  We consider Markovian susceptible-infectious-removed (SIR) dynamics on
time-invariant weighted contact networks where the infection and removal
processes are Poisson and where network links may be directed or undirected. We
prove that a particular pair-based moment closure representation generates the
expected infectious time series for networks with no cycles in the underlying
graph. Moreover, this ``deterministic'' representation of the expected
behaviour of a complex heterogeneous and finite Markovian system is
straightforward to evaluate numerically.
