prediction of Corona Virus Disease 2019 based on SIR model in China

Background : From the end of 2019 to the beginning of 2020, the Corona Virus Disease 2019 epidemic occurred in Wuhan, China, and quickly spread to the whole country. We used SIR epidemic model to predict the epidemic trend in China. Materials and Methods: Respectively fitted the Corona Virus Disease 2019 epidemic trend equations in China, Hubei, and Wuhan, predicted future trends, based on the hypothesis of the infectious disease process by the SIR model and the official announcement data of the Chinese Health Commission . Results: There will be no new cases in the non-Hubei area nationwide after March 8; there will be no new cases in Hubei that non Wuhan after March 12; Wuhan will there be no new cases after March 22 ; Conclusions: The epidemic will end soon in China, under the prevention and control measures are not relaxed.


Background
From late 2019 to early 2020, an epidemic of Corona Virus Disease 2019OVID (COVID-19) occurred in Wuhan, China [1,2], which was nearing the traditional Chinese New Year, and the mobility of people was relatively large, so the epidemic quickly spread to all provinces across the country. on March 13, 2020, China had accumulatively confirmed 81029 patients, most of them in Wuhan, with 49995 cases.
As of March 13, 2020, a total of 66990 cases had been confirmed in the world except China, They were distributed to five continents, and more than 100 countries [3,4] . In some countries, the outbreak is still on the rise stage. As the Chinese government has taken a series of measures in time to stop the spread of infectious diseases, including blocking Wuhan and Hubei, delaying the start of construction and schooling, the epidemic situation in China has been in a significant decline.
Since ancient times, infectious diseases have never stopped attacking human beings.
It will threaten our health and life, trouble our lives, and have a serious impact on economic development. The fight between it with us have never stopped. In addition to studying how to eliminate it and how to prevent its spread, we also need to understand his development trend. People have established a variety of analysis models based on the characteristics of infectious diseases [5,6,7,8]

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The SIR model refers to dividing the population into three categories: Susceptible, Infective and Removed. The first letter of these three words combine called the SIR model. It was proposed by Kermark and Mckendrick in 1927 [9]. Later, it was used by many scholars for the evaluation and analysis of infectious diseases [10,11,12,13,14,15]. The susceptible person refers to the susceptible population that has not yet been infected. Many infectious diseases such as COVID-19 and SARS can infect everyone Susceptible here refers to all healthy people who are not infected. The infected person is the patient. He can infect healthy people and become patients.
Removed refer to Removed refers to a patient who has been cured to gain immunity or died, they will no longer be infected and will withdraw from the infection system.
This model is based on the following assumptions: 1. Suppose s (t), i (t), r (t) respectively represent the proportion of Susceptible (healthy people), infected people (patients), and removed in the total population at time t in the area. The total population Is a constant N, irrespective of natural birth rate and mortality, that is, s (t) + i (t) + r (t) = 1.
2. The average number of effective contacts per patient per day is a constant λ. λ is called the daily contact rate. When a patient is in effective contact with a healthy person, the healthy person becomes infected and becomes a patient. λ can also be called the daily infection rate.
3. μ is the removal rate, which is the proportion of removals that are cured and die from the patient daily.
The equation of the SIR model can be obtained: in formula (2) is equal to in formula (1), which represents the change of removal rate of patient, k = λ, l=μ， = , Formula (2) was used to verify the plague in Mumbai, India in 1905 [9], and some scholars have used it to verify the SARS epidemic in Beijing in 2003.
COVID-19 has a latency period of several days [1,2,16], and humans are infective during the latency period. When a healthy person is infected, he is asymptomatic at first, and it is not clear that he has become an infected person. He will pass the disease to other Susceptible people that he contacts until he shows symptoms and seeks medical treatment. Isolation and treatment will not infect others. Therefore, it is difficult to determine the number of infected people in the population, but we can know the number of confirmed patients. The confirmed patients are equivalent to the removed, because once the patients are diagnosed, they will be isolated and treated, and there is almost no infectivity to the population Although medical personnel have certain risks, we assume here that they are not infective.
Since the rate of change of removed is directly proportional to the number of infected persons, the daily rate of change of removed can represent the daily rate of change of infected persons. Therefore, according to the newly Confirmed diagnosis cases every day as change rate of removed, from January 20 to March 1, 2020, a total of 42 days of data, using Matlab software to fit the data curve according to formula (2) , The fitting formulas of Wuhan, Hubei (excluding Wuhan) and the whole country (excluding Hubei) were obtained, and the end time of the epidemic was estimated 7 according to the formula. The above data comes from the official announcements of the Health Commission of China, Hubei and Wuhan, and a small part of the data comes from Baidu big data.

Results
Figure1 is the daily number of newly confirmed cases in China (excluding Hubei), and Figure 2 is a graph of epidemic trends in China except Hubei based on data fitting. Since diagnostic reagents were developed urgently after the outbreak, its production capacity may not be able to meet the rapid growth of patients. There was also insufficient testing staff for many patients, leading to many patients had not being diagnosed with the etiology, but they are extremely consistent with the COVID-19 in clinical indicators. In order to get them treated in time, the health department decided to adopt a clinical diagnosis method. These clinically diagnosed cases were not diagnosed at one time. They were centralized and treated before this day, so they lost their infectivity before that. Equation (5) is a national non-Hubei region equation fitted with Matlab software.
Equation (6) is an equation in Hubei without Wuhan, and equation (7)  Wuhan is longer than in other parts of the country. in the initial stage and outbreak of infectious diseases, there will be a shortage of medical resources. In the early COVID-19 epidemic in Wuhan, lack of masks, protective clothing, wards, beds, medical staff, and nucleic acid testing reagents and personnel shortages will cause the epidemic expand. Later, these problems were resolved and the epidemic tended to ease.
In recent days, the epidemic has grown rapidly in many countries.

Conclusions
Based on the analysis of data and models for the COVID-19 epidemic in China, this article draws the following conclusions: The number of new cases in China (excluding Hubei) will return to zero after March 8.
The number of new cases in Hubei (excluding Wuhan) will be reset to zero after March 12.
The number of new cases in Wuhan will return to zero after March 22.
The government can consider building reserve wards and beds in hospitals in response to public health emergencies.
Masks and protective clothing are important protective materials for respiratory infectious diseases.

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The epidemic in China is about to end soon, but mathematical models have his limitations, and such predictions and data are based on the premise that current prevention and control measures are not relaxed. If there is some slack, the epidemic may be further expanded. It must be very different from the conclusion of this article.

Declarations：
Ethics approval and consent to participate: Not applicable.