In this paper, we propose a generic approach to perform global sensitivity analysis (GSA) for compartmental models based on continuous-time Markov chains (CTMC). This approach enables a complete GSA for epidemic models, in which not only the effects of uncertain parameters such as epidemic parameters (transmission rate, mean sojourn duration in compartments) are quantified, but also those of intrinsic randomness and interactions between the two. The main step in our approach is to build a deterministic representation of the underlying continuous-time Markov chain by controlling the latent variables modeling intrinsic randomness. Then, model output can be written as a deterministic function of both uncertain parameters and controlled latent variables, so that it becomes possible to compute standard variance-based sensitivity indices, e.g. the so-called Sobol' indices. However, different simulation algorithms lead to different representations. We exhibit in this work three different representations for CTMC stochastic compartmental models and discuss the results obtained by implementing and comparing GSAs based on each of these representations on a SARS-CoV-2 epidemic model.

翻译：本文提出了一种通用方法，用于对基于连续时间马尔可夫链的分区模型进行全局敏感性分析。该方法能够实现对流行病模型的完整全局敏感性分析，不仅量化了流行病参数（如传播速率、分区平均停留时间）等不确定参数的影响，还量化了内在随机性以及两者交互作用的效应。该方法的核心步骤是通过控制表征内在随机性的潜在变量，构建底层连续时间马尔可夫链的确定性表示。由此，模型输出可表示为不确定参数与控制潜在变量的确定性函数，从而能够计算基于方差的标准化敏感性指标（如索博尔指数）。然而，不同模拟算法会导致不同的表示形式。本研究展示了连续时间马尔可夫链随机分区模型的三种不同表示，并以新冠病毒流行病模型为例，基于每种表示进行全局敏感性分析并比较了结果。