Contact network analysis of COVID-19 Delta variant outbreak in urban China —based on 2,050 confirmed cases in Xi’an, China

The outbreak of coronavirus disease (COVID-19) pandemic sweeps the world in late 2019 [1‐3]. By 2022, different variants of the virus evolved, such as Delta and Omicron, triggering several waves of worldwide infection [4, 5]. Having documented 617 million COVID-19 cases, more than 6.5 million deaths have been reported worldwide by October 2022.

The analysis of existing studies on COVID-19 is mostly based on epidemiology, virology and medicine, involving virus case studies, transmission model construction, gene sequencing, and clinical diagnosis [1, 5‐7]. Studies establishing contact networks between confirmed cases based on infection routes are less [8].

Human social network plays a significant role in the spread of viruses. Viruses spread along with human movement and aggregation, thus creating contact networks [9‐11]. Several studies have been conducted to analyze the spread of various viruses in populations from a network perspective, such as sexually transmitted diseases [9], AIDS [12], and the Plague [10]. These studies have found that the mode of transmission of different viruses makes the structure of the contact network very different. For example, for HIV through sex, blood and mother-to-child contact, the network structure is simple and sparse [12]. However, for airborne viruses such as novel coronavirus, the network structure is complex [3].

There are some studies based on real-world data describing the contact network at the beginning of the COVID-19 outbreak in different regions, such as China [3], Korea [8], and India [13]. However, these studies only conducted based on data from first wave of the epidemic, when people lack systematic intervention policies, drug treatments and vaccines, and the viruses they analyzed were not emerging delta or omicron variants.

In December 2021, a new wave of an outbreak caused by a Delta variant leaked from a Pakistani flight was reported in Xi’an, China. The outbreak infected more than 2000 people and was the largest COVID-19 outbreak in China since the Wuhan outbreak in 2020. By reviewing this outbreak, we can better know how the Delta variant spread, and to what extent preventive measures be effective.

Based on 2050 confirmed cases reports from December 09, 2021 to January 18, 2022 published by the Shaanxi Provincial Health Commission, we use network analysis techniques to construct and visualize the contact network of cases and calculate the network indicators. The analysis of the contact network is key to understanding the spread of disease [3, 8, 14]. First, based on the network structure, we can clarify the transmission path of the virus and assist in identifying hidden infection paths. Second, based on the diagnosis and isolation dates of pairs of infectors and infectees, we construct three variables of intervals and analyze the trend of intervals during the outbreak, which can help us to evaluate the effectiveness of non-pharmaceutical measures and predict disease trends and health care demands [1, 15]. Third, we also discuss the effect of city lockdown on the intervals and network transmission capacity.

The mean age of cases is 35.90 years with a median of 34 years. The mean degree centrality is 0.74 and the maximum number of contacts is 43. The mean value of the degree less than 1 represents the end of the outbreak. It means that one patient in the network of this outbreak is in contact with an average of 0.74 confirmed cases. The maximum value of degree centrality indicates that this outbreak had one case linked with 43 other confirmed cases. The mean PageRank score is 0.0005. At the beginning of the outbreak in 2020, the average degree centrality of eight regions in China was 1.136 and the average PageRank score was 0.0093 [3]. There is slightly more male with a percentage of 54.54%. Most cases (94.19%) have a mild symptom. Eight cases are asymptomatic infections. The results of descriptive statistics are presented in Table 1.

The mean value of the degree centrality of the contact network is less than 1, indicating that the outbreak was effectively controlled through isolation and mass screening [11]. Because a large number of infection chains are not fully clarified, the contact network for this outbreak in Xi’an is very sparse, with a density of less than 0.0001, compared to 0.004 for the same area in early 2020 [11].

Based on a report from Shaanxi Health Commission,³ this outbreak came from a single source, so its component number should be one. But the components we find are much more than one. There are two possible reasons: the first is that there is a large hidden chain of transmission that was not detected; the second possibility is that the source of this outbreak is not just offshore, but that multiple sources exist, which is an indication that the outbreak existed long before the first case was reported on December 9, 2020. Since the data limitation, it needs further genetic sequencing to clarify this question.

Because of the very large difference in network size between the initial 2020 outbreak and the current outbreak (234 confirmed cases vs. 2050 confirmed cases), the number of components cannot be directly compared. To compare the level of modules, we calculated the modularity scores of two contact networks by using the Louvain method [26, 27]. The modularity value of the 2020 contact network (0.95) and the modularity value of the current epidemic (0.99) are similar, indicating a more consistent level of differentiation of the networks in the two different periods.

A power-law distribution would form a scale-free network [28]. We fit the distribution of degree centrality to determine whether the distribution of this outbreak is a power-law distribution (aaplot program in Stata). The results of the fit are shown in Fig. 10. The fitted line is a straight line after taking the logarithm form, with an intercept term of − 0.86, a slope of − 2.70, and an R square of 98.9%, indicating that the distribution of degree centrality shows a power-law distribution. This indicates that the contact network is a scale-free network, which is consistent with the previous analysis of the contact network in Seoul, Korea [8].

Scale-free networks imply that a few cases have more contacts and most cases have fewer contacts. These super-disseminators in this kind of network accelerate the spread of the virus [29]. For example, the key nodes for the spread of Ebola are these super-dispersers [29]. In such a network, the virus can quickly spread to the entire connected fraction and cause an outbreak even if each node is exposed to a limited number of other nodes [9]. On the other hand, such a network is structurally vulnerable, i.e., by removing a few nodes with a high degree of centrality from the network, the connectivity of the network is drastically reduced. By isolating hubs of contact networks, a network structural break can be caused, and virus transmission can be effectively controlled [9].

By analyzing the diagnosis and isolation time of the network infection chains, we find that the mean value of the intervals (interval 1) between the diagnosis date and isolation date of patients is − 3.9 days. The longest interval is only 1 day. This distribution indicates that the vast majority of cases were isolated before diagnosis based on their contact tracing information. A simulation study using data analysis and epidemiological interventions in four Nordic countries found that if the mean time interval between symptom onset and isolation was reduced from 12 to 4 days, it resulted in an 85.2% reduction in infections and 88.8% reduction in deaths [30]. This suggests that the intervention strategy of this outbreak in terms of reducing interval was effective. In our observation sample, most cases tested positive for nucleic acid even during the isolation period. Figure 9 and the t-test also show that interval 1 showed a decreasing trend after the city lockdown, which indicates that as various measures such as lockdown and universal nucleic acid test progressed, more and more cases were diagnosed in isolation.

The mean value of the time intervals (interval 2) between the diagnosis time of the infector and the time of the infectee is 4.2 days. For comparison, analysis of data from early 2020 of the COVID-19 outbreak in China showed a serial interval of 7.8 days in the early stage and 2.6 days in the later stage [1]. However, vaccines and well-established contact tracing techniques were not available at that time. The trend in Fig. 9 and the t-test we performed suggest that the city lockdown did not have an impact on reducing interval 2. For reference, Hu et al. (2021) found that reducing the delay in implementing an effective detection and follow-up program from 50 days to 10 days reduced infections and deaths by 35.2 and 44.6% respectively [30]. This implies that the local health department should adopt more effective interventions during the outbreak, especially contact tracing, to reduce the interval between the infector’s diagnosis time and the infectee’s diagnosis time.

The mean value of intervals (interval 3) between the isolation time of the infector and infectee is 2.9 days. The smaller the number, the more efficient the public health department is in identifying and isolating the close contacts of confirmed cases and cutting off the source of infection. A negative value indicates that the infectee had been isolated before the infector was isolated. Figure 9 and the t-test we performed illustrate that the city lockdown did not reduce the isolation intervals. Possibly, it is because most later cases are those people with long incubation periods. In summary, our results demonstrate that city lockdowns mostly stop the further spread of the virus but hardly enhance the efficiency of confirming and tracking those already infected people.

The regression results indicate that the shorter interval of the time to diagnosis and isolation of the case (interval 1), the weaker the transmission capacity of the case. Therefore, effective and timely contact tracing and isolation measures are efficient non-pharmacological interventions. The shorter the interval between the diagnosis time of the infector and infectee (interval 2), the higher the whole network centrality (PageRank score) of the infectee. We speculate that this may be due to sample selection bias. The infectee that was quickly tracked and diagnosed was most likely already in a relatively large chain of infection and therefore had more direct and indirect contacts.

We constructed a dynamic contact network between infector and infectee based on 2050 confirmed cases of COVID-19 (Delta variation) in Xi’an by end of 2021. The network is a scale-free network with an average degree centrality of 0.741. The network contains 1291 components, and the largest component contains 64 cases and 63 infection routes. There are multiple infection routes that were not detected in this outbreak. The mean interval (interval 1) between case diagnosis time and isolation time is − 3.9 days. The mean of the interval (interval 2) between the infector’s diagnosis time and the infectee’s diagnosis time is 4.2 days. The mean of the interval (interval 3) between infector isolation time and infectee isolation time is 2.9 days. After the city lockdown, interval 1 decreases, and interval 2 and interval 3 increase.

There are some limitations to our work. First, it lies in the fact that the epidemiological survey did not fully reveal all infection routes, so the contact network of our study is only a partial reflection of the real transmission network. Second, this contact network is only based on data from one area in China. Data from more areas can be integrated in the future for multi-regional comparison.