The present work is a continuation and development of research on prediction and analysis of the spread of the COVID-19 epidemic.The proposed model adequately describes the development of the coronavirus epidemic with insufficient adherence to quarantine and social distancing. The transition from the absolute number of infected persons to their relative number per inhabitant of a settlement makes it possible to obtain universal calculation ratios.In performing the calculations, the choice of the date of the beginning of the epidemic is of great importance. Recommendations are given on how to determine the date of the beginning of the epidemic based on the analysis of statistical data on the spread of the epidemic. The coefficient of virus transmission rate k included in the calculated prognostic relation depends on the population size and the type of virus strain in the settlement in question. A simple ratio for calculating this coefficient as a function of population size is proposed.Control calculations performed using only a single empirical coefficient showed high accuracy. The calculated curves for Germany, Berlin, and its districts agree well with the corresponding statistical data. The correlation coefficients between the corresponding curves reach values of 0.93 to 0.97. The further development of the model should thus go in the direction of identifying causal links between the intensity of the epidemic and the main factors affecting this process. Some of these factors are related to the characteristics of the population’s behaviour and the infrastructure of cities. The increase in the incidence in areas with a large percentage of the population rooted in Islamic countries is one of the main factors determining the development of the epidemic in Berlin. In order to explain and clarify this conclusion, it is necessary to make further assumptions about the possible emergence of a new strain of coronavirus in Berlin and in Germany and, accordingly, about the possibility of new epidemic waves. A preliminary ratio for predicting the spread of the epidemic under conditions of simultaneous existence of both strains of coronavirus is given.Simplicity of the proposed prognostic method and high accuracy of the results allow to recommend it as an effective tool for operative analysis of various measures aimed to control the spread of COVID-19 epidemic including mass vaccination of population.

A calculation model for predicting the spread of the COVID-19 epidemic under quarantine conditions is proposed. The obtained simple analytical ratios allow estimating the factors determining the intensity of the infection spread, including changing requirements for quarantine severity. The presented method of forecasting allows to calculate both the total number of infected persons and the number of active infections. Comparison of the results of calculations according to the proposed model with the statistics for a number of cities shows their satisfactory qualitative and quantitative compliance. The proposed simple model can be useful in preliminary assessment of possible consequences of changing quarantine conditions.

A calculation model has been proposed to forecast the spread of the СOVID-19 epidemic under quarantine conditions. The resulting simple analytical relationships allow for the assessment of factors determining the intensity of the spread of infection, including the changing requirements for quarantine severity. The prediction method presented makes it possible to calculate both the total number of infected persons and the maximum rate of spread of infection.Following the publication of this work in May 2020, in October this year there was a new surge in the virus epidemic, the intensity of which depends on the population’s compliance with the rules of hygiene and social distance. Comparison of the results of the model calculations with the statistics for Berlin shows that they are of satisfactory quality. In particular, it shows that with an epidemic growth rate of around 1,000 people/day, unless additional quarantine measures are taken, the total number of infections can be expected to approach 100,000 within approximately six months. It is shown that the intensity of the virus’s spread depends on the socio-demographic composition of the population in different districts of Berlin and age structure. The possible impact of behavioural factors dependent on the psychological state of people on the spread of the epidemic, which can be assessed by analysing changes in heart rate, is discussed.

A modified model of the epidemic under conditions of mass vaccination was developed. A comparison of the model results with statistical observations in Israel shows good agreement.Model calculations are performed on the efficacy of limiting the development of an epidemic by both lockdown and vaccination. Mass vaccination of the population is the most radical method of limiting the growth of the epidemic. The introduction of a lockdown cannot completely prevent the development of an epidemic. The likelihood of the emergence of new strains of the virus is assessed. Without vaccination, the probability of more than two new virus strains per year affecting the epidemic growth process is found to be about 60%. A controlled calculation was made of the effect of the timing of changes in lockdown conditions during the vaccination period on the development of the epidemic. It was particularly shown that the cancellation of the lockdown together with the start of vaccination did not reduce the maximum number of new infections. A controlling calculation was made of the effects of gradually cancelling lockdown. On the basis of these calculations, it is possible to assess the development of the epidemic in different variants of partial lockdown cancellation.Three dimensionless complexes, made up of the intensities of transmission, vaccination and lockdown restrictions, are found to determine the epidemic’s development.The intensity of the coronavirus epidemic depends on climatic characteristics, in particular air temperature and the UV index. A relationship is given to estimate the influence of these factors on infection growth.The way forward for further development of the model is outlined. The immediate goal of modifying the model is to use it for each age group in the population and to find out the links between vaccination rates and the psychological state of the population, i.e. people’s readiness for mass vaccination.

The previously developed ASILV model for calculating epidemic spread under conditions of lockdown and mass vaccination was modified to analyse the intensity of COVID-19 infection growth in the allocated age groups. Comparison of the results of calculations of the epidemic spread, as well as the values of the seven-day incidence values with the corresponding observation data, shows their good correspondence for each of the selected age groups. The greatest influence on the overall spread of the epidemic is in the 20-40 age groups. The relatively low level of vaccination and the high intensity of contact in these age groups contributes to the emergence of new waves of the epidemic, which is especially active when the virus mutates and the lockdown conditions are relaxed. The intensity of the epidemic in the 90+ age group has some peculiarities compared to other groups, which may be explained by differences in contact patterns among individuals in this age group compared to others. Approximate ratios for estimating mortality as a function of the intensity of infection for individual age groups are provided. The proposed stratified ASILV model by age group will allow more detailed and accurate prediction of the spread of the COVID-19 epidemic, including when new, more transmissible versions of the virus mutate and emerge.

A detailed description of the model for calculating epidemic spread under conditions of lockdown and mass vaccination of the population is given (ASILV model). The proposed analytical model adequately describes the development of the epidemic in New York City. The estimates of the total number of infected persons and the seven-day incident rate made using the proposed model correlate well with the observed data in all the stages of epidemic growth. Model calculations of the spread of the epidemic under different vaccination rates allowed an assessment of the effect of vaccination on the growth of the epidemic. Analysis of seven-day incidence curves at different vaccination intensities led to the preliminary conclusion that at vaccination rates above a minimum value, the emergence of new strains did not lead to a growing epidemic.

Our previously developed simple analytical model for calculating the epidemic spread of COVID 19 is further developed. We propose a calculation method for analyzing the spread of the two-strain virus system. Comparison of the calculation results with statistical data on the example of the United Kingdom, the United States and South Africa shows their satisfactory agreement. A methodology for calculating epidemic growth under conditions of abrupt changes in lockdown conditions is proposed. It is shown that both empirical coefficients included in the model can be calculated on the basis of information on population size and quarantine conditions during the epidemic. Preliminary recommendations for determining these coefficients are given. Reliable calculation of the model coefficients will make it possible to transform the proposed calculation methodology into a higher class of models for operational and long-term forecasting of epidemic spread depending on the conditions determining this process. A method for calculating epidemic growth under conditions of simultaneous action of several virus strains is proposed. Comparison of calculation results on proposed ratios for countries with intensive recurrent epidemic growth due to virus mutation is in satisfactory agreement with statistical data. The method of calculation of epidemic growth under sharp changes of lockdown conditions is developed. To confirm the possibility of using this method it is necessary to compare the results of calculations with the data of statistics. When the results of the calculations are compared with statistical data, a systematic bias is observed from late February and early March onwards. For countries where vaccination is intensively carried out, this deviation can be explained by a decrease in the proportion of the population that can be infected by contact with infected persons. However, such differences for South Africa, where intensive vaccination is not carried out, require further investigation.

A simple calculation method is proposed based on the approximate spread model of COVID 19. A comparison of the calculation results for NYC and Berlin with observational data on the development of the epidemic in these cities shows a good match. The calculation method uses two empirical coefficients. One of them for a certain strain of the virus depends only on the population size. The second coefficient is determined by the intensity of contacts between carriers of the virus. The correlation of this coefficient with quarantine conditions and socio-demographic characteristics of cities makes it possible to use the proposed methodology not only for calculating epidemic growth but also for operational forecasting. The analysis of the passage of different epidemic waves in NYC and Berlin allows us to draw some preliminary conclusions about the effectiveness of epidemic control in both cities. The proposed model can be an additional simple and reliable tool for city administrations to continuously monitor the development of the epidemic, especially in its early stages.