This paper selects 50 states from the US for research. The data of the COVID-19 mainly came from the data of the New York Times, including the date of diagnosis, the current area, and the source of infection of patients with COVID-19. Demographic data mainly came from the US 2020 census data, the basic geographic information data of each state were derived from Google satellite map data, and the latitude and longitude coordinates mainly chose the state capital as the center position.

The variant data are derived from the Centers for Disease Control and Prevention (CDC) study that tracks the proportion of variants estimated from weekly random sampling in the Department of Health and Human Services region followed by gene sequencing tests across the region, which we use to estimate the number of variant infections in the state over a week with new cases per day.

We use the retrospective spatiotemporal analysis method, and choose the discrete Poisson model. The scanning time is set to be from 1 December 2021 to 31 January 2022, and the time interval is 1 day. As COVID-19 is highly contagious, the population with a ceiling of 50% in the space window is at risk, and the maximum circle size file is set at 30% of the population, rather than 30% of the regular population, and the regional overlap is set at zero. Referring to a large number of relevant literatures, combined with the actual situation, it is known that the outbreak of COVID-19 is fast, and the incubation period is short. Besides, the inaction of the US government to manage the outbreak makes the cycle longer. The daily pattern of COVID-19 changes rapidly, so the minimum time cluster is set to 1 day. In the test window, the number of Monte Carlo random simulation is set to 999.

In the population distribution, the US COVID-19 has nothing to do with gender, and included patients mainly in the age group of 44 to 59 years. In terms of time distribution, the US had the largest number of new cases on 10^th January, with 1,420,374 cases. On 3^rd, 18^th, and 24^th January, more than 1 million new cases were added daily with 1,003,751, 1,173,885, and 1,025,999 cases, respectively. In terms of the overall trend, the outbreak in the early stages of each state is relatively serious, and the number of confirmed cases has experienced a short lag and rapid growth. From Figure 1, we can see that the overall epidemic situation has not been effectively controlled, so the number of confirmed cases has increased cumulatively, having a certain increasing tendency. In the regional distribution, cases were mainly concentrated in the east and west of the US, and California has the largest number of confirmed cases, followed by New York.

A retrospective spatiotemporal analysis is carried out in the US. After SaTScan 9.5 is run, 17 clustering areas are obtained and arranged from large to small according to the log-likelihood ratio, and we obtain p < 0.01. The clustering areas are tested by the aboriginality test. The specific data are summarized in Table 1.

The cluster areas are mainly concentrated in Connecticut, Rhode Island, New York, Massachusetts, New Hampshire, and New Jersey from 1 December 2021 to 31 January 2022. The log-likelihood ratio is 101,152.56, and the aggregation is the highest, with a relative risk of 1.28. It also shows that the aggregation of COVID-19 in the six places during this period is strong. From 1 December 2021 to 31 January 2022, 18 states, such as Colorado, become the second agglomeration, with a log-likelihood ratio of 52,598.68 and a relative risk of 0.86. Texas from 1 December 2021 to 31 January 2022 is one of the three types of gathering areas, with a log-likelihood ratio of 42,332.33 and a relative risk of 0.81.

Combined with the daily incidence of each state, it can be observed that the starting time of the gathering area is just the time for the sudden increase of the confirmed cases of COVID-19 in the region, and the end time is the time for the growth rate of the confirmed cases to begin to decline. Combined with Table 2, the incidence of the four states involved, Rhode Island, New York, Massachusetts, and New Jersey, accounts for the top five regions of the incidence of COVID-19 in the US, and New York is the city with the second largest number of confirmed cases. Although Massachusetts and New Hampshire have fewer confirmed cases than New York, they are geographically close to New York, where the epidemic is relatively serious.

Since the research time is 62 days, we divide 360° evenly over each day, then 1 day is equivalent to 5.81°, and 1 h is equivalent to 0.21°. To avoid the infinite calculation, the calculation time of each day is 8:00 a.m., that is, the one-third corresponding degree of 1 day is taken as the degree of the day. By the spatiotemporal scanning analysis, we obtain 17 clustering areas, and take the first three clustering areas as example. In order to compare the following analysis results to previous ones, we combine the daily newly confirmed cases according to the clusters. The r, r₀, and p-values of Rayleigh test are obtained through calculation, as summarized in Table 3.

The peak day and peaks of each cluster are summarized in Table 4.

Hierarchical cluster analysis method is commonly used in classification research. This method can overcome the shortcomings of qualitative classification. According to the index characteristics of the classification object, the total feature similarity is divided into a class. In this case, the cumulative confirmed cases, the regional population, and the incidence rate are used as the indicators of each region, and imported into R software for standardization. The deviation square and clustering analysis are used to divide them into four categories. Since the latitude and longitude coordinates are involved in the spatiotemporal scanning analysis, the central coordinates of the capital are added to the index, as shown in Figure 2. Due to the mess up of text and pictures as displayed in the diagram, it should be replaced with a geographical code (US-01), as shown in Table 5.

From Figure 2, we can see that there are highly correlated with geographical location. The same category of states are adjacent states, and the case information is not reflected. Therefore, the clustering method cannot well-balance the relationship between the number of cases and their geographical locations.

The peak periods calculated by spatial-temporal scanning analysis are compared with those calculated by circular distribution method, as shown in Table 6. Combined with the actual situation, the peak period of the disease obtained by the circular distribution method is similar to the epidemic situation of COVID-19 in the region. The peak period of the disease obtained by the spatial-temporal scanning method is longer than that of the circular distribution method, and the time is generally advanced. Spatiotemporal scanning analysis can send early warning signals for COVID-19, which is a kind of fulminant and fast infectious disease, and has a higher practical value for disease prevention and control.

The clustering areas obtained by spatiotemporal scanning analysis are compared with the classification results obtained by the system clustering method, as shown in Table 7. In the Spatiotemporal Scanning Analysis (STSA), Hierarchical Cluster Analysis (HCA), and Coordinated Hierarchical Cluster Analysis (CHCA), US-44 (Rhode Island), US-25 (Massachusetts), US-09 (Connecticut), US-34 (New Jersey), and US-33 (New Hampshire) are classified into the first category, while US-36 (New York) is classified into the first category by spatiotemporal scanning. Combined with the actual situation, it can be seen that the results have a great relationship with the cumulative confirmed cases. After adding the coordinate index, the results are highly correlated with the geographical location, and the case information is weakened. The spatiotemporal scanning method makes good use of the information of regional population, case information, geographical location, and other information to give a reasonable clustering area. In terms of disease prevention and control, spatiotemporal scanning method can better provide theoretical basis for its adaptation to local conditions.

Through the abovementioned comparative analysis, it can be seen that the circular distribution method and the space-time scan method have a certain overlap interval in the peak period of disease onset, and the clustering analysis method is certainly similar with its regional aggregation. However, the spatiotemporal scanning method can provide early warning and make better use of geographical factors to determine disease outbreak areas in detail, which is more instructive for the early warning and prevention and control of COVID-19.

The spatiotemporal scanning method can provide more objective grouping basis for the further model establishment of related research. According to the epidemic law of different regions, different groups can be included in different covariate modeling. The qualitative and quantitative research on the influencing factors of COVID-19 will provide an important basis for the development of effective epidemic prevention measures by health institutions such as disease control centers in the region by analyzing the incidence characteristics of patients with COVID-19 in different regions and at different times, and combining the economic level, population flow, medical conditions, and other factors in the region.

In the study of infectious diseases, we cannot ignore the situation of some variants. Based on the time node selected in this paper, the first Omicron case was reported in the US on 1 December, so we are paying attention to Omicron at this stage. Next, we need to know more about Omicron. In fact, Omicron has a significant growth advantage over Delta, leading to rapid spread in the community with higher levels of incidence than previously seen in this pandemic. With the sharp increase of cases and the scarcity of medical resources, we should also give importance to its dissemination.

From Figure 3, we can see that the B.167.2 (Delta) accounted for 99.25% on 4 December, while B.1.1.529 (Omicron) accounted for a low proportion. After 2 weeks, the proportion of Omicron increased rapidly, reaching 40.64%, while the corresponding Delta decreased to 58.08%. After another week, the proportion of Omicron exceeded Delta, becoming the largest variant of infection. After the following 5 weeks, the proportion reached 95.31%. Within 2 months, Omicron became the mutant with the largest proportion of infection, and its propagation speed was very fast.

Based on the CDC's tracking data of variants and the prediction of the proportion of variants, we calculate the number of variants per week in different regions according to the new cases per day and the proportion of variants per week in the corresponding region. The following figure clearly shows the cumulative number of Omicron cases in the last week. In order to show the map integrally, US-02 and US-15 have changed the actual location in the map. According to the number clustering, the map is divided into four categories. We can find the features in Figure 4.

The numbers of items in clusters 1–4 are 18, 29, 2, 1, respectively, and the cluster centers are 89,703, 24,703, 217,010, 507,330 respectively, in Figure 4. The number of Omicron cases increases rapidly in 2 months, with the largest number of cases in one state, US-06, accumulating to 507,330 per week, and also with the largest number in neighboring states.

To summarize, it can be clearly seen that the rate of infection of Omicron increased rapidly, and there is a trend of diffusion from the middle to the surrounding. Population flow is one of the reasons for the rapid spread of virus. The reality of the spread from densely populated cities to other cities can also be observed from the distribution map of Omicron cases.