Dynamics of the epidemic and response to massive interventions
The dynamic changes based on the observed F(x) in Fig. 1 were presented in Fig. 2 using the first derivatives F ′ (x) (top panel of the figure) and the second derivative F ′  ′ (x) (bottom panel of the figure), respectively. Before the declaration of outbreak, information provided by the two dynamic measured was similar: not much variations were revealed relative to the changes after the outbreak. These findings suggest the nonlinear and chaotic character of the COVID-19 outbreak.
Fig. 2 The first F′(x) and second derivative F″(x) of diagnosed COVID-19 (formally 2019-nCoV infection) F(x) before, during and after declaring the outbreak in first 2 months of the Epidemic
After declaring the outbreak on January 20, information revealed by F ′  ′ (x) differed much from F ′ (x). Based on information from F ′ (x), the newly diagnosed F ′ (x) cases increased progressively with some fluctuation, then peaked on February 4, 2020, and followed by a decline. The increases in the diagnosed cases could be either due to the natural growth of the epidemic in itself, or due to the interventions to detect the infected or both. Furthermore, F ′ (x) provided no sign of epidemic decline until February 4, 2020. In other words, we have to wait for at least 14 days after the massive anti-COVID-19 epidemic without using information derived from F ′  ′ (x).
Quite different from F ′ (x), F ′′ (x) removed the time trend of F ′ (x) to show the acceleration/deceleration of diagnosed COVID-19. Consequently, F ′  ′ (x) was much more sensitive than F ′ (x) to gauge the intrinsic dynamics of the epidemic in response to the massive anti-COVID-19 action. Since January 21, 2020 after the massive anti-COVID actions, the F ′  ′ (x) suddenly became very active, as indicated by the alternative accelerations and decelerations. F ′  ′ (x) reached the peak on January 27 after the distribution of large number of test kits on January 26, which was an action based on the decision at the central government level in a meeting held by Chinese President Xi Jinping on January 24 and 25, the Chinese New Year’s Eve and New Year’s Day.
In addition, the estimated F ′′ (x) captured three significant decelerations on January 28, February 5 and 6 (two days in a row), and 8, 2020 respectively; corresponding to the intensified massive actions in locating and treating the infected, locking down more communities, plus mask use and massive pathogen sterilization in neighborhood environment. In addition to informing whether the epidemic was responsive to the massive interventions, information from F ′′ (x) signaled an overall downturn of the epidemic since the beginning of the massive anti-COVID-19 action on January 21, 2020. This was further pronounced by the band region between the two dotted lines in Fig. 2. Despite zigzags, an overall downward trend in F ′′ (x) was clearly revealed by the downward and progressively narrowing down band region. This trend strongly indicates that the epidemic could be brought under control soon with the current interventions in place.