title: Exact Equations for SIR Epidemics on Tree Graphs.
abstract: 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.
authors.affiliation: Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 7ZL, UK, kjs@liv.ac.uk.
authors.forename: K J
authors.initials: KJ
authors.lastname: Sharkey
authors.forename: I Z
authors.initials: IZ
authors.lastname: Kiss
authors.forename: R R
authors.initials: RR
authors.lastname: Wilkinson
authors.forename: P L
authors.initials: PL
authors.lastname: Simon
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology; D003198:Computer Simulation; D058872:Epidemics / Q000706:statistics & numerical data*; D006801:Humans; D008390:Markov Chains; D055641:Mathematical Concepts; D015233:Models, Statistical; D013269:Stochastic Processes; D049490:Systems Biology