Sensitivity analysis of epidemic forecasting and spreading on networks with probability generating functions

2025-06-30

AI Summary

This study investigates the sensitivity of network epidemiological predictions to input uncertainty—particularly parameter noise—distinguishing bias induced by input perturbations from inherent model stochasticity. We propose a statistical conditional-estimation-based sensitivity analysis framework, integrating probability generating functions, branching processes, and percolation theory to quantify how input noise propagates into prediction errors. Key results reveal that, contrary to conventional wisdom that sensitivity peaks at the epidemic threshold $R_0 = 1$, the maximal sensitivity in heterogeneous networks occurs for $R_0 > 1$. Moreover, network heterogeneity fundamentally reshapes the sensitivity profile. The framework enables efficient, interpretable sensitivity computation, thereby enhancing robustness assessment of epidemiological forecasting models and improving transparency in public health decision-making. (136 words)

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Epidemic forecasting tools embrace the stochasticity and heterogeneity of disease spread to predict the growth and size of outbreaks. Conceptually, stochasticity and heterogeneity are often modeled as branching processes or as percolation on contact networks. Mathematically, probability generating functions provide a flexible and efficient tool to describe these models and quickly produce forecasts. While their predictions are probabilistic-i.e., distributions of outcome-they depend deterministically on the input distribution of transmission statistics and/or contact structure. Since these inputs can be noisy data or models of high dimension, traditional sensitivity analyses are computationally prohibitive and are therefore rarely used. Here, we use statistical condition estimation to measure the sensitivity of stochastic polynomials representing noisy generating functions. In doing so, we can separate the stochasticity of their forecasts from potential noise in their input. For standard epidemic models, we find that predictions are most sensitive at the critical epidemic threshold (basic reproduction number $R_0 = 1$) only if the transmission is sufficiently homogeneous (dispersion parameter $k > 0.3$). Surprisingly, in heterogeneous systems ($k leq 0.3$), the sensitivity is highest for values of $R_{0} > 1$. We expect our methods will improve the transparency and applicability of the growing utility of probability generating functions as epidemic forecasting tools.

Problem

• Analyzing sensitivity of epidemic forecasts on networks
• Measuring impact of input noise on generating functions
• Identifying critical conditions for epidemic prediction sensitivity

Innovation

• Uses probability generating functions for epidemic forecasting
• Applies statistical condition estimation for sensitivity analysis
• Identifies sensitivity peaks at critical epidemic thresholds