networks and a significant amplification in diffusion dynamics is observed. The SPDT model also introduces some novel behaviours different from current diffusion models. In this work, a new SPDT graph model is also developed to generate synthetic traces to explore SPDT diffusion in several scenarios. The analysis shows that the emergence of new diffusion becomes common thanks to the inclusion of indirect transmissions within the SPDT model. This work finally investigates how diffusion can be controlled and develops new methods to hinder diffusion.