基于概率生成函数的流行病预测与网络传播灵敏度分析

流行病预测工具拥抱疾病传播的随机性和异质性，以预测疫情的增长和规模。概念上，随机性和异质性常被建模为分支过程或作为接触网络上的 percolation。从数学上讲，概率生成函数 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。