Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Ye, Cheng, Shen, Zi-Song, Zhang, Pan
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7128390401
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