COVID-19的随机房室模型
A Stochastic Compartmental Model for COVID-19
摘要：
我们提出了两个随机模型的冠状病毒大流行。模型的统计特性，特别是关联函数和概率密度函数，已及时计算。我们的模型概括了先前提出并发表在专业期刊上的模型，考虑了封锁措施的采用以及医院和医疗机构的关键作用。为了完成这项工作，我们分析了两种情况：存在封锁措施的SIS模型（易感=>传染=>易感）和与医院行动相结合的SIS模型（总是存在封锁措施）。我们发现，在纯SIS模型的情况下，一旦封锁措施被取消，冠状病毒将再次开始增长。然而，在第二种情况下，超过医院能力的一定阈值，冠状病毒不仅受到控制，而且其传播能力往往会随着时间的推移而减弱。因此，封锁措施与医院和卫生机构的行动的综合效果能够遏制和抑制SARS-CoV-2疫情的传播。这一结果可用于在一段时间内，当大规模分发有限数量的疫苗在一个给定的人口是不可行的。作为例子，我们分析了美国和法国的数据，其中噪声强度已由统计力学估计。特别是对于美国，我们分析了两种可能的假设：美国仍然受到第一波的感染，美国是在第二（或第三）波的SARS-CoV-2的感染。理论预测和实际数据之间的协议证实了我们的方法的有效性。
英文摘要：
We propose two stochastic models for the Coronavirus pandemic. The statistical properties of the models, in particular the correlation functions and the probability density function, have duly been computed. Our models, which generalises a model previously proposed and published in a specialised journal, take into account the adoption of the lockdown measures as well as the crucial role of the hospitals and Health Care Institutes. To accomplish this work we have analysed two scenarios: the SIS-model (Susceptible => Infectious => Susceptible) in presence of the lockdown measures and the SIS-model integrated with the action of the hospitals (always in presence of the lockdown measures). We show that in the case of the pure SIS-model, once the lockdown measures are removed, the Coronavirus will start growing again. However, in the second scenario, beyond a certain threshold of the hospital capacities, the Coronavirus is not only kept under control, but its capacity to spread tends to diminish in time. Therefore, the combined effect of the lockdown measures with the action of the hospitals and health Institutes is able to contain and dampen the spread of the SARS-CoV-2 epidemic. This result can be used during a period of time when the massive distribution of delivery of a limited number of vaccines in a given population is not yet feasible. By way of example, we analysed the data for USA and France where the intensities of the noise have been estimated by Statistical Mechanics. In particular, for USA we have analysed two possible hypotheses: USA is still subject to the first wave of infection by and USA is in the second (or third) wave of SARS-CoV-2 infection.The agreement between theoretical predictions and real data confirms the validity of our approach.
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