Heterogeneity and effectiveness analysis of COVID-19 prevention and control in major cities in China through time-varying reproduction number estimation

COVID-19 emerged in Wuhan, China, at the end of 2019 and rapidly spread domestically and internationally, prompting widespread public health emergency responses and stringent control measures such as social distancing, extensive testing, and quarantine. Given the rapid spread and policy heterogeneity across locations, assessing how effectively different Chinese cities controlled transmission is crucial. The effective reproduction number (R) is a key indicator of transmission and intervention effectiveness, yet many early studies provided static R estimates that do not reflect temporal changes under evolving control measures. This study focuses on 25 worst-hit Chinese cities (accounting for 92% of national cases by February 10, 2020) to answer: How effective were city-level control measures? When did control measures begin to significantly reduce transmission (R < 1)? And is the effectiveness of control consistent across cities? By dynamically estimating time-varying R and analyzing correlations among city-specific R time series, the study aims to quantify heterogeneity in control effectiveness and identify turning points to inform policy adjustment and epidemic forecasting.

Prior work estimated basic or early effective reproduction numbers for COVID-19 and key epidemiologic delays to forecast trends in China and elsewhere. However, these estimates were often static and did not capture dynamic changes in transmission under interventions. Time-dependent reproduction number frameworks have been applied in other epidemics (e.g., Ebola) and regions (e.g., USA, African countries), suggesting the value of time-varying R for monitoring. Existing COVID-19 studies emphasized overall transmission rather than city-level differences, despite variations in policy-making and resource mobilization. This study addresses these gaps by applying a time-varying R estimation at the city level and investigating cross-city similarities and differences via serial correlation analysis.

Data: Daily confirmed COVID-19 cases were collected for 25 worst-hit Chinese cities (Beijing, Shanghai, Hangzhou, Wenzhou, Nanchang, Xinyang, Wuhan, Huangshi, Shiyan, Yichang, Xiangyang, Ezhou, Jingmen, Tianmen, Xiaogan, Jingzhou, Huanggang, Xianning, Suizhou, Xiantao, Enshi, Changsha, Guangzhou, Shenzhen, Chongqing) from January 11 to February 10, 2020, sourced from the National Health Commission and provincial/municipal health commissions. The merged dataset contained 34,737 confirmed cases in these cities (92% of China’s 37,726 total by Feb 10). Cities with relatively low diagnosis were excluded. Time-varying R estimation: Transmission was modeled as a Poisson process where the expected incidence at time t is Rt times the sum over past incidences weighted by an infectivity profile ws (approximated by the serial interval distribution). The instantaneous reproduction number Rt was assumed constant over a sliding time window of length τ, yielding Rτ,t. Bayesian inference with a Gamma prior (α = 1, β = 5) produced a Gamma posterior for Rτ,t with parameters (α + sum of incidences in the window, β + sum of infectiousness terms in the window). Implementation used the R package EpiEstim. Key inputs/assumptions: Daily confirmed cases were treated as incidence. The serial interval distribution had mean 7.5 days and SD 3.4 days (95% CI approximately 5.3–19 days). The main analysis used a time window τ = 3 days to allow faster detection of changes; sensitivity analyses considered τ = 2, 4, 5, 6, 7. To ensure stable estimation, R calculation started after three criteria were satisfied: (1) after at least one full time window (τ), (2) after at least 11 cumulative cases since the epidemic start to meet a coefficient of variation threshold, and (3) after at least one mean serial interval duration (7.5 days). The maximum of these times defined the start of R estimation. Due to drastic reductions in intercity mobility after January 23, 2020 (lockdowns in Wuhan and other Hubei cities), imported case effects between cities from Jan 30 to Feb 10 were assumed minimal for the primary analysis, though residual imported cases could bias estimates. Correlation analysis: To assess heterogeneity/similarity in control dynamics, Pearson correlation coefficients were computed for city R time series over a common period (Feb 2 to Feb 10; n = 9 time points). Corresponding p-values tested significance (p < 0.05 deemed significant). Derived metrics: For each city, R1 denotes R on Feb 10, 2020, and ΔR denotes the average decline in R over the preceding 5 days. These metrics were used to classify cities’ control status (e.g., R1 < 1 and ΔR > 0 indicates effective, declining transmission).

- Coverage: By Feb 10, 2020, the 25 cities reported 34,737 confirmed cases (92% of China’s 37,726 total). Wuhan had 18,455; other high-burden cities included Xiaogan (2,620), Huanggang (2,284), Suizhou (1,095), Xiangyang (1,089), Jingzhou (1,075), among others. - Overall R trends: All cities exhibited a clear overall downward trend in R during the study period, indicating effectiveness of implemented measures. However, substantial heterogeneity existed in the shape and timing of declines across cities. - Cross-city similarity: Correlation analysis of R time series (Feb 2–10) showed significant similarities among most cities. Exceptions with weaker or non-significant correlations included Ezhou, Tianmen, Xiaogan, and Wuhan, suggesting distinct transmission/control dynamics there. - Status on Feb 10 (R1) and recent change (ΔR): Many cities were in the favorable quadrant (R1 < 1 and ΔR > 0), indicating effective control and decreasing risk. Cities with continuing concern included: - Tianmen: R1 = 2.17 (95% CI 1.73–2.67), ΔR = 0.20 - Ezhou: R1 = 1.85 (95% CI 1.62–2.10), ΔR = −0.11 - Enshi: R1 = 1.22 (95% CI 0.88–1.62), ΔR = 0.04 - Wuhan: R1 = 1.50 (95% CI 1.46–1.54), ΔR = 0.52 (still >1 but improving) - Turning point timing: For most cities (excluding Wuhan, Ezhou, Enshi, Xiaogan/Tianmen variants depending on passage), the average time from initiating a first-level public health emergency response to achieving R < 1 was 14.9 days (95% CI 14.4–15.5). The turning point for control was around February 7, 2020. - Temporal reversals: Some cities (Ezhou, Enshi, Tianmen) showed R decreasing initially but then rising again, implying risk of resurgence without sustained interventions.

Tracking the instantaneous reproduction number provides a timely gauge of intervention effectiveness and transmission dynamics. The observed overall decline in R across all 25 cities indicates that intensive measures (lockdowns, distancing, testing, quarantine) were broadly effective. Nonetheless, heterogeneity in the shape and pace of R declines underscores differences in local policies, implementation, mobility patterns, and epidemic seeding. Significant correlations among most cities’ R time series suggest a common pattern of control dynamics despite geographic differences, reflecting coordinated national responses. Cities where R remained above 1 on February 10 (Tianmen, Ezhou, Enshi, and Wuhan) faced ongoing transmission risks; however, Wuhan’s relatively large recent decline suggested momentum toward control. The approximate two-week lag from emergency response initiation to achieving R < 1 in most cities offers a practical benchmark for evaluating policy impact timelines. Persistent or rebounding R in a few cities highlights the need for sustained and possibly intensified measures. The analysis emphasizes continuous monitoring due to potential biases from undetected or imported cases and the risk of resurgence, including from asymptomatic or pre-symptomatic transmission and later imported infections.

This study quantified city-level heterogeneity and effectiveness of COVID-19 control in 25 major Chinese cities using time-varying reproduction number estimation and correlation analysis. Most cities achieved R < 1 by early February 2020, typically about two weeks after initiating first-level public health emergency responses, indicating effective containment. However, several cities (notably Tianmen, Ezhou, Enshi, and Wuhan) still had R > 1 on February 10, necessitating continued or enhanced interventions. The approach demonstrates the value of real-time R tracking to detect turning points and guide adaptive policy. Future work should integrate detailed distinctions between local and imported cases, improve data granularity, and continue sensitivity analyses of estimation parameters to refine real-time assessments and forecast inflection points under different intervention scenarios.

- Imported cases: The analysis largely did not account for imported cases between cities, assuming minimal impact after mobility restrictions from January 23. Residual imported cases and long incubation periods could bias R estimates. - Data granularity: Publicly reported data did not differentiate local versus imported cases, limiting the ability to estimate R conditioned on transmission source. - Estimation window and start-time criteria: R estimates depend on the chosen time window (τ). Although trends were robust, the exact timing of R dropping below 1 can shift with τ. Start-time constraints (minimum cases, serial interval) also affect the usable time series length and earliest estimates. - Forecasting limits: Current trends may not persist due to behavioral changes, reporting delays, or new introductions; thus, real-time updating is necessary. - Generalizability: Cities with lower diagnosis or excluded due to sparse data were not analyzed, potentially limiting generalization beyond the 25 worst-hit cities.