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

TL;DR

This paper introduces a sensitivity analysis method for epidemic forecasts based on probability generating functions, revealing how prediction sensitivity varies with contact heterogeneity and epidemic thresholds.

Contribution

It applies statistical condition estimation to stochastic polynomials, enabling efficient sensitivity analysis of epidemic forecasts with noisy input data.

Findings

Predictions are most sensitive at the epidemic threshold when transmission is homogeneous.

Heterogeneous systems show highest sensitivity for R0 > 1.

Method improves understanding of forecast robustness under data noise.

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.