对受流行病学启发的连续时间马尔可夫链模型模拟进行全局敏感性分析
Performing global sensitivity analysis on simulations of a continuous-time Markov chain model motivated by epidemiology
AI总结：
本文应用基于方差的敏感性分析方法，结合三种连续时间马尔可夫链精确模拟算法，量化了流行病学模型中不确定参数与内在随机性及其交互作用的影响，并首次探讨了模拟算法选择对敏感性分析结果的作用。
摘要：
本文应用 Navarro Jimenez 等人（2016）在化学反应网络框架中引入的方法，对受流行病学启发的连续时间马尔可夫链（continuous-time Markov chain）模型模拟进行全局敏感性分析。我们的目标不仅是量化不确定参数（如流行病学参数：传播率、各仓室的平均逗留时间）的影响，还要量化内在随机性以及流行病学参数与内在随机性之间交互作用的影响。为此，遵循 Navarro Jimenez 等人的提议，我们利用三种最先进的连续时间马尔可夫链精确模拟算法，并将其与 Sobol（1993）引入的基于方差的敏感性分析通用工具相结合。此外，我们还讨论了模拟算法的选择对敏感性分析结果的影响。据我们所知，这种讨论尚属首次。在数值实验部分，我们基于从 SARS-CoV-2 流行病学模型的不同精确模拟算法获得的模拟结果，实现并比较了三种敏感性分析。
英文摘要：
In this paper we apply a methodology introduced in Navarro Jimenez et al (2016) in the framework of chemical reaction networks to perform a global sensitivity analysis on simulations of a continuous-time Markov chain model motivated by epidemiology. Our goal is to quantify not only the effects of uncertain parameters such as epidemic parameters (transmission rate, mean sojourn duration in compartments), but also those of intrinsic randomness and interactions between epidemic parameters and intrinsic randomness. For that purpose, following what was proposed in Navarro Jimenez et al, we leverage three exact simulation algorithms for continuous-time Markov chains from the state of the art which we combine with common tools from variance-based sensitivity analysis as introduced in Sobol (1993). Also, we discuss the impact of the choice of the simulation algorithm used for the simulations on the results of sensitivity analysis. Such a discussion is new, at least to our knowledge. In a numerical section, we implement and compare three sensitivity analyses based on simulations obtained from different exact simulation algorithms of a SARS-CoV-2 epidemic model.
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