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 becomespossible 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（CTMC）的房室模型进行全局灵敏度分析。该方法能够对流行病模型实现完整的全局灵敏度分析，不仅量化了流行病参数（如传播率、在房室中的平均停留时间）等不确定参数的影响，还量化了内在随机性以及二者之间相互作用的影响。该方法的核心步骤是通过控制表征内在随机性的潜变量，构建底层连续时间马尔可夫链的确定性表示。如此一来，模型输出可被写为不确定参数与受控潜变量的确定性函数，从而使得计算基于方差的经典灵敏度指标（例如Sobol’指标）成为可能。然而，不同模拟算法会导致不同的表示方式。本文展示了CTMC随机房室模型的三种不同表示方法，并基于每种表示方法对SARS-CoV-2流行病模型实施了全局灵敏度分析，进而讨论了相关结果的比较。