Threshold conditions for curbing COVID-19 with a dynamic zero-case policy derived from 101 outbreaks in China

Abstract

By 31 May 2022, original/Alpha, Delta and Omicron strains induced 101 outbreaks of COVID-19 in mainland China. Most outbreaks were cleared by combining non-pharmaceutical interventions (NPIs) with vaccines, but continuous virus variations challenged the dynamic zero-case policy (DZCP), posing questions of what are the prerequisites and threshold levels for success? And what are the independent effects of vaccination in each outbreak? Using a modified classic infectious disease dynamic model and an iterative relationship for new infections per day, the effectiveness of vaccines and NPIs was deduced, from which the independent effectiveness of vaccines was derived. There was a negative correlation between vaccination coverage rates and virus transmission. For the Delta strain, a 61.8% increase in the vaccination rate (VR) reduced the control reproduction number (CRN) by about 27%. For the Omicron strain, a 20.43% increase in VR, including booster shots, reduced the CRN by 42.16%. The implementation speed of NPIs against the original/Alpha strain was faster than the virus's transmission speed, and vaccines significantly accelerated the DZCP against the Delta strain. The CRN ([Formula: see text]) during the exponential growth phase and the peak time and intensity of NPIs were key factors affecting a comprehensive theoretical threshold condition for DZCP success, illustrated by contour diagrams for the CRN under different conditions. The DZCP maintained the [Formula: see text] of 101 outbreaks below the safe threshold level, but the strength of NPIs was close to saturation especially for Omicron, and there was little room for improvement. Only by curbing the rise in the early stage and shortening the exponential growth period could clearing be achieved quickly. Strengthening China's vaccine immune barrier can improve China's ability to prevent and control epidemics and provide greater scope for the selection and adjustment of NPIs. Otherwise, there will be rapid rises in infection rates and an extremely high peak and huge pressure on the healthcare system, and a potential increase in excess mortality.

Keywords: COVID-19; China; Epidemic waves; Mathematical model; Mitigation; Non-pharmaceutical interventions.

Fig. 1

101 epidemic waves in mainland China and data analyses. a Time series of 101 epidemic waves (from 1 Jan 2020 to 31 May 2022) in mainland China caused by the original/Alpha, Delta and Omicron strains, with three large-scale outbreaks including those in Hubei, Shanghai and Jilin individually marked; b The mean peak values and durations of clearing times of 101 epidemic waves for different virus strains. When calculating the average value of the peak value, we excluded the data for five Provinces and cities exceeding 500 due to the peak values of these five provinces being significantly higher than those of other provinces, identified as outliers by Boxplot, namely 14,840 in Hubei (original/Alpha, 13 February 2020), 27,605 in Shanghai (Omicron, 13 April 2022), 555 in Shandong (Omicron, 11 March 2022), 4427 in Jilin (Omicron, 2 April 2022) and 555 in Hebei (Omicron, 19 March 2022). c Four stages of the epidemics including the free rising period with regular epidemic NPIs (${\tau }_1$), containment exponential growth period (${\tau }_2$), plateau period (${\tau }_3$) and exponential decline period (${\tau }_4$). The duration of clearing times ($T_c={\tau }_1+{\tau }_2+{\tau }_3+{\tau }_4$) can be calculated from the real time series and the theoretical formula given in the Methods (Extended Data Online content)

Fig. 2

Analysis of synergistic and independent effects of vaccine and NPIs. a Comparison between the exponential growth curve obtained when the $R_0$ of the original variant is 3 (blue curve) and the exponential growth curve during the free rising period of the epidemic (red curve) in Wuhan, in 2020. b Early relevant information on 6 outbreaks caused by the Delta mutant in Shaanxi, Liaoning and other places in China in 2021 (for comparative purposes, data for Yangzhou City in Jiangsu Province are also provided), including vaccination rate (proportion of total doses to total population) and the control reproduction number (CRN) $R_{c1}$. c The early relevant information on 9 outbreaks caused by the Omicron mutant in Hebei, Guangdong, Tianjin and other places in China in 2022, including the vaccination rate (by 28 January 2022) and the values of the CRN $R_{c1}$. d Comparison of two outbreaks in Shaanxi and Liaoning caused by Delta and Omicron mutants in 2021 and 2022 indicates that even under stronger NPIs and higher vaccine coverage rate, the Omicron strain is more infectious in China. e Correlation analysis and linear regression between vaccination rate and $R_{c1}$ for 6 outbreaks caused by the Delta mutant. ${\mathit{Cor}}_p$ and ${\mathit{Cor}}_s$ represent the Pearson and Spearman correlation ceoficents, respectively. f Correlation analysis and linear regression between vaccination rate and $R_{c1}$ for 9 outbreaks caused by the Omicron mutant. ${\mathit{Cor}}_p$ and ${\mathit{Cor}}_s$ represent the Pearson and Spearman correlation ceoficents, respectively

Fig. 3

Different stages of epidemic evolutions and the dynamic zeroing processes. Using linear regression lines to fit logarithmic data and growth curves to fit original data caused by the Alpha, Delta and Omicron variants, we analyzed the impact of NPI strategies on dynamic zeroing in four periods. The slope of the rising straight line reflects the severity and risk of the epidemic and the timeliness of the NPIs, and the slope of the falling straight line reflects the strength of the NPI measures. Subplots a, b and d represent the linear regression lines and logarithms of data on epidemics caused by the Alpha, Delta and Omicron variants. Subplots c and e represent fitting the original data caused by the Delta and Omicron variants, calculated from the linear regression results shown in subplots b and d (Guangdong and Hebei provinces had slight rebounds during their decline periods, so there are two linear regression fitting curves for these declines)

Fig. 4

Determination of epidemic duration and threshold level of the NPIs’ strength. Based on the strength of NPIs $(S_c)$ and the formula for $T_c$ without considering the plateau period (${\tau }_3$), the maximum value of $R_{c1}$ during the exponential growth stage that can be dynamically cleared in the later decline stage under different intensities of NPIs can be obtained. The contour diagram of the clearing time $T_c$ with respect to the CRN $R_{c1}$ during the early EGS, the peak time τ and the intensity of NPI measures $S_c$. Numbers marked on lines of the figure represent values of $T_c$, and dots represent the values of $R_{c1}$ and τ of these regions. The horizontal line $R_{c1}^T$ represents the threshold value of whether the epidemic can be dynamically cleared or not, which indicates that the epidemic cannot be cleared once $R_{c1}$ exceeds $R_{c1}^T$