Title: Scaling Epidemic Inference on Contact Networks: Theory and Algorithms
Venue: NeurIPS 2025
Accepted: yes
Keywords: Computational Epidemiology

Graph Theory

Algorithm Acceleration
Abstract: Computational epidemiology is crucial in understanding and controlling infectious diseases, as highlighted by large-scale outbreaks such as COVID-19. Given the inherent uncertainty and variability of disease spread, Monte Carlo (MC) simulations are widely used to predict infection peaks, estimate reproduction numbers, and evaluate the impact of non-pharmaceutical interventions (NPIs). While effective, MC-based methods require numerous runs to achieve statistically reliable estimates and variance, which suffer from high computational costs. In this work, we present a unified theoretical framework for analyzing disease spread dynamics on both directed and undirected contact networks, and propose an algorithm, **RAPID**, that significantly improves computational efficiency. Our contributions are threefold. First, we derive an asymptotic variance lower bound for MC estimates and identify the key factors influencing estimation variance. Second, we provide a theoretical analysis of the probabilistic disease spread process using linear approximations and derive the convergence conditions under non-reinfection epidemic models. Finally, we conduct extensive experiments on six real-world datasets, demonstrating our method's effectiveness and robustness in estimating the nodes' final state distribution. Specifically, our proposed method consistently produces accurate estimates aligned with results from a large number of MC simulations, while maintaining a runtime comparable to a single MC simulation. Our code and datasets are available at https://github.com/GuanghuiMin/RAPID.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper addresses the problem of estimating node-level infection probabilities at convergence under the stochastic SIR (Susceptible-Infected-Recovered) model on large contact networks. It begins by deriving a lower bound on the variance of Monte Carlo (MC) estimators, highlighting the impact of transmission parameters and network structure on simulation cost. The authors then propose a linear approximation to the nonlinear infection dynamics, and prove a convergence condition for non-reinfection models. Building on these theoretical insights, the paper introduces RAPID, a deterministic and residual-aware propagation algorithm that selectively updates nodes based on estimated influence from neighbors. RAPID is empirically evaluated on six real-world networks, showing comparable accuracy to multi-run MC simulations with significantly reduced runtime.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths:** The paper is clearly written, well-organized, and technically competent. The authors thoughtfully implement a deterministic approximation algorithm (RAPID) for node-level inference in SIR epidemic models and benchmark it on several real-world networks. The residual-based propagation idea is a reasonable engineering technique to improve computational efficiency, and the empirical runtime comparisons are thorough. The paper also provides a self-contained narrative connecting theoretical motivation, algorithm design, and experiments, which helps with clarity.\n\n**Weaknesses:** Despite its technical completeness, the paper lacks significance and relevance to the NeurIPS community. It is not a machine learning paper in any meaningful sense—there is no learning component, no connection to generative modeling, deep learning, or agentic AI—and it is difficult to imagine which NeurIPS area the paper would fit into if accepted. The core problem of estimating infection probabilities under SIR dynamics is well-studied, and the approximations proposed here (e.g., linearization of nonlinear dynamics, residual propagation) are reminiscent of existing approaches such as the Fokker–Planck formulation of Langevin dynamics and PDE-based moment matching methods. The theoretical results rely heavily on strong assumptions (e.g., independence between infection paths, mean-field approximations), which cast doubt on the validity of the variance bound and the linearized update at the node level. These assumptions are neither controlled nor justified, and the results risk being misleading if interpreted as rigorous. The convergence theorem is also superficial, essentially restating a trivial absorbing property of SIR processes. On the empirical side, the datasets used are either outdated or loosely related to actual contact networks, and more realistic options (e.g., temporal mobility or sensor-based proximity networks) are overlooked. Overall, the paper offers neither new theoretical insight nor practical modeling contributions that rise to the level of significance expected at NeurIPS.\n\nQUESTIONS:\n1. **Clarify relevance to NeurIPS.** The paper currently reads as a computational epidemiology or network modeling study, with no learning component and limited connection to the broader ML community. If there is a machine learning angle—e.g., inference under uncertainty, approximation of stochastic processes, or use of RAPID as part of a learning pipeline—please make this connection explicit. Without it, it's difficult to see how the work fits within the NeurIPS scope.\n\n2. **Justify novelty beyond existing approximation methods.** The use of linear approximations and deterministic propagation resembles techniques already present in the literature (e.g., Fokker–Planck, mean-field approximations, and message passing). Please clarify what’s truly new here: either in the theoretical analysis, the algorithmic contribution, or the application framing.\n\n3. **Use more realistic contact network data.** The current experiments are based on communication or social graphs that don’t reflect how physical contact or transmission actually occurs. To better support the practical value of RAPID, please consider evaluating on more appropriate datasets—e.g., **time-resolved proximity networks** from **Sociopatterns** (e.g., high school, hospital, workplace settings), **mobility-derived contact graphs** from datasets like **SafeGraph**, or **Bluetooth-based contact traces** (e.g., from MIT's Reality Mining or COVID-related studies). Showing that RAPID produces meaningful predictions on these real-world contact networks—despite soundness concerns—could help demonstrate practical utility.\n\n4. **Clarify when your approximations are accurate.** The theoretical results rely on assumptions like independence of infection paths and small infection probabilities. Can you provide intuition or empirical evidence on when your approximations hold or break down?\n\n**What could change my evaluation:** A clear and convincing explanation of how this work contributes to machine learning, along with stronger justification for its novelty and practical impact, would help address my main concerns.\n\nLIMITATIONS:\nNo. The paper does not discuss potential negative societal impact, though it is unlikely to have one given the focus on epidemic simulation.", "TITLE": "Official Review", "RECOMMENDATION": 2, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 1, "ORIGINALITY": 1, "DATE": "2025-06-24"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper addresses a stochastic graph/contact network-based epidemic inference problem with the SIR equations as the backbone. The problem is coined \\textbf{\"Individual-Level Epidemic Inference\"}, where the goal is to estimate the steady-state probability distribution of the 3 states: Susceptible, Infectious and Recovered for each node in the graph. \n\nIn particular, the authors first analyze the efficiency (variance of the estimator) of Monte Carlo-based simulation methods with respect to the network structure and SIR model parameters. Then, they analyze a proposed baseline Propagation for Infection Dynamics (\\textbf{PID}) that relies on message passing updates of the SIR probabilities over time and show the neighborhood-level approximations and global convergence, which are then utilized to derive a more computationally efficient algorithm coined Residual-Aware Propagation for Infection Dynamics (\\textbf{RAPID}). Relying on the theoretical results of convergence, they define a \\textbf{propagation residual} term that is used to determine whether to update a node or not, thereby lowering the overall number of nodes that need to be updated. Moreover, worst-case time complexity is derived for RAPID.\n\nEmpirical results include a variety of graph-based datasets, including an undirected graph, and is based on the SIR parameters of the Nipah Virus. The accuracy and computational efficiency of RAPID are demonstrated and are clearly more superior than both Monte Carlo simulation and PID.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n- Many theorems are proposed to address the properties of Monte Carlo simulation and PID\n\n- The efficiency and accuracy are clear compared to the selected baselines\n\n- The proposed algorithms are neatly implemented/proposed and they are easy to follow and justify (based on the theoretical results)\n\nWeaknesses:\n- The variance lower bound is proved in Theorem 3.1 for Monte Carlo, but it is not clear what purpose it serves as there is no comparison to PID or RAPID, both empirically or theoretically. Empirically, it would at least help if the confidence intervals were shown.\n\n- The experiments are all somewhat \"synthetic\" since they use the Nipah Virus parameters on different graphs. Therefore I think there needs to be better and more realistic experimental settings that make the case that RAPID can be used for infectious disease modeling. In addition, the ground-truth is taken to be the Monte Carlo simulation results, but it would have been better if the results were compared against actual observations (e.g. if modeling COVID spread [1], you can look at the actual observed infection/death counts, $R_t$ values or just the general trend of infections). \n\n- I also think the vast literature of inference of SIR models using Bayesian inference (e.g. approximate Bayesian computation (ABC) or MCMC) are not mentioned or compared with at all, reducing the paper's significance. \n\n[1] https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-College-COVID19-NPI-modelling-16-03-2020.pdf\n\nQUESTIONS:\n- Although it is not explained in the paper (which it should be), the Monte Carlo simulations have stochasticity coming from random sampling of the initial infection node set (as I found out in the code https://anonymous.4open.science/r/rapid-8080/simulations/mc.py). What is the reason for not doing this for PID or RAPID? I would have thought that different initial conditions may yield different steady state results, and therefore you can get a distribution over the 3 states over all the random seeds?\n\n- Can this framework be transferred into the Bayesian inference setting with infection/deaths observations of pathogens (e.g. COVID-19)? \n\n- Why is RAPID's accuracy higher than PID, considering that it is an approximation to PID? Is it because it is converging faster than PID? But then shouldn't all models be run until convergence in your experiments?\n\n- It is said that the ground-truth infection probabilities are calculated using 50-run Monte Carlo simulations. How accurate are these results (maybe hard to tell as this is a simulation) and how big are the variance? If the variance is not negligible, then it is not a very reliable ground-truth.\n\nLIMITATIONS:\n- I think there is not enough discussion of the limitations of both their modeling framework and the proposed RAPID algorithm, particular its application to real world problems such as disease modeling. \n- The variance is mentioned at the beginning for Monte Carlo, but then not analyzed for PID and RAPID. \n- I see no issues with negative societal impacts of the work since this is pure methodological work", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis manuscript proposed 3 theoretical analysis on propagation model, and an algorithm called RAPID (Residual Aware Propagation for Infection Dynamics) based on the theoretical analysis, to efficiently approximate disease spread over networks. It addresses the high computational cost of traditional Monte Carlo (MC) simulation-based approaches by proposing three theoretical contributions:\n1. A variance lower bound for the MC estimator\n2. A linear approximation of nonlinear epidemic dynamics\n3. A convergence condition for non-reinfection epidemic models\nBased on these theoretical insights, the authors build RAPID to estimate individual-level infection dynamics more efficiently. The algorithm is tested on multiple datasets and shows promising improvements in runtime and comparable accuracy. The supplementary material also discusses extension to the SEIR model and provides a hyperparameter sensitivity analysis.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. The theoretical analysis looks solid.\n2. The RAPID algorithm (and the baseline PID algorithm) is well-structured and clearly presented.\n3. The authors conduct experiments across multiple datasets and include a detailed hyperparameter sensitivity discussion.\n4. SEIR extension and propagation modeling on individual level add applicability and relevance.\n\nWeaknesses:\n1. Like authors have discussed, the model is limited to non-reinfection dynamics, which restricts its scope for diseases like COVID-19 or flu where reinfection is a factor.\n2. The preheating phase is not fully justified. Though the authors conducted sensitivity study, there is no ablation study showing its impact, and to choose the proper value remain unclear to me.\n3. Some baseline experiments results are not very clear, see questions 3 and 4.\n\nQUESTIONS:\n1. Could the authors provide more insight or empirical justification for the preheating phase? Like what is the theoretical rationale behind using this initialization step? How should p be selected? Will that be possible if the authors could conduct ablation study on the preheating phase’s impact?\n2. I checked the code, seems like bitcoin-Alpha data is not under /data/.\n3. In paper 5.1 Baselines, the authors list Network centrality measures, MC-based inference, and probability-based inference (PID), but in all results tables, there are MC-5, MC-10, MC-50, PID, so where is Network centrality measures and how it works?\n4. In manuscript, why MC-50 showed in Table 4 but not in Table 3?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}

comments: SUMMARY:
Researchers use Monte Carlo simulation to estimate the probability of infection over networks given disease dynamics. However, these methods have a high computational cost. This paper suggests a creative new solution for approximating the probability of node infection quickly. The authors also specify  convergence-criterion for non-reinfection epidemic models and bound Monte Carlo estimation error in an epidemics-over-networks context.

STRENGTHS AND WEAKNESSES:
Strengths: This paper is very clearly written. The authors setup their problem and define their contributions well. RAPID is a creative algorithm, and they demonstrate that it performs well empirically across many metrics and datasets. It seems like a novel, useful, and practical tool for the field. Additionally, their theoretical contributions are interesting and help motivate aspects of their algorithm. 

Weaknesses: The error inherent to their theoretical simplifications is not well explained. It seems that they use a lot of approximations in Theorems 3.1 and 3.2, and it’s difficult to understand (especially in Theorem 3.1) when these will be more/less accurate. Additionally, it would be useful to understand which network/disease contexts would predictably result in RAPID experiencing problems relative to Monte Carlo estimation.

QUESTIONS:
1. What are the most predictable weaknesses of the linear approximation used in RAPID?

2. How does one choose $\epsilon$?

3. In the complexity analysis, is it only possible for nodes to be activated once?

4. What is $\ell_{ij}$ under equation 5? (I may have missed the definition somewhere)

I think it would clearer to move the ideas in remark 1 of the appendix (under section B.2) to the main body somewhere.

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 3
IMPACT: 2
ORIGINALITY: 3
DATE: 2025-07-03