Journal of Current Scientific Research

Journal of Current Scientific Research

Current Issue Volume No: 1 Issue No: 1

Review-article Article Open Access
  • Available online freely Peer Reviewed

  • Mathematical Modeling Of Covid-19

    Zhao Bin 1
        Jiang Xia 2     Cao Jinming 3    

    1 School of Science, Hubei University of Technology, Wuhan, Hubei, China. 

    2 Hospital, Hubei University of Technology, Wuhan, Hubei, China. 

    3 School of Information and Mathematics, Yangtze University, Jingzhou, Hubei, China. 

    Abstract

    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 rooms345, 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.
    Author Contributions
    Received May 12, 2020     Accepted Jan 13, 2021     Published Jan 20, 2021

    Copyright© 2021 Zhao Bin, et al.
    License
    Creative Commons License   This work is licensed under a Creative Commons Attribution 4.0 International License. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

    Competing interests

    The authors have declared that no competing interests exist.

    Funding Interests:

    Citation:

    Zhao Bin, Jiang Xia, Cao Jinming (2021) Mathematical Modeling Of Covid-19 Journal of Current Scientific Research. - 1(1):1-11
    DOI 10.14302/issn.2766-8681.jcsr-21-3701

    Introduction

    Introduction

    With the outbreak and spread of the COVID-19, 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 epidemic7, although to our country's economic development and people's lives have brought a great impact. But in the current situation, COVID-19 has been effectively controlled in China.

    Although the epidemic of China has been effectively controlled, COVID-19 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 re-outbreak of the COVID-19 infection.

    In fact, there are many imminent questions about the spread of COVID-19. 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 COVID-19? What kinds of mathematical models are available to help us answer these questions?

    Results

    Results The Result of Hubei Province (Consider Birth Rate and Natural Mortality)

    The final fitting results are shown in the Figure 3, Figure 4 below. The Figure 3 shows the first period in Hubei Province, and the other shows the second period. The graphs contain curves composed of actual data, and curves formed by the calculated data. The deduced curves not only fit the curve composed of actual data, but also predict the future.

    2020.1.23-2020.2.10 Data fitting result (consider birth rate and natural mortality) 2020.2.21-2020.4.28 Data fitting result (consider birth rate and natural mortality)

    Susceptible has a large deviation from the actual during the period of 21 February to 28 April (the degree of deviation increases with time). Therefore, we consider to simplify the above model, which is without considering the impact of birth rate and natural mortality, then the model 2 is established.

     The Result of Hubei Province (Not Consider Birth Rate and Natural Mortality)

    The final fitting results are shown in the Figure 5, Figure 6 below. The meanings of the curves are the same as in Figure 3, Figure 4.

    2020.1.23-2020.2.10 Data fitting result (not consider birth rate and natural mortality) 2020.2.21-2020.4.28 Data fitting result (not consider birth rate and natural mortality)

    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 controlled13.

     The Result of the United States (Not Consider Birth Rate and Natural Mortality)

    The final fitting result of the United States is shown in the Figure 7 below. The meanings of the curves are the same as the Figures above.

    It can be seen from the Figure 7 that the turning point of the U.S. epidemic will not appear until mid-June. This is because the United States initially paid little attention to this epidemic, and the government and citizens did not even take corresponding preventive and control measures. If the U.S. government can strengthen control like the Chinese government, then the inflection point of the U.S. epidemic will appear earlier.

    2020.2.23-2020.4.28 Data fitting result (not consider birth rate and natural mortality)     The Result of SIR-Based Simulation Estimates (By Netlogo)

    The final simulation fitting result is shown in the Figure 8 below. The meanings of the curves are the same as the Figures above.

    We used the parameters listed in Methods section for simulation. It is found that the simulation curves are consistent with the trend of the curves that we use the calculated values, and also coincide with the trend of the actual curves. As shown in the Figure 8 that according to the given parameters, this virus will disappear after more than 1 year. So we can conclude that if we do not give comprehensive control to the spread of COVID-19, the realistic situation will be worse than the simulation.

    Simulation fitting result from Netlogo

    Discussion

    Discussion

    There is no doubt that the propagation of COVID-19 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 fminconfunction in MATLAB, and obtain the most realistic predicted values. At the same time, when analyzing I(t), the case of death due to illness is taken into account, and the people who died of illness is attributed to R(t), which is more in line with the actual situation and can reduce the setting of unknown coefficients.

    Our model of infectious disease which is established by ordinary differential equations has a wide range of operating prospect, except for infectious disease itself (e.g.COVID-19 and SARS) of the prediction, prevention and control, there are a lot of social behaviors and incidents in our life follow the rule similar to the model of the spread of infectious disease. The infectious disease model can be widely used in the diffusion of innovation, the network public opinion spread, the spread of financial risk, and other areas of the social science research1415. The diffusion process of management accounting matters, which is shown in the Table 3 and Figure 9 below, clearly uses the familiar infectious disease model for analysis..

    Management accounting practice diffusion system and infectious disease model
    Classes Corresponding infectious disease model Explanations for different classes
    ManagementAccounting Practice  Source of infection Enterprises introduce new management accounting practices
       Neutral(s)   People who are possible to be infected by COVID-19 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 re-infected by COVID-19 and people who died because of the COVID-19 The group of employees whose cognitive costs andinformation collection costs become larger, their benefits become smaller,and their overall net income are negative
    Process of management accounting matters

    Conclusion

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