Tensor product approach to modelling epidemics on networks

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.

References in corpus (4)

• The density-matrix renormalization group in the age of matrix product states
• State space truncation with quantified errors for accurate solutions to discrete Chemical Master Equation
• Perfect Sampling of the Master Equation for Gene Regulatory Networks
• Tensor-train approximation of the chemical master equation and its application for parameter inference

Cited by in corpus (3)

• TensorKrowch: Smooth integration of tensor networks in machine learning
• Chemical master equation parameter exploration using DMRG
• Tensor product algorithms for inference of contact network from epidemiological data