Mathematical descriptions of infectious disease outbreaks are fundamental to understanding how transmission occurs. Reductively, two approaches are used: individual based simulators and governing equation models, and both approaches have a multitude of pros and cons. In this talk I will connect these two worlds via general branching processes. I will discuss (at a high level) the rather beautiful mathematics that arises from these branching processes and how these can help us understand the assumptions underpinning mathematical models for infectious disease. I will then explain how this new maths can help us understand uncertainty better, and show some simple examples. This talk will be a little technical, but I will focus as much as possible on intuition and the big picture.