Population Outflow from Wuhan Determines the Spread and Distribution of the COVID-19 Epidemic in China

doi:10.21203/rs.3.rs-17315/v1

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Population Outflow from Wuhan Determines the Spread and Distribution of the COVID-19 Epidemic in China

https://doi.org/10.21203/rs.3.rs-17315/v1

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Sudden, large-scale, and diffuse human migration can amplify localized outbreaks into pandemics. Rapid and accurate tracking of human population mobility using reliable mobile phone data could therefore be helpful for policy responses. Here, we examine mobile phone geolocation data for all 18,514,920 counts of individuals egressing or transiting through the prefecture of Wuhan, China, between January 1 and 24, 2020. First, we document the efficacy of quarantine measures in ceasing population movement.

Second, we show that the distribution of population outflow from Wuhan accurately predicts the relative frequency of, and geographical distribution of, COVID-19 infections through February 12, 2020, across all of China, up to two weeks in advance. Third, we present a risk model that not only predicts confirmed cases, but also identifies high- transmission-risk locales at an early stage. Fourth, we develop a mobility-data-driven modeling framework to statistically derive the growth pattern of COVID-19 and its spread; this model can yield a benchmark trend and an index for assessing COVID-19 risk for different geographic locations (290 prefectures). Prefectures above the index’s 90% confidence interval are likely experiencing more local transmissions than imported cases; prefectures below the 90% confidence interval are controlling the spread of the virus more effectively (or, alternatively, are at greater risk of information inaccuracy). This approach can be used by policy makers in developing nations, which typically have mobile phone infrastructure but limited healthcare capabilities, to make rapid and accurate risk assessments ahead of second-wave outbreaks in order to overcome resource and logistics limitations.

Epidemiology

human mobility data

COVID-19

geographic distribution

population-outflow risk model

In a world interconnected by rapid, large-scale, and far-ranging transportation links, localized disease outbreaks have the potential to transform into pandemics 1–5. During such outbreaks, having accurate and timely data regarding the quantity and direction of human population movements is invaluable for tracking and forecasting the spread of contagious diseases. Such data can allow for predictive forecasting of location, scale, and timing of disease spread in advance of second-wave, propagating outbreaks, which can provide governments and health officials with crucial guidance in making timely resource allocation and public health policy decisions. Accurate and rapid advance forecasting is particularly valuable for developing nations that have limited medical and financial resources, large populations, and less efficient logistics capabilities.

Tracking human population movements is especially exigent in the context of China’s COVID–19 outbreak, which occurred in the run-up to the Chinese Lunar New Year eve on January 24, 2020 and the accompanying annual chunyun mass migration. In recent Lunar New Year travel seasons, approximately 3 billion trips are made in China. The potential scale and range of the outbreak’s possible diffusion is particularly alarming considering the position of Wuhan (a prefecture-city in the province of Hubei) as a central hub in China’s rail and aviation network.

Here, we use nationwide mobile phone geolocation data to track population outflow from Wuhan prefecture before and during the outbreak of COVID–19, centered on the Lunar New Year travel period, which we link to infection count by location at the prefecture level (a basic Chinese sub-provincial administrative unit that includes a city and its surrounding towns and countryside, which we refer to as prefecture). Our data is for 290 prefectures in 30 provinces and regions in mainland China (average population 4.46 million, 92.9% of China’s population).

Mobile phone geolocation data, which has long been used to study of human mobility patterns, provides precise, verifiable, and live data on mobile phone user movements.6–12 When aggregated, such data can capture the scale and diffuse movements of entire populations. A key advantage of mobile phone data is its ubiquity, even in developing nations: the majority of people around the world have a mobile phone, including 1.08 billion people in China.13 Given this comprehensiveness, such data are less susceptible to sampling biases, particularly in developing nation contexts, which is of crucial importance for accurate epidemiological modeling.

Our approach differs in some ways from prior work linking human mobility and disease spread,1–5, 14–17 both in terms of the real-time data we use and our analytic, model-based approach. Due to the lack of complete individual-level, population-scale, temporal-spatial data during a live epidemic outbreak, prior epidemiological models have relied on statistical estimates (e.g., based on the number of airline flights) rather than actual, quantitative, and relatively complete observations of human mobility. Such models must estimate disease spread from an estimate of quantity, speed, and distribution of human mobility, and can be off by several multiples due to data limitations.1–5 Other very recent research on COVID–19 has used historical mobility data (e.g., previous years’ chunyun migrations) to estimate case exportation during the current outbreak.15, 17 The benefits of observing rather than estimating population movements are substantial, however, since policy decisions based on even slightly inaccurate predictions can have important consequences; under-reaction can result in disease spread, and over-reaction can lead to medically, socially, and economically harmful policy decisions.

Moreover, our approach here is different from more standard (and also powerful) approaches to epidemiological modelling14–18, and takes advantage of the detailed data we have about mobility originating at the source of the outbreak and transiting to other locales. In addition to empirically mapping the relationship between observed population outflows and the spread of COVID–19, we use a population-outflow risk model to test the extent to which the mobility characteristics of the population can capture the dynamics of the spread of the virus over time and space. Most predictive epidemiological models forecast total infections, transmission dynamics, and outbreak growth under various interventions,1–5, 14–18 whereas here, we predict the growth pattern of the spread of the virus, in and across geographical locales over time; consequently, we can project the distribution and intensity of the spread of the virus.

We first use human mobility data (as well as other possible predictive variables available to planners, such as a prefecture’s population) to model the final distribution and geographical structure of COVID–19 infections over time across different geographic areas in China. We then use the difference between the number of expected infection cases and the number of observed cases confirmed by local authorities to calculate secondary transmission risk. Prefectures that are above the 90% confidence interval are more likely to be suffering second-wave infections, and prefectures below the 90% confidence interval are more likely to have better controlled the spread of the virus (or to have problems with data reporting). This live model, which is parsimonious and easy and quick to implement, can be used to provide a dynamic understanding of infection risks for locations where epidemiological data is sparse, or ahead of updated data reporting by local officials.

To measure population outflow from Wuhan, we used a country-wide temporal-spatial dataset, provided by a major national carrier, tracking all mobile phone user movement out of Wuhan (including customers of the two other national carriers) between January 1 and January 24, 2020. The symptom onset of the first recorded case in Wuhan was December 1, 2019; as of February 12, 44,747 infection cases had been verified in China.15–17, 19–26 Our time period of observation includes the time that news reports about the outbreak first appeared (mainly on December 31, 2019 and January 9, 2020) and the annual Lunar New Year migration (which culminated on January 23, 2020). The dataset, based on mobile phone geolocation data, included any mobile phone user who had spent at least 2 hours in Wuhan prefecture during this period, and tracked the total daily flow of such individuals to all other prefectures throughout China.

We defined population outflow as the total count of such individuals entering any given prefecture from Wuhan during the observation period. This definition of population outflow is conservative; since Wuhan (population 11.08 million in 2018) is a major transportation hub, especially for rail and aviation, many of these individuals were through travelers rather than residents. The definition is also weighted by number of visits to Wuhan since some people may have entered and exited Wuhan on multiple occasions in January (especially if they lived in neighboring prefectures). This can also be thought of as a linear weighting of additional infection and transmission risk from repeated visits to the initial outbreak location. There were 18,514,920 counts of movements (population outflow) from Wuhan; 16,840,364 to other prefectures within Hubei and 1,674,556 to prefectures in other provinces. During the study period, there was population outflow from Wuhan to all prefectures in our dataset (min. value = 4).

Key dates during this period were January 24, Lunar New Year’s Eve (outbound holiday travel is typically completed before this evening, when Chinese families traditionally reunite for dinner), and January 23, when Wuhan was quarantined. We observed the efficacy of the quarantine, as illustrated in Fig. 1b and 1c. It was manifested in a 47% (36%) drop of inter- (intra-) provincial population outflow on January 23 compared to January 22, and a further of 91% (74%) drop on January 24 (Lunar New Year’s eve) compared to January 23. Of note, 98% of the January 24 population outflow (160,674) was intra-provincial (of which 150,206 were to 4 prefectures bordering Wuhan; 6,679 were to other prefectures in the province; and only 3,789 were to outside provinces). With the imposition of the quarantine, first with respect to Wuhan (and two neighboring prefectures) at 10 a.m. on January 23 (and then with respect to 12 other prefectures in Hubei by the end of the day on January 24), population outflow from Wuhan ceased. So we do not include data on mobility after that date.

We combined the human mobility dataset with the count and geographical location of COVID–19 confirmed cases nationwide, provided by the Chinese Center of Disease Control and Prevention (CCDC), which used a consistent (and stringently enforced) procedure for case ascertainment and reporting during this time period. As of February 12, 2020, there were 44,747 infection cases in China; 25,289 cases occurred outside of Wuhan in 299 prefectures; and there have been 1,015 fatalities overall.26

The relative frequency and geographical distribution of infections follows two basic patterns (Fig. 1): infections were highest in prefectures that were geographically closest to Wuhan (e.g., in Anhui, Chongqing, Henan, Hunan, Jiangxi, Sichuan), or had the strongest social and economic ties (e.g., in Beijing, Fujian, Guangdong, Jiangsu, Shandong, Shanghai, Zhejiang) despite being geographically further.

Population outflow from Wuhan, the outbreak epicenter, may be hypothesized to export the virus to other locations, where it causes local first-wave infections (either directly imported cases or local transmissions15–17, 23–25). And indeed, we find a strong correlation between population outflow from Wuhan and number of infections in each prefecture (Fig. 2a, b; see also Supplementary Fig. 1). Consistent with our hypothesis, the cumulative number of infections is highly correlated with cumulative population outflow from Wuhan over time, and the correlation increases over time from r = 0.328 on January 24 to 0.861 on February 12 (p <.001 for both) (Fig. 2a, b, c). Since there is relatively little travel throughout the country during this period (when people are traditionally at home), and because of the quarantine, the population outflow variable is comparable to a lagged variable in a time series. The correlation exhibited the same robust pattern even when using different time windows of population outflow out of Wuhan ranging from 2 to 15 days (Supplementary Fig. 2).

We next compared the predictive strength of population outflow against certain other factors, over the same time period. First, we used the relative frequency of Baidu search for the top virus-related terms in each prefecture (e.g., Wuhan pneumonia, novel coronavirus, flu, SARS, atypical pneumonia, surgical mask)27. Separately, we also evaluated each prefecture’s GDP and population as possible predictors (Fig. 2c). Each of these factors became less predictive of local outbreak size over time, either for cumulative or daily reported cases (Fig. 2c, Supplementary Fig. 5) The pattern for search is the most striking since it is the most predictive factor on January 31, with r = 0.735. The relative frequency of search engine terms is usually interpreted as a measure of interest or concern, which has received prior attention as a potential proxy for the incidence of seasonal influenza, which it tracks reasonably well in a 2-week time frame27–29. However, since search tracks both cumulative and daily infection count poorly (Supplementary Fig. 3–5), a Google Flu Trends style ‘COVID–19 trends’ Baidu index is likely to be low in predictive strength28. The initially high and then declining predictive strength of search may reflect the fact that initially high volumes of information search about the virus signaled stronger risk perception in any given prefecture (e.g., because of early reported cases, having more relatives in Wuhan, etc.), but that, over time, information saturation reduced the impetus for search (Supplementary Fig. 3).

A naive model of mobility might assume that people from Wuhan are more likely to go to the largest prefectures, which tend to be the most developed in China, and create more infection cases among a larger susceptible population. However, we find a relative decline in the predictive strength of prefecture’s population size and also GDP over time (Fig. 2c). Taken together with the high correlation of population outflow from Wuhan with infection numbers in destination locations, this pattern suggests that population outflow from Wuhan was to a more diverse set of prefectures and was determined by a more nuanced set of factors than just prefecture population size, which is consistent with the scale and rationale for migration during the Chinese New Year holiday. Indeed, we observe population outflow from Wuhan to almost every prefecture in China. This pattern of results is also consistent with the specifically social reasons for the choice of destination by many migrants and travelers, as shown in prior work, whether this involves short-distance rail travel or outright emigration.30–32 For instance, previous research shows similar patterns of post-disaster migration in other nations and has found that presence of social connections is a key determinant of destination selection.10

We next use two sets of models, one cross-sectional and the other dynamic, to statistically model and benchmark the extent to which population outflow patterns from Wuhan predicts the spread and distribution of COVID–19 infections across China.

We first modeled daily infection data using an exponential model (model 1 in the Supplementary Information) that also includes prefecture’s population size and GDP as control variables (this model is a multiplicative form of Poisson regression model; see Supplementary Information). We applied a supervised machine learning approach with confirmed cases as the dependent variable to estimate the parameters of a model with Wuhan population outflow as the sole variable (R2 = 0.285 on January 24 to 0.833 on February 12) and a model with population size and GDP as co-variates (R2 = 0.710 on January 24 to 0.937 on February 12) (Supplementary Tables 1–2). Although these additional variables improve fit, the parameter for population outflow from Wuhan becomes increasingly dominant, while a prefecture’s GDP and population become increasingly less predictive over time in general. Overall, the models’ performance continuously improved as more infection cases were confirmed, suggesting that the spreading pattern of the virus gradually converges to the distribution of the population outflow from Wuhan to other prefectures in China.

The logic behind this convergence over time, as well as the model’s predictive strength, is that population outflow from Wuhan to other prefectures in China fundamentally determines the eventual distribution of total infections around the country. During the earliest phase of the viral outbreak, before the quarantine of Wuhan, there was a relative lack of awareness of the virus, and few countermeasures at the collective or individual levels preventing the spread of the virus. The transmission of COVID–19 should thus have spread randomly across the entire prefecture of Wuhan; that is, our results imply that the number of infected people was uniformly distributed (statistically speaking) in the population outflowing from Wuhan into different prefectures across the country.

Using the daily predicted cases in model (1) (details in the Supplementary Information), we are also able to calculate a daily risk score for prefectures based on the difference between their predicted and confirmed cases on any given date. Higher-than-expected levels of infections suggests greater viral transmissibility or more second-wave transmissions (i.e., spread from infected individuals not from Wuhan). Thus, we regard prefectures with more confirmed than predicted cases as having higher second-wave transmission risks (‘underperforming’ compared to the benchmark derived from the outflow population from Wuhan). On the other hand, ‘over- performing’ prefectures with fewer cases than expected are also noteworthy—since they could either have implemented highly successful public health measures or be at higher risk from inaccurate data reporting. Supplementary Figure S6 identifies prefectures with second-wave transmission risk index values over the upper bound of the 90% confidence interval on January 29, for example. Our model identified Wenzhou as having the most severe second-wave transmission risk that day; and the government announced a full quarantine on the prefecture on February 2. The predictive strength of population flow from Wuhan and the overall fit of model (1) over time can also act as an early warning index of an epidemiological phase transition; they reflect the degree to which first-wave infections are dominant at any point in time. If model strength declines significantly at any location, this may indicate that second-wave (propagating) infections may be overtaking imported cases.

We next developed a dynamic model to explore changes in distribution and growth of COVID–19 across all prefectures, over time (rather than on individual dates) (Supplementary Information 2.1). We do so by using a Cox proportional hazards model framework and replacing the constant scaling parameter of model (1) with a time-varying hazard rate function—by choosing a logistic or Gompertz function, which has an S-shaped property that epidemic events typically follow. Using the hazard model, we are able to incorporate all infection cases across all dates to statistically derive the COVID–19’s epidemic curve and growth pattern across China.

We used the same machine learning method as before to estimate the parameters (see Supplementary Information). When using only the single variable of population outflow from Wuhan to other prefectures, we observe R2 = 0.815 (inclusion of population and GDP increases R2 to 0.933; Supplementary Table 3). The surfaces in Figure 3 illustrate the basic features of our models with the data regarding confirmed cases for two separated clusters: prefectures in Hubei (excluding Wuhan), and prefectures outside of Hubei province.

We use a similar logic as before in contrasting expected and observed outcomes to gauge epidemiological risk. Here, model predictions serve as reference patterns across time (as opposed to the reference points that a cross-sectional model generates) (Supplementary Figure 7). These curves serve as benchmark trends, and the differences in the growth trends between predicted and confirmed cases can signal higher levels of COVID–19 second-wave transmission. We use the integral of the differences over time to create a total transmission risk index (normalized by subtracting the mean and dividing by the standard deviation), and identify a list of prefectures above and below the 90% confidence interval of the index (Supplementary Figure 8, Supplementary Table 4). Indeed, our model identifies a list of statistically significant “underperformers”; in most of these cases, we observed the subsequent imposition of quarantine, reflecting local leaders’ assessments that, indeed, the epidemic warranted heavier measures (see the Supplementary Information for these prefectures and our analysis, along with Supplementary Table S4 and Supplementary Figures 7 and 9). On the other hand, prefectures with lower trends than expected by our model might have had more successful public health measures in controlling the spread of the virus.

To provide convergent evidence regarding our model assumptions, we also used different types of model functions and get the same results (see the Supplementary Information). In addition, we used the entropy of the infection rate normalized by population outflow from Wuhan to other prefectures to test how stable population outflow is in predicting the distribution structure of the virus (Supplementary Fig. 10). Entropy increased in the first week of the study period and remained flat thereafter, which suggests that the rates of confirmed infection cases based on population outflow from Wuhan remained uniform across Chinese prefectures. One possible reason for our model’s robustness beyond January 24 (in the still-early stages of this epidemic) may relate to the fact that, as recent research has shown, most early transmissions have occurred in family clusters,23 which would explain why infection growth remains proportional to population outflow from Wuhan (with average household size as a possible scaling factor) (see Supplementary Information).

In sum, using detailed, real-time, individual-level, mobile phone geolocation data, we track the transit of people from Wuhan to the rest of China with daily precision until January 24, 2020. The precise geographic distribution of people anticipates the location, intensity, and timing of outbreaks in the rest of China during the follow-up period, through February 12, 2020. These data outperform other measures, such as population size and wealth or location-specific information regarding internet searches. We use the observation that population outflow from Wuhan drives infection spread to model the epidemic curves of COVID–19 across different locales. Deviations from model predictions built upon mobility data (in both static and dynamic models) also served as tools to detect the burden of secondary cases.

The logic of our mobility-data based population-flow model differs from classic epidemiological models that rely on assumptions regarding population mixing, population compartment sizes, and viral properties. We do not need to make assumptions about the parameters in a classic SIR model in order to quantify epidemic risks here, though we do, of course, make other parametric assumptions. Notably, models combining detailed knowledge of transmission dynamics that are conventionally used in SIR models along with mobility data are also conceivable.33 This is an important area for future work with COVID–19.

In addition, we note that, here, we have focused on the relative relationship between different areas regarding the relative strength of the outbreak in each area, rather than the absolute number of cases, though we are able to predict the number of cases by using reported data to calibrate the parameters of the model. In a sense, a key contribution of our approach is to robustly characterize the structure or relative distribution of cases across different geographic areas, which is driven fundamentally by the outflow population from Wuhan before the outbreak occurred at the national level. Moreover, one of the benefits of our approach is that non-systematic inaccuracy of COVID–19 case-finding is relatively unimportant as long as we capture the distribution of population flow accurately over time, which we do.

Our structural analysis of the spread of the COVID–19 has important potential applications. The approach is generalizable to any dataset that captures people’s mobility (e.g., train ticketing or car tolling data). First, we show that our model, based on population movements from the initial source of the outbreak, can predict the final distribution structure of infections over different geographical locales, even from close to the start of the outbreak, i.e., two weeks in advance. Second, it provides a live model (that can be updated with new population flow data) to facilitate policy decisions, for example the relative allocation and distribution of medical resources and manpower across specific geographic locales based on the predicted structure of infections. This consideration is particularly important for developing countries with limited resources. If the average infection rate and reproduction number are estimated or assumed, the model can also predict number of infections (e.g., to predict materiel needs) with greater accuracy than traditional modeling approaches. Third, the predicted geographic distribution of virus spread can provide a live, dynamic performance metric when contrasted against real-time reports of infections, and, as we show, can identify which prefectures have higher virus transmission risk and also which prefectures have unusually effective policies or case-ascertainment or reporting inaccuracies. As COVID–19 continues to spread worldwide, starting from seeds in locations in countries outside China, this approach might be useful elsewhere, too.

Other techniques to forecast the levels of an epidemic in defined populations in advance have, of course, been proposed before—whether the use of online searching by the general public27–29 or the use of network sensors (the monitoring of particular people who are at heightened risk for falling ill given their network position).34–35 Our approach relies on real-time (or quickly available—at least in many developing world settings) data regarding population flow. Indeed, historical (i.e., baseline) information about population flows—undisturbed by the imposition of quarantines or by publicity regarding outbreaks, both of which happened here—could also be valuable to public health experts and government officials when new outbreaks occur. And, as we show, this outperforms the search-engine metrics. Future investigations may extend this approach by using datasets tracking population movements out of other Chinese prefectures, or comprehensive international travel data.1–5, 33

When people move, they take contagious diseases with them. Their movements are thus a harbinger of the future status of an epidemic, and offer the prospect of using data-analytic techniques to control an epidemic before it strikes too hard.

Supplementary Information. Attached.

Acknowledgements. We thank an unnamed national carrier for providing the anonymized data allowing computation of population movements. This research was supported by the National Natural Science Foundation of China (71490722, 71771213, 71690233, 71704052), by the Research Grants Council of Hong Kong (17506316, 14505217), and by Shenzhen Institute of Artificial Intelligence and Robotics for Society. We thank the staff members at an unnamed major Chinese telecom carrier and CCDC for their assistance in data preparation.

Author Contributions. All authors made equal contributions to the paper. JSJ, JMJ, and NAC conceived the research. JMJ, YY, XL, and GX analysed the data. JSJ and NAC wrote the paper. JMJ obtained funding. All authors contributed to research design, analytic development, and critical revisions.

Competing Interests. The authors declare no competing interests.

Correspondence. Correspondence regarding this article should be addressed to Jianmin Jia ([email protected])

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