A Study of a Fractional-order Model of Coronavius Disease 2019(COVID-19) after Mass Caccination

Abstract

New coronavirus (COVID-19) broke out at the end of 2019. Today, the epidemic has spread all over the world. The number of confirmed cases is 250 million and the number of deaths has reached about 5000000, which undoubtedly caused serious public health disasters all over the world. In the face of the problem that the virus continues to mutate and the virus spreads faster and survives for a longer time after mutation, as well as the situation of asymptomatic infected persons, the study of the transmission law and epidemic trend of COVID-19 provides theoretical support for how to effectively prevent epidemics, which is of great research value. Most of the previous studies on COVID-19 adopt SIR model and variants of SIR model, and there are few theoretical studies on the impact of asymptomatic infection on the transmission, prevention and control of infectious diseases.Because the time of large-scale vaccination of COVID-19 vaccine in China is about the middle of 2021, so far, no scholars have studied the transmission law and prevention and control of COVID-19 virus after large-scale vaccination. In addition,most researchers use the integer-order models.Generally speaking, integer-order may not capture satisfactory model attributes. Based on this, this paper proposes a SEQIR model with quarantine item, sets up seven fractional order equations, studies and compares the epidemic prevention measures taken by the two places in the face of the re outbreak of the epidemic before mass vaccination (Beijing) and after vaccination (Hunan), calculates the size of the basic regeneration number $R_{0}$ in the two places and reports according to the real data of the two places, different numerical simulations are carried out.Studies have shown that mass vaccination and nucleic acid detection can effectively reduce the transmission of the virus. In addition, in the area where the epidemic situation is concentrated, a large number of nucleic acid tests in time can enable asymptomatic infected persons to be detected in time. After isolating asymptomatic infected people, asymptomatic infected people will infect fewer susceptible people.