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Analyzing the COVID-19 pandemic is a critical factor in developing effective policies to deal with similar challenges in the future. However, many parameters (e.g., the actual number of infected people, the effectiveness of vaccination) are still subject to considerable debate because they are unobservable. To model a pandemic and estimate unobserved parameters, researchers use compartmental models. Most often, in such models, the transition rates are considered as constants, which allows simulating only one epidemiological wave. However, multiple waves have been reported for COVID-19 caused by different strains of the virus. This paper presents an approach based on the reconstruction of real distributions of transition rates using genetic algorithms, which makes it possible to create a model that describes several pandemic peaks. The model is fitted on registered COVID-19 cases in four countries with different pandemic control strategies (Germany, Sweden, UK, and US). Mean absolute percentage error (MAPE) was chosen as the objective function, the MAPE values of 2.168%, 2.096%, 1.208% and 1.703% were achieved for the listed countries, respectively. Simulation results are consistent with the empirical statistics of medical studies, which confirms the quality of the model. In addition to observables such as registered infected, the output of the model contains variables that cannot be measured directly. Among them are the proportion of the population protected by vaccines, the size of the exposed compartment, and the number of unregistered cases of COVID-19. According to the results, at the peak of the pandemic, between 14% (Sweden) and 25% (the UK) of the population were infected. At the same time, the number of unregistered cases exceeds the number of registered cases by 17 and 3.4 times, respectively. The average duration of the vaccine induced immune period is shorter than claimed by vaccine manufacturers, and the effectiveness of vaccination has declined sharply since the appearance of the Delta and Omicron strains. However, on average, vaccination reduces the risk of infection by about 65–70%. [ABSTRACT FROM AUTHOR]