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Specialty section: This article was submitted to Social Physics, a section of the journal Frontiers in Physics

This is an open-access article distributed under the terms of the

In this study, the trend of the epidemic situation of COVID-19 is analyzed based on the analysis method for network topology. Combining with the sliding window method, the dynamic networks with different topologies for each window are built to reflect the relationship of the data on different days. Then, the static statistical features on network topologies at different times are extracted during the dynamic evolution of complex networks. A new trend function defined on the average degree and clustering coefficient of the network is tailored to measure the characteristics of the trend. Through the value of the trend function, we can analyze the trend of the epidemic situation in real time. It is found that if the value of the trend function tends to decrease, it means that the epidemic will have to be effectively controlled. Finally, we put forward some suggestions for early control of the epidemic.

Since December 2019, patients with pneumonia of unknown cause have appeared in some medical institutions. By now, the number of cases caused by coronavirus (COVID-19) has increased. The World Health Organization (WHO) declared the COVID-19 disease a pandemic on March 11, 2020. The cumulative confirmed cases have reached almost 3,220,000 as of May 1, 2020 worldwide. For new outbreaks, it is significant to understand the transmission dynamics of infection, which can help governments take effective measures to contain them and reduce the number of spread. In the survey of other two pandemics caused by coronavirus severe acute respiratory syndrome coronavirus (SARS-CoV) and Middle East respiratory syndrome coronavirus (MERS-CoV), scientists have put forward many effective measures to build the transmission models, such as the transmission analysis based on genome research (

Since the outbreak of COVID-19, scholars have conducted relevant research through different models. Zhu and Chen give a statistical analysis of COVID-19 with early transmission model (

With the development of complex networks, the spread analysis of epidemics on complex networks has attracted wide attention in the literature. Based on the SIR model in complex networks, Xia et al. have investigated the effects of delaying the time to recovery and of nonuniform transmission on the propagation of diseases on structured populations (

In the study of complex network diseases (

The article is organized as follows.

This section introduces the construction of the networks and the topological features extracted from the networks.

Here, we select four regions for the analysis, including Wuhan, South Korea, Russia, and Germany. The total number of confirmed cases is extracted for every day in each region. We get a time series

The dynamic evolution analysis method is an important way for data analysis based on the features of network topology. In dynamic evolution, the feature measurement of networks is a function of time. In the same evolution mode, two subnetworks obtained at different times have different features. Therefore, it is a very important and effective way to analyze and classify the network by using static statistical features at different times during the dynamic evolution of networks (

Sliding windows are used to form the time series. The length of sliding windows is chosen as 9 days, and the step size is 1 day. The figure shows the process of constructing time series.

For one of the sliding window

The degree

In this section, we combine the daily number of confirmed cases in Wuhan, South Korea, Russia, and Germany to build the networks and analyze the epidemic situation in the four regions through the topological characteristics of the networks.

We use the daily number of diagnoses from January 22, 2020 to May 16, 2020 as the data set. So, for each region, we can get the total number of diagnoses per day for 116 days. First, from

Networks at the 43rd day of the four regions. The number of connections in the network reflects the change degree of nine-day growth rate.

We use the equations in

Growth rate and the evolution of trend function of Germany.

The evolution of the trend function in the four regions is shown in

Evolution of trend function for the four regions: Wuhan, South Korea, Russia, and Germany. The value of the abscissa is the number of days passed from January 22, 2020, and the ordinate is the value of the trend function I. The larger the I value, the larger is the clustering coefficient and mean sum.

From

In

From above analysis, we can analyze and predict the epidemic situation in South Korea and Russia. From

Note that the effective control of the epidemic in this article refers to the fact that the daily growth rate is almost zero, that is, there is almost no new infection, rather than the change in the daily growth rate of 0, or in other words, the next day is approximately equal to the daily growth rate of the previous day, as mentioned in some articles. For example, for the platform period mentioned in

In this article, we proposed a trend analysis method based on network construction with sliding windows to extract the characteristics of network dynamic evolution over time and analyzed the epidemic trend in four typical regions. In the analysis, we found that some regions had better control of the epidemic, while others were still in the process of outbreak. So, we put forward some suggestions and hope that the epidemic situation in various countries can be effectively controlled as soon as possible.

The proposed method in this article is easy but efficient for the trend analysis of COVID-19. In general, since COVID-19 patients’ mid-term course of disease develops rapidly, it is hard to accurately judge the cycle from mild to severe. Moreover, the issue of infectivity in the incubation period and the infectious power of those infected patients during the recovery period remains to be studied, which may be the cause of second outbreak in Germany. The intensity of different infection generation and the difference of infection are still unknown. The question of whether the virus will disappear or persist in the population remains to be resolved.

Many countries have taken effective measures to the epidemic, such as closing churches, bars, and gymnasiums. In severe cases, some countries such as China seal off the city from all outside contact to stop the spread of the plague. We can learn from the above analysis that Wuhan has got the epidemic under control in a relatively short time. In order to block the transmission chain of the virus, it is a very effective method to trace the confirmed patient’s activity route and contacts. For countries like Russia where the epidemic is still serious, which can be observed from the trend in

Publicly available datasets were analyzed in this study. This data can be found here

JZ and QL designed and performed the research. JZ, YJ, TL, and HL wrote the manuscript.

This work was supported in part by the National Natural Science Foundation of China under Grant 61876036.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.