Zheng Hua, Bonasera Aldo
School of Physics and Information Technology, Shaanxi Normal University, Xi'an, 710119 China.
Cyclotron Institute, Texas A&M University, College Station, TX 77843 USA.
Eur Phys J Plus. 2020;135(10):799. doi: 10.1140/epjp/s13360-020-00811-z. Epub 2020 Oct 9.
We discuss a two-step model for the rise and decay of a new coronavirus (Severe Acute Respiratory Syndrome-CoV-2) first reported in December 2019, COVID-19. The first stage is well described by the same equation for turbulent flows, population growth and chaotic maps: a small number of infected, , grows exponentially to a saturation value, . The typical growth time (aggressive spreading of the virus) is given by where is the Lyapunov exponent. After a time determined by social distancing and/or other measures, the spread decreases exponentially analogous to nuclear decays and non-chaotic maps. Some countries, like China, S. Korea and Italy, are in this second stage while others including the USA are near the end of the growth stage. The model predicted 15,000 (±2250) casualties for the Lombardy region (Italy) at the end of the spreading around May 10, 2020. Without the quarantine, the casualties would have been more than 50,000, one hundred days after the start of the pandemic. The data from the 50 US states are of very poor quality because of an extremely late and confused response to the pandemic, resulting unfortunately in a large number of casualties, more than 70,000 on May 6, 2020, and more than 170,000 on August 21, 2020. S. Korea, notwithstanding the high population density ( ) and the closeness to China, responded best to the pandemic with 255 deceased as of May 6, 2020, and 301 on August 21, 2020.
我们讨论了一种针对2019年12月首次报告的新型冠状病毒（严重急性呼吸综合征冠状病毒2，即COVID-19）的兴衰的两步模型。第一阶段可以用与湍流、人口增长和混沌映射相同的方程很好地描述：少量感染者(I)呈指数增长至饱和值(I_{max})。典型的增长时间（病毒的快速传播）由(t_{growth}=\frac{1}{\lambda}\ln\frac{I_{max}}{I_0})给出，其中(\lambda)是李雅普诺夫指数。在经过由社交距离和/或其他措施确定的时间(t_{suppression})后，传播类似于核衰变和非混沌映射那样呈指数下降。一些国家，如中国、韩国和意大利，处于第二阶段，而包括美国在内的其他国家接近增长阶段的末期。该模型预测，到2020年5月10日左右传播结束时，意大利伦巴第大区将有15000（±2250）人伤亡。如果没有隔离措施，在疫情开始一百天后，伤亡人数将超过50000人。由于对疫情的反应极其迟缓且混乱，美国50个州的数据质量非常差，不幸导致大量人员伤亡，2020年5月6日超过70000人，2020年8月21日超过170000人。韩国尽管人口密度高（(51.8)人/平方公里）且与中国接壤，但对疫情的应对最好，截至2020年5月6日有255人死亡，2020年8月21日有301人死亡。
