The authors have declared that no competing interests exist.
The novel coronavirus (COVID19) 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 COVID19 outbreaks at Hubei Province and the United States, fits the given data and predicts future trends.
Based on the theoretical basis of traditional differential equations and SIR infectious disease model
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 midApril, 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 midJune. 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.
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 rooms
With the outbreak and spread of the COVID19, the Chinese government decided to suspend work and schools, and closed down the entire Hubei Province. With the active cooperation of the central leadership and people, we take strong measures to prevent and control the epidemic
Although the epidemic of China has been effectively controlled, COVID19 is rampaging around the world by now, with the United States affected the worst. Therefore, the current study of the epidemic situation will not only have a significant influence on the future development of our society, but also through theoretical thinking, accumulate more important experiences and lessons, and provide a good reference value for the future outbreak of the virus, creating conditions for the prediction and control of the spread of infectious diseases.
At the same time, the analysis of foreign epidemic situation, confirm the truth of the Human Community of Destiny. Only to understand the epidemic situation abroad, can better prevent and control foreign imports and avoid the domestic reoutbreak of the COVID19 infection.
In fact, there are many imminent questions about the spread of COVID19. How to analyze the development trend of epidemic situation in China and the United States? When will the inflection point of the infection rate appear in the United States? Can existing interventions effectively control the COVID19? What kinds of mathematical models are available to help us answer these questions?
The data source of Hubei Province is based on the authoritative data released by Health Commission of Hubei Province on its official platform starting from 20 January, 2020. The Hubei Province’s data collected in this paper is from 23 January, 2020 to 28 April, 2020, including cumulatively diagnosed cases, cumulative deaths, and cumulative cures
Based on all the data we have, since COVID19 is a pandemic, we establish a model of epidemic
However, due to the limited data we have collected, in particular the number of asymptomatic infections that were not officially announced until 31 March, we can only model based on known data, including cumulatively diagnosed cases, cumulative deaths, and cumulative cures. Therefore, we choose the SIR model as the basic mathematical model, and combine with some other factors to modify the differential equation system to make it more realistic
The same is true in the United States, where the SIR model can only be built with limited data. However, we do not decide to divide time periods like what we do to analyze the data of Hubei Province, because America is not able to control the situation by now, there is no point to do that.
At last, by the data we analyze in Hubei Province and America models, we create a closed community to simulate virus spread through Netlogo.
As shown in the following
As the
On the other hand, as it is discussed earlier in the paper, we have not collected birth and natural mortality in the United States, so when modeling the United States, we can only assume that no one is born and died naturally. Because the situation in U.S. is not optimistic, we decide that we model it in just one period, and the rest of which is the same as Hubei Province.
The symbols we use to establish the model are followed in
Classes  Explanations for different classes 

People who may be infected by the COVID19 

People who are infected with the virus currently 

People who are cured after infection and would not be reinfected by COVID19 and people who died because of the COVID19 
Classes  Explanations for different symbols 

Population in total 

Birth rate 

Natural mortality 

The novel coronavirus pneumonia mortality 

Spread rate 

Spread rate in before control period 

Spread rate in after control period 

Cure rate 

Cure rate in before control period 

Cure rate in after control period 
Through the above two figures, we can get the corresponding differential equation expression. The amount of change of the infected person during this period of time (t+ Δt) is
And expand (t+ Δt) using Taylor's formula, we can get
Then the equation could be changed into
Because the number of the infected is declining, we can convert equation into
If we consider the influence of birth and natural death in Hubei Province model, which is divided into 2 periods to study, we improve the equation to ((1), (2)stand for Hubei Province)
If we do not consider the influence of birth and natural death, the equations would be changed to ((3), (4), (5),stand for Hubei Province, stands for America)
By using a simulation software called Netlogo, we create a SIR model that simulates virus transmission using the builtin simulation repository. The parameters that are set, including total number, virus transmission rate, cure rate, initial number of cases, etc. We set these parameters based on the actual data, the specific parameters are set as follows.
This simulation takes place in a closed environment (Small World) and assumes that no one is born and died naturally. But unlike the
This paper uses the known data, takes days as the basic time unit, and determines the parameters (spread rate
The values of the remaining coefficients (
The specific parameters and coefficients settings are shown below. ((7) stands for considering births and natural deaths, (8) stands for not considering births and natural deaths)
The final fitting results are shown in the
The final fitting results are shown in the
As can be seen from the above Figures, the simplified model fitting effect is much better. And according to the analysis of the figure, the turning point will be reached in about 35 days from 23 January, and the infected will gradually decline thereafter. According to the predicted curves, around 20 March, under the effective control of the country, there will be no major changes in the future, which is quite consistent with the fact that the last mobile cabin hospital of Wuhan was closed on 10 March and the epidemic has been effectively controlled
The final fitting result of the United States is shown in the
It can be seen from the
The final simulation fitting result is shown in the
We used the parameters listed in
There is no doubt that the propagation of COVID19 in the population will be affected by the intricacies of many factors.
In the establishment of the epidemic model in Hubei Province, we divide the time of the use of the mobile cabin hospitals into two periods: before and after control. And we provide the data of spread rate and cure rate for comparison, based on the actual situation of the novel coronavirus during transmission. At the beginning of modelling, the birth rate and natural mortality are taken into account, and there are some deviations with the actual data. Therefore, a simpler model is selected later. The birth rate and natural mortality are not taken into consideration, and the predicted results are more consistent with the actual data. Thus, it is concluded that the impact of births and natural deaths on the curves is more and more obvious with time.
For all models, although parameters such as spread rate and cure rate are difficult to determine, we estimate them roughly based on the early data, and then realize the parameter optimization with the
Our model of infectious disease which is established by ordinary differential equations has a wide range of operating prospect, except for infectious disease itself (
Classes  Corresponding infectious disease model  Explanations for different classes 
ManagementAccounting Practice  Source of infection  Enterprises introduce new management accounting practices 

People who are possible to be infected by COVID19 but not yet  The learning cost, information collection cost, businessadjustment cost and income balance caused by the new management accounting practice, and the net income will affect the employee group with lessimpact 
Supporter(I)  People who are infected by the viruscurrently  The group of employees with increasedtangible andintangible benefits 
Opponent(R)  People who are cured after infection and would not be reinfected by COVID19 and people who died because of the COVID19  The group of employees whose cognitive costs andinformation collection costs become larger, their benefits become smaller,and their overall net income are negative 
For the analysis of the epidemic situation in Hubei Province, only divide the time line into two periods, which are before and after control, is not enough at all. The parameters will definitely change with time in the actual situation, whereas it is hard to determine the equations of those parameters. Besides, because the data of asymptomatic infected persons are released late, we cannot establish SEIRbased model for fitting and prediction.
When fitting the model of Hubei Province, it is obvious that there is a sudden deviation between the actual
In the analysis of the U.S. epidemic, because of insufficient data, the impact of the birth rate and mortality on the U.S. epidemic is not considered.
In addition, none of the established models divide infected people into isolated and unisolated individuals, or whether they receive effective treatment after being isolated. This is because in the early stage of the outbreak, countries are not fully prepared for epidemic prevention, thus leading to the future to the failure of some patients to receive timely treatment.
We have no conflict of interests to disclose and the manuscript has been read and approved by all named authors.
This work was supported by the Philosophical and Social Sciences Research Project of Hubei Education Department (19Y049), and the Staring Research Foundation for the Ph.D. of Hubei University of Technology (BSQD2019054), Hubei Province, China.