Palopoli Luigi, Fontanelli Daniele, Frego Marco, Roveri Marco
University of Trento, Department of Information Engineering and Computer Science, Via Sommarive 9 - Povo, 38123 Trento (TN), Italy.
University of Trento, Department of Industrial Engineering, Via Sommarive 9, 38122 Povo (TN), Italy.
Automatica (Oxf). 2023 May;151:110921. doi: 10.1016/j.automatica.2023.110921. Epub 2023 Feb 15.
We propose a Markovian stochastic approach to model the spread of a SARS-CoV-2-like infection within a closed group of humans. The model takes the form of a Partially Observable Markov Decision Process (POMDP), whose states are given by the number of subjects in different health conditions. The model also exposes the different parameters that have an impact on the spread of the disease and the various decision variables that can be used to control it (e.g, social distancing, number of tests administered to single out infected subjects). The model describes the stochastic phenomena that underlie the spread of the epidemic and captures, in the form of deterministic parameters, some fundamental limitations in the availability of resources (hospital beds and test swabs). The model lends itself to different uses. For a given control policy, it is possible to if it satisfies an analytical property on the stochastic evolution of the state (e.g., to compute probability that the hospital beds will reach a fill level, or that a specified percentage of the population will die). If the control policy is not given, it is possible to apply POMDP techniques to identify an optimal control policy that fulfils some specified probabilistic goals. Whilst the paper primarily aims at the model description, we show with numeric examples some of its potential applications.
我们提出一种马尔可夫随机方法，用于对封闭人群中类似SARS-CoV-2感染的传播进行建模。该模型采用部分可观测马尔可夫决策过程（POMDP）的形式，其状态由处于不同健康状况的个体数量给出。该模型还揭示了对疾病传播有影响的不同参数以及可用于控制疾病的各种决策变量（例如，社交距离、为甄别感染个体而进行的检测数量）。该模型描述了疫情传播背后的随机现象，并以确定性参数的形式捕捉了资源（医院床位和检测拭子）可用性方面的一些基本限制。该模型适用于不同用途。对于给定的控制策略，可以确定它是否满足关于状态随机演化的分析性质（例如，计算医院床位达到满负荷水平的概率，或者特定比例的人群死亡的概率）。如果未给定控制策略，则可以应用POMDP技术来确定满足某些指定概率目标的最优控制策略。虽然本文主要旨在描述模型，但我们通过数值示例展示了其一些潜在应用。
