We have presented in the current analytic research the generating formulae and results of direct mathematical modelling of non-classical trends for COVID-19’s evolution in world which, nevertheless, can be divided into two types: (1) the general trends for European countries such as Germany presented by the curve of modified sigmoid-type with up-inclination of the upper limit of saturation (at the end of first wave of pandemic) as well as for other cases of key countries that suffered from pandemic such as USA, India, Brazil, Russia (we conclude that the same type of coronavirus pandemic is valid for most of the countries in world with similar scenarios of the same type for general trends); (2) non-classical general trends for Middle East countries (such as Iran), with the appropriate bulge on graphical plots at the beginning of first wave of pandemic. We expect that the second wave of pandemic will pass its peak at the end of December 2020 for various countries. Moreover, the second wave of pandemic will have come to end at first decade of January 2021 in Germany and Iran (but at the end of January 2021 in India as well), so we should restrict ourselves in modelling the first and second waves of pandemic within this time period for these countries. Thus, the model of first approximation is considered here which allows to understand the mean-time trends of COVID-19 evolution for the first + second waves of pandemic for USA, Brazil and Russia, or predict the approximated time period of the upcoming third wave of pandemic in cases of India, Germany and Iran.

我们在当前的分析研究中提出了 COVID-19 在世界演变的非经典趋势的直接数学建模的生成公式和结果，但可以分为两种类型：（1）欧洲国家的总体趋势，例如如德国所呈现的修正 sigmoid 型曲线随着饱和度上限的上升（在第一波大流行结束时）以及美国、印度、巴西、俄罗斯等主要遭受大流行的国家的其他病例（我们得出的结论是，同类型的冠状病毒大流行适用于世界上大多数国家，其总体趋势具有相同类型的相似情景）；(2) 中东国家（如伊朗）的非经典总体趋势，在第一波大流行开始时的图表上有适当的凸起。我们预计，各国的第二波大流行将在 2020 年 12 月下旬达到顶峰。此外，第二波大流行将在 2021 年 1 月的第一个十年在德国和伊朗结束（但在印度也将在 2021 年 1 月结束），因此，我们应该限制自己在这段时间内为这些国家模拟第一波和第二波大流行。因此，这里考虑了第一近似模型，它允许了解美国、巴西和俄罗斯的第一波和第二波大流行的 COVID-19 演变的平均时间趋势，或预测即将到来的第三波的大致时间段印度、德国和伊朗的大流行。