Epidemic data is based on the real-time dynamic data of COVID-19 in Wuhan city and Hubei province from January 1 to April 8, 2020 released by The People’s Daily and Ding Xiang yuan. According to a notice issued by the Wuhan COVID-19 prevention and Control Headquarters, Wuhan suspended traffic and closed the exit routes from Wuhan at 10:00 am on January 23,2020, and the city is closed on January 23. At the same time, other prefecture-level cities in Hubei province have also carried out traffic control. Wuhan was closed until April 8,2020, and other regions in Hubei province also lifted traffic control before and after April 8. As of April 8,2020, the cumulative number of COVID-19 cases in Wuhan city and Hubei province was 67,803 and 5,0008, respectively. Figure 2 shows the spatial distribution of the number of COVID-19 cumulative infections in the study area as of April 8,2020.
The Baidu migration scale index data: From Baidu migration network, the emigration scale index and the immigration scale index of Wuhan city and Hubei province from January 1 to April 8,2019 and January 1 to April 8, 2020. Baidu migration is a big data visualization project launched by Baidu with the theme of “crowd migration”. Migration scale index: The overall scale of migration at the provincial level is divided into inter-provincial migration and migration out; the migration in or migration out at the city level is differentiated. The urban migration boundary adopts the shape and government division of the city, including the district, county, township and village under the jurisdiction of the city. The migration scale index of this paper is equal to the sum of the emigration scale index and immigration scale index.
SEIR model and relevant parameters
The National Health Commission stated in its 26 January 2020 release that COVID-19 is contagious during the incubation period. Therefore, the SEIR model can simulate the transmission process of virus accurately. The epidemic model of SEIR, which includes latent infectivity, involves susceptible population, exposed population, infected population and removed population. This model sets the assumptions:(1) The transmission process of the epidemic is limited to human-to-human transmission. The transmission mode is contact transmission, and other forms of transmission are not considered for the time being. (2) There is no effective curing medicine or vaccine at this stage. (3) The influence of external environment on parameters such as case fatality rate is not considered. (4) Natural births, deaths and international movements of the population are not considered.
Figure 3 shows Si，Ei，Ii，Ri and represents the number of susceptible persons, exposed persons, infected persons and removed persons on day I respectively. “r” represents the average number of daily contacts per infected person. “r1”represents the average number of daily contacts per exposed person. “α”represents the prevalence rate of an exposed person. “β” represents the probability of transmission by contacting with an infected person. “β2” represents the probability of transmission by contacting with an exposed person. “γ” represents the recovery rate of infected persons. “k” represents the death rate of infected persons. The differential equations of SEIR model are as follows.
Among them, “i” is the number of days of transmission of COVID-19. “N” is the total number of persons. (N=Si+Ii+Ri+Ei) The determination of parameters in the model are as follows.
The total number N: The statistics bureau of Hubei Province showed that the permanent resident population of Hubei province was 59.27 million at the end of 2018, and that of Wuhan city was 11,21.2 million at the end of 2017.
When COVID-19 is spreading rapidly, Wuhan city and Hubei province adopt corresponding intervention measures to inhibit the spread of the epidemic. Assuming that both the average number of daily contacts per infected person and exposed person are 10 before Wuhan city and Hubei province take traffic control measures.
Using the data published by the National Health Commission, referring to the β and β2 of some relevant studies, and then we use the residual sum of squares between the predicted value and the true value minimized by the least square method, estimating the value of β and β2 by the following formula.(β=β2≈0.048)
The recovery rate of infected persons γ: According to the daily count of newly diagnosed and cured persons (no control of government) in Wuhan city and Hubei province before January 23, 2020, the value of γ is about 0.125. (γ≈0.125)
The prevalence rate of an exposed person α: Referring relevant literatures, the prevalence rate of an exposed person is determined to be 0.1.(α=Ii/Ei)
The basic regeneration number R0: R0 refers to the number of people infected by each patient during the course of the illness at the beginning of the illness, assuming that all persons are susceptible. Based on the SEIR model, R0 is calculated as follows.
λ is the rate of early infection in the formula.Yi is the number of infected persons up to the time of “i”. Referring to relevant literatures, Tg is between 7 and 10 in this article, and P is calculated as 0.7. By substituting the P value into the above formula, R0 is calculated to be between 1.89 and 2.35, and the R0 calculation result is reasonable.