Tensor product approach to modelling epidemics on networks

TL;DR

This paper introduces tensor product algorithms to efficiently solve epidemic models on networks, outperforming traditional stochastic simulation methods in speed and accuracy, especially for rare event probabilities.

Contribution

It applies tensor product algorithms to epidemic network models, significantly improving computational efficiency and accuracy over standard stochastic simulation approaches.

Findings

Tensor product algorithms converge faster than SSA.

They provide more accurate probability estimates for rare events.

Numerical results demonstrate improved performance on network epidemic models.

Abstract

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.