论文标题
SARS-COV-2病毒传播的马尔可夫模型
A Markovian Model for the Spread of the SARS-CoV-2 Virus
论文作者
论文摘要
我们提出了马尔可夫随机方法，以模拟在封闭的人类中SARS-COV-2样感染的传播。该模型采用了部分可观察到的马尔可夫决策过程（POMDP）的形式，该过程的状态由不同健康状况下的受试者数量给出。该模型还暴露了对疾病的传播以及可用于控制它的各种决策变量产生影响的不同参数（例如，社会距离，对单身受感染受试者进行的测试数量）。该模型描述了以确定性参数的形式捕获流行病和捕获的随机现象，这是资源可用性（医院床和测试拭子）的一些基本限制。该模型将自己用于不同的用途。对于给定的控制策略，可以验证它是否满足国家随机演变的分析性能（例如，计算医院病床达到填充水平的可能性，或者指定的人口的指定百分比将死亡）。如果没有给出控制策略，则可以应用POMDP技术来确定实现某些指定概率目标的最佳控制策略。尽管本文主要针对模型描述，但我们以数字示例显示了一些潜在的应用。
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 verify 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.
