A kinetic model considering the decline of antibody level and vaccination of COVID-19

Abstract

In order to evaluate the decline in antibody levels and the impact of vaccination on the spread of the epidemic, we establish COVID-19 dynamic models that consider the decline in antibody levels and the effects of vaccination, and retrospectively evaluate the epidemic situation in England. Based on the epidemic data in England from September 1 to October 31, 2020, considering the continuous decline in the antibody level of COVID-19 recovers, an improved SEIR infectious disease dynamics model that considers the reinfection of recovers due to the decline in antibody levels is established. The kinetic parameters of the SEIR model are obtained by fitting. On this basis, a SEIRV infectious disease dynamic model with vaccination is established to study the impact of different vaccination rates and vaccine failure rates on the development of the epidemic in England. We obtain the lower the vaccine failure rate, the fewer new cases. When the vaccination rate is fixed at 0.005 (equivalent to 250000 people vaccinated every day), the peak of the epidemic will decrease with the decrease of vaccine failure rate. The peak value when the failure rate is 0.001 is 81.4% lower than the peak value when the failure rate is 0.01, and the peak value when the failure rate is 0.01 is 89.5% lower than the peak value when the failure rate is 0.02. When the failure rate is less than 0.01, the peak time will advance with the decrease of failure rate; when the failure rate is greater than 0.01, the peak time will be delayed with the decrease of failure rate; when the failure rate is 0.01, the peak time is 528 days later than that when the failure rate is 0.001 and 295 days later than that when the failure rate is 0.05. On the 60th day of vaccination, the vaccine failure rate of 0.002 decreases the number of cases by 5.8% compared with the vaccine failure rate of 0.01; on the 70th day of vaccination, the vaccine failure rate of 0.002 reduces the number of cases by 9.1% compared with the vaccine failure rate of 0.01. Therefore, with the extension of time, the vaccine with low failure rate has a more obvious effect on reducing the number of cases than the vaccine with high failure rate. When the vaccine failure rate is fixed at 0.005, we study the impact of different vaccination rates on the spread of the epidemic in England, the result shows that the peak of epidemic situation decreases with the increase of vaccination rate, and the peak time advance with the increase of vaccination rate, when the vaccination rate is 0.025, the peak decreases by 74.8% and the peak time was 114 days earlier than that when the vaccination rate is 0.005. Therefore, the higher the vaccine efficiency and vaccination rate, the lower the peak of the epidemic. On the basis of improving the effectiveness of vaccines, increasing the vaccination rate is of practical significance for controlling the spread of the epidemic.