  To improve mathematical models of epidemics it is essential to move beyond
the traditional assumption of homogeneous well--mixed population and involve
more precise information on the network of contacts and transport links by
which a stochastic process of the epidemics spreads. In general, the number of
states of the network grows exponentially with its size, and a master equation
description suffers from the curse of dimensionality. Almost all methods widely
used in practice are versions of the stochastic simulation algorithm (SSA),
which is notoriously known for its slow convergence. In this paper we
numerically solve the chemical master equation for an SIR model on a general
network using recently proposed tensor product algorithms. In numerical
experiments we show that tensor product algorithms converge much faster than
SSA and deliver more accurate results, which becomes particularly important for
uncovering the probabilities of rare events, e.g. for number of infected people
to exceed a (high) threshold.

Physics and Society;Numerical Analysis;Numerical Analysis;Probability