This paper presents classification and analysis of the mathematical models of the spread of COVID-19 in different groups of population such as family, school, office (3–100 people), town (100–5000 people), city, region (0.5–15 million people), country, continent, and the world. The classification covers major types of models (time-series, differential, imitation ones, neural networks models and their combinations). The time-series models are based on analysis of time series using filtration, regression and network methods. The differential models are those derived from systems of ordinary and stochastic differential equations as well as partial differential equations. The imitation models include cellular automata and agent-based models. The fourth group in the classification consists of combinations of nonlinear Markov chains and optimal control theory, derived by methods of the mean-field game theory. COVID-19 is a novel and complicated disease, and the parameters of most models are, as a rule, unknown and estimated by solving inverse problems. The paper contains an analysis of major algorithms of solving inverse problems: stochastic optimization, nature-inspired algorithms (genetic, differential evolution, particle swarm, etc.), assimilation methods, big-data analysis, and machine learning.

中文翻译：

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用于 COVID-19 传播建模的人工智能

本文对COVID-19在家庭、学校、办公室（3-100人）、城镇（100-5000人）、城市、地区（0.5- 1500 万人）、国家、大陆和世界。该分类涵盖了主要类型的模型（时间序列模型、微分模型、仿模型、神经网络模型及其组合）。时间序列模型基于使用过滤、回归和网络方法对时间序列进行分析。微分模型是从常微分方程组、随机微分方程组以及偏微分方程组导出的模型。模仿模型包括元胞自动机和基于代理的模型。分类中的第四组由非线性马尔可夫链和最优控制理论的组合组成，通过平均场博弈论方法推导出来。 COVID-19 是一种新型且复杂的疾病，大多数模型的参数通常是未知的，并且通过求解逆问题来估计。论文分析了求解反问题的主要算法：随机优化、自然启发算法（遗传、差分进化、粒子群等）、同化方法、大数据分析和机器学习。