ABSTRACT

We investigate inverse problems of finding unknown parameters of mathematical models SEIR-HCD and SEIR-D of COVID-19 spread with additional information about the number of detected cases, mortality, self-isolation coefficient, and tests performed for the city of Moscow and Novosibirsk region since 23.03.2020. In SEIR-HCD the population is divided into seven groups, and in SEIR-D into five groups with similar characteristics and transition probabilities depending on the specific region of interest. An identifiability analysis of SEIR-HCD is made to reveal the least sensitive unknown parameters as related to the additional information. The parameters are corrected by minimizing some objective functionals which is made by stochastic methods (simulated annealing, differential evolution, and genetic algorithm). Prognostic scenarios for COVID-19 spread in Moscow and in Novosibirsk region are developed, and the applicability of the models is analyzed.

中文翻译：

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莫斯科和新西伯利亚地区COVID-19的数学建模和预测

摘要

我们调查发现COVID-19传播的数学模型SEIR-HCD和SEIR-D的未知参数的逆问题，以及有关检测到的病例数，死亡率，自我孤立系数以及对莫斯科市和新西伯利亚市进行的测试的附加信息自2020年3月23日开始。在SEIR-HCD中，人口分为七个组，而在SEIR-D中，分为五个组，它们具有相似的特征和转移概率，具体取决于感兴趣的特定区域。对SEIR-HCD进行可识别性分析，以揭示与其他信息有关的最不敏感的未知参数。通过最小化由随机方法（模拟退火，差分进化和遗传算法）制成的一些目标函数来校正参数。