Functional dependence of COVID-19 growth rate on lockdown conditions and rate of vaccination.

It is shown that derived from the solution of differential equations analytical model adequately describes development epidemics with changes in both lockdown conditions and the effective rate of mass vaccination of the population. As in previous studies, the control calculations are in good agreement with observations at all stages of epidemic growth. One of the two model coefficients is uniquely related to the lockdown efficiency parameter. We obtained an approximate correlation between this parameter and the main conditions of lockdown, in particular, physical distancing, reduction in social contacts and strictness of the mask regime. The calculation of the incident over a seven-day period using the proposed model is in good agreement with the observational data. Analysis of both curves shows that a better agreement can be obtained by taking into account the lag time of the epidemic response of about 10 days. From the reverse calculation a time-varying curve of the infection rate associated with the "new" virus strain under mutation conditions is obtained, which is qualitatively confirmed by the sequencing data. Based on these studies, it is possible to conclude that the ASILV analytical model developed here can be used to reliably and promptly predict epidemic development under conditions of lockdown and mass vaccination without the use of numerical methods. The functional relationships identified allow us to conduct a rapid analysis of the impact of each of the model parameters on the overall process of the epidemic. In contrast to previous studies, the calculations of the proposed model were performed using EXCEL, rather than a standard calculator. This is due to the need to account for multiple changes in lockdown conditions and vaccination rates.