The majority of epidemic models fall into two categories: 1) deterministic models represented by differential equations and 2) stochastic models which can be evaluated by simulation. In this presentation I will discuss the precise connection between these models. Until recently, exact correspondence was only established in situations exhibiting large degrees of symmetry or for infinite populations.
I will consider SIR dynamics on finite static contact networks. I will give an overview of two provably exact deterministic representations of the underlying stochastic model for tree-like networks. These are the message passing description of Karrer and Newman and my pair-based moment closure representation. I will discuss relationship between the two representations and the relative merits of both.