Machine Learning Classifiers Help to Manage COVID-19 Distribution in China
The coronavirus disease 2019 (COVID-19) first appeared in Wuhan, China in December 2019. It spread very quickly from Hubei to the rest of China within only 30 days [1]. As of February 14, 2020, 78.91% of the total confirmed cases in China were in Hubei province which is in midland China and 60.33% of the total confirmed cases in Hubei were in Wuhan [2]. In this project we use K-Means clustering and regression analysis to classify the cities in China based on location and infection rate. The goal is analyzing the demographic and geographic characteristics of the clusters containing less than 5 members with high infection rate. We found that all the cities in the smal (Preprint)
Authors: Rahmani Bahareh , Wei Jasmine , Yao Mingxuan , Alsahfi Zakaria , Ye Taiping , Snir Eli 
Published: January 2022

BACKGROUND

COVID 19 is an infectious disease which is caused by the coronavirus. It is currently spreading worldwide at a faster rate since it was first reported in Wuhan city in China in 2019 [3]. WHO declared COVID 19 as a world pandemic in March 20 and as of now, there are almost 108 million confirmed cases and over 2.4 million deaths [4]. It causes a painful breathing human disease, which has taken a large number of lives [3]. Cities in China have managed the spread of this virus [5]. This regional spread of the virus seems to have had a major effect on the social, political, economics, and environment in different countries that have altered existing interactions [6].
To manage COVID-19 countries have enacted several measures such as travel bans, the use of masks in public places, and social distance [7]. In China, there were several measures placed which include: active case surveillance, environment sanitation and disinfection, strict quarantine and follow-up, public awareness through reporting of confirmed cases, and many others [8]. There is also monitoring of people's body temperatures in the railway, airport, freeway toll station, subway entry, neighborhood entry point, and so on [8].
This research uses K-means clustering to define data subtypes in such a way that datasets are nearly identical in the same cluster [9].
We describe the data in section 2. Methodology, including regression analysis and k-means analyses, comes in section 3. We will show the results and discussion in section 4. And finally is section 5 we suggest ways to stop the spread of this virus.

OBJECTIVE

COVID19 data are from all 329 cities in China from March 2020 to June 2020. The data was collected from WHO reports on the coronavirus and National Health Commission (NHC) [4]. Features included are the population of all cities in China, their location, and region. Total confirmed (Tc) cases are collected to be used in the analysis and management of this virus. The spread rate is calculated by dividing Tc by the city’s population:
T_C/population∙10,000=Spread Rate,

METHODS

3.1 K-Means Clustering
We built K-Means clustering model over 329 cities in China. The analysis divided cities into 20 clusters to check the relationship between China cities' confirmed cases and geographic location of cities. The K-Means clustering algorithm divides the data into k-clusters such that similar cities are grouped together. Based on the measure of Tc we define the “distance” between cities. The algorithm minimizes distances within clusters, while maximizing the distance between clusters . Each cluster represents the mean value of cities within the cluster [10]. The cost function of the K-Means clustering is the distances between the observations in the cluster and centroid. The objective function finds the best k value that minimizes the cost function [11]. K-Means clustering method is applied to maximize the Silhouette values of cities and their respective cluster centers. The Silhouette is a method to evaluate the validity of clusters. It finds out the optimum k value by a ratio scale data (as the method of Euclidean distances do) that defines well-separated cluster [12]. We measured the Silhouette values of all clusters with different k values and chose the best k. Higher Silhouette values indicate better clustering. We found that when k equals 20, the Silhouette values are largest, indicating the best clustering within the Silhouette method.
K-Means is an unsupervised learning method. So the label of clusters are not important. In this study we used both supervised and unsupervised learning methods to make our results stronger.

3.2 Linear Regression
One approach to evaluating how geographic, demographic, and economic factors affect the number of cases of Covid-19 is through supervised learning using linear regression. We hypothesize that these three factors are related to the number of cases of the virus in 08-2020. The data for 329 cities in 8 geographic regions allows evaluating several such models.
In developing the regression model, we made two decisions. The first involves incorporating the geographic data. The second focuses on how to view the large heterogeneity in the number of cases of Covid-19. As seen everywhere in the world, Covid-19 appears to be highly concentrated in some cities, while other cities may exhibit only a few cases. One approach is to treat this variation as reasonable. The drawback of this approach is that cities with large concentration of Covid-19 have a substantial effect on the results of the model. Another view is that there are numerous outliers in the data. If the objective of the model is to evaluate average effects, outliers should be removed. Each approach has its merits. We present both sets of results in section 4.

RESULTS

The bubble chart of Figure 1 shows the classification result. The diameter of the circle is proportional to the number of cities in the group. The numbers inside each circle is the spread rate value for the cities.
There are 6 clusters that have fewer than 5 cities and spread rate higher than 2.8. We would discuss the demographic and geographic characteristics of these clusters and explain why these cities have high spread rate. Below is the map of Hubei Province in Midland China (Figure 2), where most COVID-19 cases were confirmed, the map illustrates the geographic distribution of cities in Hubei Province [13].
Cluster 1: Wuhan
Wuhan is the only city , in Cluster 1. Wuhan is the first city in China where COVID19 was identified. [14] Wuhan has the largest TC_pop of around 45 (per ten thousand population). Also, with its huge population of 11 million people and great population density, Wuhan is exposed to the risk of rapid increase in COVID19 cases in a short period. As a transmit center in Mildland China, Wuhan has a well-connected network of transportation. People from nearby cities pour into Wuhan for employment and education opportunities. Another reason that causes the large number of cases is that Wuhan is a tourist city, travelers increase the regional density of population, thus making it easy for COVID19 to spread in Wuhan.
Cluster 2: Huangshi and Huanggang
These 2 cities are in the same province as Wuhan (Hubei Province) and both are in Midland China. Though the population of Huanggang is about three times that of Huangshi, the by 2nd of August, both cities have similar spread rates (Tc) of 4.1-4.6. Neither of them is a tourist city, so the floating population of the two cities tend to be small. However, when we look at the geographic location within the Hubei Province of the two cities, we find that Huangshi and Huanggang lie at the two sides of the Yangtze river, which is the longest river in China. Cluster 3 is charcherized by, similar spread rates, tourism development, and geographic location.
Cluster 7: Ezhou
What distinguishes Ezhou distinguished from other clusters is its middle-sized population and high spread rate. This may be because Ezhou is geographically close to Wuhan, the capital city of Hubei Province, and thus many people go to work in Wuhan during the day and return to Ezhou where they live. As a result, the city has very large number of confirmed cases of COVID-19.
Cluster 12: Xiaogan
As a city of Hubei Province, Xiaogan lies on the northern part of Yangtze River. Xiaogan and Wuhan are located across the Yangtze River. Xiaogan is a mid-sized city with a population of around 5 million, but by 2nd Aug 2020, it is populated with 3,518 cases. It has a large TC_Pop of 7. Like Ezhou in cluster 7, Xiaogan is in Cluster 12 alone because of the change in the infected population in the short time span and the relatively large spread rate. Just as Ezhou, Xiaogan is grographically close to Wuhan, and maybe this closeness explains why some nearby cities of Wuhan are in clusters by high spread.
Cluster 13: Jingmen, Jingzhou, Xianning
All the cities are from Hubei Province in Midland China. None of them is a tourist city. Jingmen and Xianning have similar populations, while Jingzhou has twice the population. The number of confirmed cases in Jingzhou is twice that of the other two cities, yielding a spread rate for the three cities of around 3.
Cluster 15: Suizhou
Suizhou is 200 kilometers away from Wuhan. [15] Compared with Xiaogan, Huanggang and Huangshi, Suizhou is far away from Wuhan. According to the statistical yearbook of 2019 published by Hubei Province, Suizhou City has a population of 2.22 million, ranking 12th in the province; Suizhou's GDP is 10.11 million yuan, ranking 11th in the province. [16] These data make Suizhou look nothing special. Let's take a look at the Suizhou’s epidemic data. Even in the early stage of prevention and control, Suizhou had a large number of infections. The infection rate (TC_Pop) of Suizhou was the fourth in Hubei Province. The characteristics of cities with large number of confirmed cases in China are as follows: 1. Close to Wuhan; 2. Large population; 3. Frequent contact with Wuhan. Suizhou is a city in Hubei Province, which does not have the above three characteristics, but still has a large number of confirmed cases. This underscores the complexities of managing a virus such COVID-19, and the need for statistical modeling to identify drivers of the spread of the virus.
4.2 Linear Regression
The data includes 329 cities in 8 geographical regions. By looking at the distribution of cities to regions, we chose the Southwest region as the base category. One justification is that it has a fairly large proportion of the cities at 16%. It also has one of the lowest number of cases at 27.87 in an average city. Our linear regression model forecasts the number of cases as a function of Population (in tens of thousands), a binary variable for whether the cities enjoys strong tourism, and the remaining 7 regions.
We present 2 regression models. Model (a) includes all 329 cities. In Model (b) we use an iterative approach to removing outliers. Since the number of Covid-19 cases is highly concentrated in a few cities, these cities can be viewed as outliers. If the purpose of the analysis is to evaluate average effects of the number of cases of the virus, outliers should be removed. As seen in Table 3, the differences between the models are substantial.
The iterative method for removing outliers developed several regression models. In each step we identified those cities with Studentized Residuals more extreme than ±3.5. These observations are deemed outliers. (This is justified under the assumption of a Normal distribution for the errors.) These outliers are removed and the regression is developed again. In the first step, only one observation is removed (Wuhan). In the second step, 5 more observations are removed. In all, 43 cities were removed in 14 iterations.
The two models present very different pictures regarding the number of Covid-19 cases in China. Both models conclude that Midland China experiences more Covid than the Southwest region. They also both recognize that tourism is an important factor in the spread of the virus. That’s about all the models have in common. Even the magnitude of the coefficients is substantially different in both models.
Based on table 3, from Model (a) one concludes that the average number of Covid-19 cases in a city in the Midland region is 1,000 more than in the Southwest region. We reject the null hypothesis, although only at a p-value a bit below 0.05. Here the null hypothesis evaluates whether the number of cases is the Midland region is identical to the number of cases in the Southwest. The conclusion is that there is a statistically significant difference.
In contrast, Model (b) finds that the difference between the Midland region and the Southwest is only 23.8 cases, in an average city, but it significant even at a very low p-value. The difference is quite stark. The reason for these differences is that Model (b) does not include cities with the highest number of Covid-19 cases, including Wuhan. Removing these outliers may give us a better identification for the average effects of different factors.
Looking at regional differences, Model (b) also identifies that two more regions have statistically significant more cases than the Southwest. These are the East, at almost 8 more cases in an average city, and the Northeast, and almost 9 more cases. It may be interesting to note that both models do not identify significant differences for other regions in China.
The other common significant factor in both models also emphasizes the differences in the models. Model (a) suggests that a tourist city has 2,527 more cases than one without tourism. In model (b) the result is substantially subdued at only 18.5 more cases. Again, removing Wuhan and a few large outliers is at the heart of these differences.
The one other finding from Model (b) is that population is a statistically significant driver for the number of cases. Larger cities do have more cases of Covid-19, at approximately 1 more case per 10,000 population. We now see that the result is significant at even very low p-value. This result isn’t observed in Model (a), because Wuhan and other moderately-sized cities incur the vast majority of Covid-19 cases in China. For example, Wuhan has over 50,000 cases, while Beijing and Shanghai, much larger cities, have less than 2,500 cases each.
From a statistical perspective, Model (b) is much better, which shouldn’t be a surprise. Model (b) has few outliers. For Model (a) the R2 is 0.072, while the RMSE is 2,722.8. In Model (b) these are 0.584 and 15.92, respectively. Overall, both models are statistically significant.From a statistical perspective, Model (b) is much better, which shouldn’t be a surprise. Model (b) has few outliers. For Model (a) the R2 is 0.072, while the RMSE is 2,722.8. In Model (b) these are 0.584 and 15.92, respectively. Overall, both models are statistically significant.

CONCLUSIONS

The regression results confirm the need for Cluster Analysis. From the regression, we see that traditional supervised models identify many cities as outliers. The Cluster Analysis is an effective way to deal with outliers. The multiple clusters capture substantial differences across cities. Many of the outliers removed in Model (b) of the regression are clustered into a few different groups. For example, the extreme number of cases in Wuhan lead to it being in its own cluster. Other cities, near Wuhan, were also clustered together.
The regression model is effective at identifying average trends in the data. After removing outliers, we see the importance of city size on the spread of the virus. Tourism, which is hypothesized to be important in the cluster analysis, is now quantified. Even after removing outliers, tourism cities have 18 more cases than cities without tourism. The regression model also accentuates regional differences. Some of the results from the regression model are not highlighted in Cluster Analysis.
In summary, unsupervised and unsupervised learning methods complement each other when investigating the spread of Covid-19. With frequent “bursts” in the spread of the virus, unsupervised models provide insights into the outliers. Those cities with very high or very low spread are identified. Conversely, there is also a need to understand the average spread of Covid-19. For that, a regression model is useful. Together, these types of models help policymakers effectively allocate limited resources to combat Covid-19.