The COVID-19 pandemic, originating in Wuhan, China, rapidly spread globally, prompting the World Health Organization to declare a Public Health Emergency of International Concern. China implemented stringent measures, including social distancing, widespread testing, and quarantining, to curb the outbreak. The effectiveness of these policies varied across different cities. This study aimed to assess the effectiveness of these measures in 25 of China's hardest-hit cities by investigating the temporal dynamics of the effective reproduction number (R). The effective reproduction number (R), representing the average number of secondary infections caused by a single infected individual, is a crucial indicator for evaluating the success of epidemic control strategies. While previous research focused on static R estimations, this study employed a time-varying approach to better capture the dynamic nature of the epidemic and its response to control measures. The research questions addressed include: How effective were the control measures in different cities? When did these measures start showing a significant impact? Was the effectiveness consistent across cities? The study focused on 25 cities accounting for 92% of China's confirmed cases by February 10, 2020, using their daily confirmed case data to estimate the time-varying R.

Existing research on early COVID-19 transmission dynamics often estimated a static basic reproduction number (R₀). However, this approach fails to capture the dynamic changes in R due to implemented control measures. Studies estimating the R of early COVID-19 propagation have yielded static values, which don't reflect the dynamic changes in transmission rates resulting from public health interventions. Some studies did predict the trends using epidemiologic time-delay distributions and basic reproduction numbers, but these lacked the dynamic estimation of the time-varying R. The time-dependent reproduction number has been employed to quantify the temporal dynamics of other disease outbreaks, highlighting the need for a similar approach in analyzing COVID-19 control efforts. Furthermore, previous research mainly focused on the overall transmission rate of COVID-19 without considering the significant variations in epidemic trends among different cities due to differing policy responses and resource allocation. This study aimed to fill this gap by adopting a dynamic approach, analyzing the temporal dynamics of R across multiple cities, thereby providing a more nuanced understanding of the effectiveness of COVID-19 control efforts.

The study utilized data on the daily number of confirmed COVID-19 cases in 25 of the worst-affected cities in China from January 11 to February 10, 2020, obtained from the National Health Commission and provincial Municipal Health Commissions. A time-varying reproduction number estimation method was used to estimate the daily R values for each city. This method models COVID-19 transmission as a Poisson process, assuming the infectiousness profile is independent of calendar time. The instantaneous reproduction number (Rt) at time t is estimated, considering the probability distribution (ws) describing the average infectiousness profile after infection. The likelihood of incidence (It) given Rt is calculated using a Poisson distribution, considering previous incidences. A Bayesian approach employing a gamma distribution with parameters (α, β) represents Rt. The posterior distribution of Rt is calculated using a gamma prior distribution (α = 1, β = 5). The R package "EpiEstim" was utilized for the implementation of this method. The number of confirmed cases per day served as the incidence data. The method's parameters include the time window (τ, set to 3) and the infectiousness profile (w). The posterior coefficient of variation of R was constrained to be below a certain threshold (CV = 0.3) to ensure reliable estimates. The serial interval distribution (mean ± SD of 7.5 ± 3.4 days) was used to approximate w. A serial correlation method was employed to analyze the correlation of the R time series among cities. The correlation coefficient between two cities' R time series was calculated using the formula: corr(X, Y) = C(X, Y) / √[C(X, X)C(Y, Y)], where C(X, Y) represents the covariance between the two time series, and n is the length of the time series (9 days, from February 2nd to 10th). This analysis assesses the homogeneity or heterogeneity of the control measures’ effectiveness across cities.

By February 10, 2020, the 25 cities studied accounted for 92% of China's confirmed COVID-19 cases, with Wuhan having the highest number (18,455). The time-varying R values for all cities showed a general downward trend, indicating the effectiveness of implemented control measures. However, the trends varied significantly among cities. A serial correlation analysis revealed that, except for Wuhan, Tianmen, Xiaogan, and Ezhou, most other cities exhibited significant correlations in their R time series, suggesting a similarity in the effectiveness of their COVID-19 control measures. Further analysis examining the relationship between R values on February 10 (R1) and the average decline in R over the preceding 5 days (ΔR) revealed a pattern. Cities in the lower-right quadrant of the generated graph (R1 < 1 and ΔR > 0) demonstrated effective COVID-19 control. These cities, mostly outside of Hubei province, had R values below 1 by February 10th and a positive ΔR, signifying a decreasing risk of infection. Conversely, cities in the upper-left quadrant (R1 > 1 and ΔR > 0) – including Tianmen, Ezhou, and Enshi – displayed high R values and an increasing risk of infection despite an initial decline. Wuhan also had an R value above 1, but with a large positive ΔR, indicating a positive trend. An analysis of the time it took for each city to reach an R value below 1 (the 'turning point') revealed that, excluding Wuhan, Ezhou, Enshi, and Xiaogan, it took an average of 14.9 days after initiating a first-level public health emergency response. This suggests that the control measures implemented were effective in most cities after a period of about two weeks.

The study's findings underscore the heterogeneous nature of COVID-19 control effectiveness across Chinese cities. While the overall downward trend in R values confirms the impact of control measures, the differences among cities highlight the importance of tailoring interventions to local contexts. The correlation analysis points to similar control effectiveness in a majority of cities, though the severity of the outbreak varied. The identification of critical time points for each city’s turning point (R<1) provides valuable data for future preparedness and response. The approximately two-week delay between the public health emergency response and the achievement of R<1 in most cities may serve as a benchmark for future interventions. The persistent challenges faced by Wuhan, Tianmen, Ezhou, and Enshi emphasize the need for sustained and potentially more intensive measures in areas with initially high infection rates and complex transmission dynamics. Further research could explore the specific policy measures responsible for the observed differences, such as variations in testing capacity, contact tracing efficiency, public compliance, or resource allocation. The study provides crucial insights for policy-making and resource allocation strategies during future outbreaks.

This study demonstrates the usefulness of employing a time-varying reproduction number to track the effectiveness of COVID-19 prevention and control measures. The findings highlight the heterogeneous nature of the epidemic's response to control efforts across different cities. The identification of a consistent ‘turning point’ (approximately two weeks after a first-level public health emergency response) provides valuable insights for future outbreak management. However, persistent challenges in some cities warrant ongoing and potentially enhanced interventions. Future research should focus on analyzing the specific factors contributing to the observed heterogeneity and refining predictive models to improve outbreak control strategies.

The study relied on publicly reported data, which may not fully capture the true extent of infections, potentially underestimating the R value and the effectiveness of control measures. The lack of detailed data on imported cases versus locally acquired cases could affect the accuracy of R estimations, especially after January 30, 2020. The sensitivity of the time-varying R estimation to different time window sizes was also explored, suggesting that the choice of time window can slightly impact the timing of the turning point but doesn’t change the overall trend. Finally, the study’s conclusions are confined to the specific period and geographical location under examination, and their generalizability to other contexts requires further investigation.