Contact network analysis of patients with Novel Coronavirus Pneumonia - Based on 237 cases in Shaanxi Province

The spread of novel coronavirus is closely related to the structure of human social networks. Based on 237 cases in Shaanxi Province, using epidemiological retrospective statistics, data visualization, and social network analysis methods, this paper summarized characteristics of patients with new coronary pneumonia in Shaanxi Province, and analyzes these patients’ dynamic contact network structure. The study found that there are many clustered infections through strong ties, about one-third cases are caused by relatives' infection. In the early stages of the epidemic, it was mainly imported cases, and in the later stages, it was mainly local infection cases. The infected people were mainly middle-aged men. Symptoms of imported cases occurred on average 3 days after they arrived, and medical measures were taken on average 5 days later. All cases showed symptoms in less than 2 days on average and were then taken to medical treatment. The virus contact network can be divided into multiple disconnected components. The largest component has 12 patients. The average degree centrality in the network is 0.987. The average betweenness degree is 0. The average closeness degree is 0.452. The average PageRank index is 0.0042. The number of contacts of patients is unevenly distributed in the network.

Introduction synchrotron oscillation of disease outbreaks in different places 13. Unlike contact network, spatial network of viruses has distinct scale-free network features 15. Studies of contact networks for SARS have shown that only differences in network structure can significantly change the curve of the outbreak 16. For viruses with a basic regeneration number less than 2, changes in the network structure also have a significant impact on spread of the disease 17.
In epidemiological studies of novel coronavirus pneumonia, the Lancet first published 41 cases of novel coronary pneumonia, with a brief description of demographic characteristics of the patients 18.
The median age of those patients was 49, and 66% of them had seafood market contact history in Wuhan, China. There was a case of family cluster infection in their samples. Another analysis of 99 patients showed that average age of patients was 55 years old and the standard deviation was 13 years old, including 67 males and 32 females, 49 of whom had a history of South China seafood market exposure 19. Further analysis of 835 cases in Hubei Province of China showed that the average age of the patients was 49 years old, the male to female ratio was 2.7 to 1, and the fatality rate was 2.9% 7. Relevant modeling shows that the basic regeneration number of novel coronavirus is between 2-3, which is weaker than SARS 2 4. Summarizing the existing research, the early outbreak of the virus was based on the clustered infection in the South China Seafood Market in Wuhan. The group with the highest virus infection rate was men who were older than 55 years. The virus is mainly transmitted through droplets and contact, and has a strong ability to spread. Family-based cluster transmission is more common 2 5.
This study collected all confirmed cases published in Shaanxi Province of China from January 23, 2020 to February 16, 2020, a total of 237 cases. First, this paper analyzes the epidemiological characteristics of patients with novel coronavirus pneumonia in Shaanxi province, and then studies the transmission route and contact network.

Methods
Methods. This paper mainly adopts two research methods. One is descriptive epidemiological research method, to digitally portrait the novel coronavirus pneumonia infected people in Shaanxi Province and analyze their epidemiological characteristics. The other is social network analysis method. I build and visualize the patient's contact network and calculate relevant network indicators, including degree centrality, closeness centrality, betweenness centrality and PageRank index. The dynamic change of the network has an important impact on the risk of infection. The phase change structure of the dynamic network is very different from the static network 20 21. But the research on coronavirus dynamic contact network is still less. I construct a dynamic network for corresponding analysis.
Data. All the samples of this study are from the officially announced cases of Health Committee of Shaanxi Province of China. The cases are form January 23 to February 16, 2020. After February 16th, the case growth in Shaanxi Province slowed down significantly. The paper analyzes and encodes the text of each reports.
All methods were carried out in accordance with relevant guidelines and regulations. The study received approval from the Ethics Committee of Xi'an Jiaotong University Health Science Center. The committee waived the need for informed consent as part of the study approval, since this was a retrospective data analysis. Second, code the routes of infection no matter it is a stranger tie, strong tie, or weak tie. People's social networks consist of these three types of ties 22. Strong ties refer to close friends, acquaintances and family members who have more daily contact, deeper affection intensity and highlevel trust. Weak ties are those connections of lower contact frequency, lower affection intensity and lower level trust than strong contacts. Data from the Shaanxi Health and Medical Commission did not fully specify people infected by which kind of tie. I coded the data according to the following rules: If the case shows the infection was from their own family members or close contacts, then speculates that it is a strong tie. If the case is not clearly stated, we code it according to the household registration, work conditions, and travel conditions stated in the case. Therefore, the three routes of infection are not mutually exclusive in the data presentation. If it is possible to infect through one route, the code is 1, Otherwise 0. For example, if the patient has lived and worked in Hubei Province for a long time, and the place of infection is also in Hubei, the study speculates that she/he may be infected through three ways: strangers, weak ties and strong ties. But if the patient only stopped in Wuhan when the train returned to Shaanxi, the study speculates that he is only likely to be infected by a stranger. In addition, the study also counted whether patients had a relative infection.
Third, the Shaanxi Health Commission's data lists the patient's contacts with each other. Based on the case data, we construct a patient contact matrix in chronological order, visualize the daily dynamic network, and calculate the corresponding network indicators.

Results
Basic characteristics of patients with novel coronavirus pneumonia in Shaanxi Province. Table 1 summaries the frequency and percentage of related variables, which can outline the basic situation of patients. Specifically, there are slightly more male patients and slightly more patients infected in Shaanxi Province. About 59% patients may be infected by strangers, and about 60% may be infected by weak ties such as general colleagues and friends. About 74% patients may be infected by strong ties such as close friends and relatives. 37% patients' relatives were also infected, which indicates that there are more clustered infections in the province.     It shows in figure 3 that with time goes, the average onset time of symptoms has a tendency to increase, which means that the later imported cases are often patients with a longer incubation period. Therefore, they were not detected in the early stage. At the beginning of the epidemic, Shaanxi Province has adopted measures such as quarantine for patients with short incubation periods. It can be seen that with the change of time, the average diagnosis time has a decrease trend, which means that the later prevention and control measures are taken in a timely manner.
Many patients develop the disease during the quarantine period, which reduces the risk of spread caused by the virus incubation period.
The transmission route of novel coronavirus is mainly respiratory droplets and contact transmission.
From the perspective of social network, infection occurs in three kinds of connection: strangers, weak ties (such as ordinary friends, colleagues, etc.), strong ties (such as couples, family members, relatives, etc.). Figure 4 shows the types of contacts that patients may be infected with over time. In addition to the three main contacts, it also shows whether there is a relative infection of the patient.
The change in type of ties was mainly related to the number of people infected. Our main concern is the proportion of each infection route. It can be seen that the strong ties infection route has always been relatively higher proportion than other routes, which shows that the spread of novel coronavirus in Shaanxi is mainly cluster infection. This also shows that the epidemic situation in Shaanxi has been effectively controlled, and has not caused a large number of stranger infections that are most likely to cause panic. However, there was a relatively high outbreak of stranger infections on February 7, mainly because of the cluster infection in Xi'an Duocai Shopping Center, where customers and businesses were infected, and many of them did not know each other. Correspondingly, it also shows that the clustered strong ties infection is the way that needs to be controlled in the epidemic prevention and control, which is basically consistent with the conclusions of various previous studies. Figure  They were a couple, natives of Shaanxi, who had symptoms after return from Wuhan by driving. They went to local hospitals 5 days after they had symptoms. The source of infection for case 160 at a later stage could also be traced to this cluster. However, there are fewer new clusters in the later period, which indicates that the control of virus transmission is better. In the later period, only cases 234-237 formed a fully-connected component. They belong to one family. There are still many unconnected cases in the network, most of which are imported cases. It is no longer possible to track their infection source outside the province. Table 3 reports four centrality measurement of the contact network. Degree centrality expresses that, on average, how many other patients the focal patient has contact with, which is slightly larger than the basic regeneration number. Table 3 shows that the average degree of centrality is less than 1.

Dynamic Contact Network of Novel Coronavirus Pneumonia Patients
The smallest degree is 0. The largest is 11, indicating that the patient (case 26 in figure 5) has contacted 11 other patients. According to the degree of centrality, it can be speculated that the basic regeneration number of novel coronavirus in Shaanxi Province is less than 1, which means that the  Figure 6, we know that a small number of people have a higher degree of centrality. But only three patients have a degree of centrality greater than 5.
Most patients' degree centrality is zero. This shows that although the degree distribution of patients Declarations Figure 1 Age distribution of novel coronavirus pneumonia patients in Shaanxi Province, China.   Social network infection route of patients with novel coronavirus in Shaanxi Province.
Strangers refers to how many of the cases announced that day may have been infected by strangers. Weak ties indicate how many people may be infected by weak tie contacts.
Strong ties refer to how many people may be infected by strong tie contacts. Relatives refer to whether any of the patient's relatives are infected. Dynamic contact network of patients with novel coronavirus pneumonia in Shaanxi Province.
In the network, nodes represent patients, and edges represent transmission routes between patients. The larger the node size, the greater the number of the patient connected with.
The number on the node is the case number. The larger the number, the later the patient is  Distribution of degree centrality of contact network of novel coronavirus pneumonia patients in Shaanxi Province.