Tensor network dynamical message passing for epidemic models

TL;DR

This paper introduces Tensor Network Dynamical Message Passing (TNDMP), a novel framework that improves epidemic modeling by accurately capturing network correlations while maintaining computational efficiency.

Contribution

The paper presents TNDMP, a new tensor network-based approach that unifies and extends existing epidemic modeling methods through a rigorous Susceptible-Induced Factorization property.

Findings

TNDMP outperforms existing methods in predicting epidemic thresholds.

The framework accurately captures short-range correlations and network loops.

Existing heuristics like DMP and PA are special cases of TNDMP.

Abstract

While epidemiological modeling is pivotal for informing public health strategies, a fundamental trade-off limits its predictive fidelity: exact stochastic simulations are often computationally intractable for large-scale systems, whereas efficient analytical approximations typically fail to account for essential short-range correlations and network loops. Here, we resolve this trade-off by introducing Tensor Network Dynamical Message Passing (TNDMP), a framework grounded in a rigorous property we term \textit{Susceptible-Induced Factorization}. This theoretical insight reveals that a susceptible node acts as a dynamical decoupler, factorizing the global evolution operator into localized components. Leveraging this, TNDMP provides a dual-mode algorithmic suite: an exact algorithm that computes local observables with minimal redundancy on tractable topologies and a scalable and tunable approximation for complex real-world networks. We demonstrate that widely adopted heuristics, such as Dynamical Message Passing (DMP) and Pair Approximation (PA), are mathematically recoverable as low-order limits of our framework. Numerical validation in synthetic and real-world networks confirms that TNDMP significantly outperforms existing methods to predict epidemic thresholds and steady states, offering a rigorous bridge between the efficiency of message passing and the accuracy of tensor network formalisms.