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.
- Dimensional reduction
- Kolmogorov equation
ASJC Scopus subject areas
- Biochemistry, Genetics and Molecular Biology(all)
- Environmental Science(all)
- Agricultural and Biological Sciences(all)
- Computational Theory and Mathematics