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Mathematical Modeling of Covid-19

Background
The novel coronavirus (COVID-19) suddenly appeared in Wuhan, Hubei since December 2019, and quickly swept across China, then the whole world. Today, after more than 100 days of fighting against the virus, China's epidemic has been effectively controlled, but when we looking at the entire world, the novel coronavirus has rampaged globally, especially in the United States and many European countries. This paper mainly studies the impact of COVID-19 outbreaks at Hubei Province and the United States, fits the given data and predicts future trends.

Methods
Based on the theoretical basis of traditional differential equations and SIR infectious disease model1, and combined with the actual situation to improve the model. Hubei Province is modeled in different time periods, and the effects of birth rate and natural mortality on the model are analyzed. Since the birth rate and natural mortality in the United States in recent years cannot be found, the epidemic situation in the United States can only be analyzed based on the absence of births and natural deaths. Finally, we used Netlogo2 to establish a closed environment (Small World), and combined with known data to conduct simulation experiments on COVID-19 infection.

Findings
Through the analysis of given data through the SIR model, it is found that before the Chinese government has taken comprehensive measures to cure patients (before 10 February), the number of patients in Hubei Province will reach the peak at the end of February, and will gradually decline thereafter, and on 20 March, the epidemic will be effectively controlled in the future, which coincides with the fact that Wuhan closed the last mobile cabin hospital on 10 March. On the other hand, after the Chinese government tried its best to cure the patients (after 21 February), the number of patients continued to decline over time and will reach 0 in mid-April, which is also consistent with the actual data. According to the factors of birth and natural death, the sensitivity analysis of the above model found that when the epidemic situation is at its peak, it has little effect on the curve, but when the epidemic situation gradually flattens, it still has a certain effect on the trend of the curve. Finally, looking at the situation in the United States, due to the high transmission rate, the number of patients in the United States continues to rise and is expected to reach its maximum in mid-June. We also use Netlogo to simulate the environment in which the virus spread, and find that the general trend of the curves is also consistent with the actual curves.

Interpretation
The Chinese government has taken various measures to deal with the novel coronavirus pneumonia, including the establishment of two temporary hospitals and dozens of sheltered hospitals, the temporary transformation of university dormitories into isolation rooms3, 4, 5, the closure of Wuhan, the ban on the movement of people and so on. These measures have helped to reduce the spread of the virus and greatly increased the patient's cure rate. But the US government ’s actions are not as effective as China’s, not only because the government ’s actions are inappropriate and untimely, and the people’s opposition to isolation has not subsided. As a result, the virus has spread widely in the United States. More than one million people have been infected with the virus, and tens of thousands of people have died from COVID-196.