2.1 Study design

This study was designed as a quantitative study of the contribution of multi-dimensional factors to the spread of COVID-19, using the effective reproductive number as an indicator, and to the occurrence of multiple waves of infections. Specifically, this study focused on the following aspects: (1) the quantification of the overall contribution of multi-dimensional factors, before and after vaccine implementation; (2) a comparative analysis of the factors influencing the rising and fading stages of the pandemic, in countries with or without rebound waves, and before and after vaccine implementation; and (3) rebound risk forecasting for the spread of COVID-19.

2.2 Data

Daily numbers of COVID-19 cases were collected from 39 countries up to 30 June 2021. These 39 countries were selected based on the following principles: (1) they represented countries from five continents, (2) the total number of cases in these countries was among the highest during the study period and (3) data for multi-dimensional factors during the same period were available. The COVID-19 pandemic was divided into two phases—the pre-vaccine era and the post-vaccine era—using the date when vaccination began in each country as the dividing date. Of the 39 countries selected, seven single-peak countries without a rebound wave and 13 double-peak countries with a rebound wave were identified in the pre-vaccine era (Figure S1), while 36 multi-peak countries with multiple rebound waves (excluding China, Australia and New Zealand, which had no rebound wave) were identified in the post-vaccine era. A rebound wave was identified when the number of new COVID-19 cases exceeded the average value of the peak in the pre-vaccine era for three consecutive weeks.

The factors analyzed were divided into the following groups: policy-related factors (including 13 specific non-pharmaceutical interventions in the previous week and at the current time point), travel-related factors (including domestic and foreign air passenger flow in the previous month and the current month), socioeconomic factors (population, population density, per capita income, aging ratio and sex ratio), environmental factors (maximum temperature, minimum temperature, average temperature, relative humidity and absolute humidity) and medical factors (number of doctors per 1000 residents, number of nurses, number of pharmacists, number of beds, medical expenditure quota, cardiovascular death rate and diabetes prevalence). Additionally, the number of daily vaccinations was considered as a vaccine-related factor, and information regarding existing virus variants was included in the mutant-related factor category. All of these data were analyzed at the national level.

Effective reproductive number: The daily effective reproductive number ($${R_t}$$) was used as an indicator of the spread of COVID-19. $${R_t}$$ indicates the average number of secondary cases caused by one infected person per day (Fernández-Naranjo et al., 2021), and it was calculated based on the Susceptible-Infected-Recovered model (Arroyo-Marioli et al., 2021; Kermack & Mckendrick, 1927). When $${R_t}$$ ≤ 1, maintaining the current prevention and control measures is expected to gradually control an infectious disease epidemic. In contrast, when $${R_t} > $$1, the infectious disease will continue to spread, suggesting that the prevention and control measures need to be optimized and strengthened. The $${R_t}$$ values for COVID-19 in the 39 countries included in the analysis were obtained from Our World in Data (https://ourworldindata.org/covid-cases).

Policy-related factors: These data were obtained from the Oxford COVID-19 Government Response Tracker (OxCGRT, https://github.com/OxCGRT/covid-policy-tracker), which includes data on the level of specific measures (strictness of implementation) taken by governments during the outbreak. Thirteen specific measures were analyzed, as detailed in Table S1. These classification variables were converted into a score in the range of [0,100]. The details of this calculation are presented in the Materials and Methods section of the Appendix.

Travel-related factors: Data on air passenger flow, based on monthly statistical measures at the national level, were collected from the Official Aviation Guide. These data included global passenger flow to the countries (foreign flights) and intra-country air passenger flow (domestic flights). A 1-month lag time was also included (Cao et al., 2020) for these data.

Socioeconomic factors: The number of residents (population), population density (density), per capita national income (GDP), percentage of the population aged ≥65 years (old%) and sex ratio (the ratio of men to woman, sex ratio) were collected from Our World in Data (https://ourworldindata.org/covid-cases).

Medical factors: Health resource data were obtained from the World Bank (https://data.worldbank). These data included the number of doctors (doctor), nurses (nurse), pharmacists (pharmacist) and beds (beds) and the health expenditure per 1000 people (health expenditure). Additional health data, such as the cardiovascular death rate (cardiovascular death rate) and diabetes prevalence (diabetes prevalence), were obtained from Our World in Data (https://ourworldindata.org).

Environmental factors: The daily maximum temperature, minimum temperature, average temperature, relative humidity and absolute humidity during the study period were collected from the National Oceanic and Atmospheric Administration (https://www.noaa.gov/).

Mutant-related factors: The five major virus strains (alpha, beta, delta, gamma and lambda) were considered, and the temporal proportions referred to Alpha for Beta, Delta, Gamma and Lambda in each region were included as free variables in the analysis. These proportions were based on the weekly time scale in 39 countries obtained from the Global Initiative on Sharing Avian Influenza Data (https://www.gisaid.org/hcov19-variants/).

Vaccine factor: The number of daily COVID-19 vaccinations (daily vaccination population) in the 39 countries was obtained from Our World in Data (https://ourworldindata.org/covid-cases).

All time scales were unified as daily scales using the pandas time-series resampling method (https://pandas.pydata.org/). Moreover, considering the latent period of COVID-19, lag effects for policy- and travel-related factors were also considered and incorporated into the model (see the Materials and Methods section in the Appendix for more details).

2.3 Machine learning framework

Interpretable machine learning frameworks were used to determine the nonlinear contribution of systematic factors to the $${R_t}$$ value. Specifically, multiple candidates nonlinear regression models, including random forest, support vector machine and extreme gradient boosting (XGBoost) (Chen & Guestrin, 2016) models, were used, and important factors were selected using the sequential floating selection (SFS) algorithm (Fjf et al., 1994; Pudil et al., 1994). The overall framework is shown in Figure S2. SFS is a sequential feature selection method based on the greedy search that can remove functions from all feature sets and evaluate error functions. If the error reaches the optimal level, the combination of the remaining features is regarded as the best feature combination. A Bayesian search algorithm was used to identify the root mean square error (RMSE) of the parameter sets by fitting the model. The effect of generalization was evaluated by 10-fold cross-validation (S. M. Lundberg et al., 2020). Two temporally non-overlapping datasets were built based on the pre-vaccine era (a training set up to 31 October 2020, and a testing set from 1 November to 30 November 2020) and post-vaccine era (a training set from January 2021 to 31 May 2021, and a testing set from 1 June to 30 June 2021) datasets. The model with the lowest fitting error was selected based on two training sets, and this model was used in subsequent analyses.

2.4 Ranking contribution of the factors

2.5 Model evaluation and short-term pandemic rebound risk prediction

A rebound risk model was built by considering the daily increasing ($${R_t}$$ > 1) or decreasing ($${R_t}$$ ≤ 1) trend as the subject (binary) and all factors selected as covariables. The RMSE and $${R^2}$$ values were used to evaluate the model fit to $${R_t}$$ using 10-fold cross-validation for the training set. The accuracy, precision, recall, F1 score and area under the curve were used to evaluate the rebound risk.

3.1 Contribution of systematic factors to the spread of COVID-19 in pre- and post-vaccine eras

On the basis of designed framework (Figure S2), the XGBoost model was selected (Table S2) and 1-week lag was used (Table S3) for subsequent analyses, as it showed the best fit with the training set (Table S2). Therefore, XGBoost with SHAP analysis (see Materials and Methods section for further details) was chosen to identify important factors contributing to the spread of COVID-19 ($${R_t}$$) in 39 countries, before and after vaccine implementation, and only top 20 factors were shown and discussed. Overall, the RMSE and$$\ {R^2}$$ values, as evaluation measures of the model, were 0.109 and 0.725, respectively, in the pre-vaccine era, and 0.021 and 0.988, respectively, in the post-vaccine era. In the pre-vaccine era, policy-related (60.81%) and travel-related factors (18.84%) were the primary contributors to the spread of COVID-19. Socioeconomic and medical factors accounted for 9.31% and 6.58% of the spread of COVID-19, but environmental factors only accounted for 4.48% (Figure 1a and Figure S3a). In the post-vaccine era, the contribution pattern changed significantly, with policy-related factors reduced to 28.34% and travel-related, environmental, medical and socioeconomic factors reaching 21.67%, 9.62%, 8.64% and 8.20%, respectively. The contributions of mutant-related and vaccine factors reached 16.49% and 7.06%, respectively (Figure 1b and Figure S3b).

Of the travel-related factors assessed in the pre-vaccine era, only population movement caused by foreign flights was identified as an important factor, contributing 18.84% (Figure 1a). Of the policy-related factors, the three greatest contributors were income support (previous week), stay-at-home requirements (previous week) and workplace closure (previous and current week), with contributions of 10.23%, 8.29%, 7.70% and 6.59%, respectively. Of the socioeconomic factors, GDP was the dominant contributor, with 5.80%. The contribution of single medical and environmental factors was low, with the highest percentages of 3.95% for the number of nurses and 2.69% for relative humidity, respectively. Although foreign flights (previous month) remained as the dominant factor with the highest contribution in the post-vaccine era (7.75%), the contributions from domestic flights in the current and previous months were 7.56% and 6.36%, respectively. Mutant-related factors contributed significantly to the dynamics of COVID-19 in the post-vaccine era, with 7.56%, 4.69% and 4.24% contributions for delta, gamma and beta variants. The vaccine factor also made a significant contribution to the spread of COVID-19 in the post-vaccine era, with a contribution of 7.06%. As a result, the contributions from policy-related factors were significantly reduced in the post-vaccine era, with the top three factors—workplace closure in the previous week and the cancellation of public events in the current and previous weeks—contributing 5.63%, 5.63% and 4.66%, respectively.

At the country level, the overall pattern in the pre-vaccine era was the same as the pattern observed at the global level, with policy- and travel-related factors making the greatest contributions (Table S4). Nevertheless, heterogeneity existed among countries, with the contribution of policy-related factors in several countries, such as Sweden, Mexico and Bulgaria, being as high as 70%. However, the contribution of travel-related factors in many countries, such as Spain, the United States and Cameroon, was 30%. Moreover, the contributions of socioeconomic, environmental and medical factors were low in all countries evaluated. Of note, there were noticeable differences in the contributions of these factors in different countries. For example, the contribution of socioeconomic factors in Colombia, Kenya and Chile was 16.17%, 14.89% and 14.64%, respectively; the contribution of environmental factors in Argentina, Ecuador and Colombia was 15.67%, 13.60% and 13.21%, respectively; and the contribution of medical factors in Algeria and Canada was 11.27% and 9.89%, respectively. In the post-vaccine era, a significant decrease in the dominance of policy-related factors was seen (Table S4), and the contribution of vaccine factor was relatively high in some countries, such as Bangladesh, Canada and South Africa, which showed contributions of 15.03%, 12.54% and 10.66%, respectively. At the same time, the contribution of variant viral strains in these countries was also prominent, reaching 32.67%, 25.92% and 28.16%, respectively.

3.2 Factors related to the rebound of COVID-19

As COVID-19 continued to spread, different countries responded differently, leading to different outcomes, with rebound waves occurring in many countries. In the pre-vaccine era, 13 of the 39 countries analyzed had a clear rebound wave with double peaks in the number of new cases, whereas seven countries had no rebound wave, but a clear single peak (Figure S1). In addition, the first peak was further divided into the rising and fading stages, and the second peak was classified as the rebound stage. In the post-vaccine era, 36 of the 39 countries analyzed experienced multiple rebound waves, with more than one peak. Models were then built for the seven double-peak countries with rebound waves, 13 single-peak countries without a rebound wave in the pre-vaccine era and 36 countries with multiple rebounds in the post-vaccine era (Table S5). These models had RMSE values of 0.634, 0.298 and 0.021 and$$\ {R^2}$$ values of 0.824, 0.712 and 0.988, respectively (Figure 2).

Overall, factors in the rising and fading stages had similar effects on the$$\ $$spread of COVID-19 in single-peak countries (Figure 2a). Policy- and travel-related factors were dominant during the rising stage (contributions of 33.7% and 18.7% in the rising and fading stages, respectively), but policy-related factors were predominant in the fading stage, reaching a contribution of 37.7% (Figure 2a). However, approximately half (45.8%) of the contribution to the spread of COVID-19 in double-peak countries was from factors in the rebound stage. Policy-related factors showed contributions of 32.6% and 25.0% during the rebound and fading stages, respectively (Figure 2b). In the post-vaccine era, the results of the model including countries with multiple rebounds were similar to the results of the model that included all 39 countries (Figure 1b), with policy- and travel-related factors accounting for more than half of the contribution, although the contribution from policy-related factors significantly decreased (Figure 2c). Mutant-related and vaccine factors contributed 17.7% and 7.3%, respectively, to the spread of COVID-19 in the post-vaccine era. The contributions from environmental and medical factors increased to 9.6% and 8.7% in the post-vaccine era.

In single-peak countries (Figure 2d), the contribution of domestic flights (previous month) in the rising stage was 18.71%, with effective SHAP values of 0.23, indicating a positive contribution to the spread of COVID-19. Other important factors in single-peak countries were policy-related factors, such as contact tracing (contribution, 9.90%; effective SHAP value, −1.14) and the cancellation of public events (contribution, 7.11%; effective SHAP value, −0.64) in the rising stage and school closure in the previous week (contribution, 8.03%; effective SHAP value, −0.79) and international travel controls (contribution, 7.34%; effective SHAP value, −0.32) in the fading stage. All of these factors decreased the spread of COVID-19 (Figure 2d). However, a more diverse range of factors from different categories was involved in double-peak countries, many of which were present in the rebound stage (12/20, Figure 2e). In particular, foreign flights in the rising stage (contribution, 9.09%) and domestic flights in the fading stage (contribution, 7.66%) increased the spread of COVID-19, with effective SHAP values of 1.43 and 1.15, respectively. The cancellation of public events in the fading stage (contribution, 8.58%) and testing policies (previous week) in the rebound stage (contribution, 7.73%) reduced the spread of COVID-19, with effective SHAP values of −2.69 and −0.04, respectively. The contribution of foreign flights continued to decrease in the post-vaccine era (contribution, 6.39%; effective SHAP value, −1.56; negative effect). The Delta variant became the most influential contributor to the spread of COVID-19 in the post-vaccine era (contribution, 8.12%; SHAP value, 9.18). Other virus variants, such as gamma and beta, also had a promoting effect on the spread of COVID-19 in the post-vaccine era, with SHAP values of 1.37 and 5.37, respectively. The strong inhibitory effect of the vaccine was evident (contribution, 7.26%; SHAP value, −9.28). Unexpectedly, most policies had a boosting effect on the spread of COVID-19, with SHAP values > 0, for five of the six factors evaluated (Figure 2f).

3.3 Rebound risk forecasting

After understanding the different contributions from various factors, we sought to determine whether the rebound risk of COVID-19 could be predicted. Predictive models were built based on data from 20 selected countries in the pre-vaccine era and 36 countries in the post-vaccine era. A high risk of rebound was defined as $${R_t}\ $$> 1, and a low risk of rebound was defined as $${R_t}\ $$≤ 1. Daily forecasting was then performed for the following 30 days, based on actual data for all of the contributing factors in the model. COVID-19 rebound was defined as $${R_t}$$ > 1 for more than half of the 30 days. The accuracy of the risk forecast was 0.78 and 0.81 in the pre-vaccine and post-vaccine eras, respectively (Table 1 and Table S6).