Background: The purpose of the work is to analyze population adaptation to SARS-CoV-2 in Europe in March–May 2020, predict herd immunity formation in the nearest several months on the basis of our SIR modified epidemiological model of the virus spread and elaborate recommendations to governments regarding a second wave of COVID-19 pandemic. Methods: Outer (1,006,512 RT-PCR tests results for SARS-CoV-2) and proprietary (34,660 respiratory samples) epidemiological data was used. Fifteen European countries were studied. Dates of research: March 2 – May 22, 2020. Results: As of April 21, 2020, the mean population infection rate (PIR) for the European countries considered, was 9.66%. It decreased to 6.85% by May 22, 2020. The model predicted 5.68% PIR, giving accuracy of 79.40%. SARS-CoV-2 basic reproduction number is limited by an extremum that may be observed for closed communities. A concept of effective reproduction number is introduced as a function of r0 with maximum at r0 = 4.671 and value reff. = 0.315 for the full-lockdown mode and r0 = 5.539 and reff. = 0.552 for the no-lockdown mode of SARS-CoV-2 containment. Full-lockdown and no-lockdown modes resulted in the outcomes not strikingly different from each other in terms of herd immunity values. Conclusion: In case of a second wave of COVID-19 disease in Europe, it will coincide with seasonal common cold surge, spanning from mid-September 2020 to mid-February 2021, with a median in November–December 2020. Strict epidemiological surveillance must be observed in Europe at that time. © 2020 Formosan Medical Association