The novel coronavirus pandemic generates extensive attention in political and scholarly domains. Its potentially lasting prospects, economic and social consequences call for a better understanding of its nature. The widespread expectations of large portions of the population to be infected or vaccinated before containing the COVID-19 epidemics rely on assuming a homogeneous population. In reality, people differ in the propensity to catch the infection and spread it further. Here, we incorporate population heterogeneity into the Kermack-McKendrick SIR compartmental model and show the cost of the pandemic may be much lower than usually assumed. We also indicate the crucial role of correctly planning lockdown interventions. We found that an efficient lockdown strategy may reduce the cost of the epidemic to as low as several percents in a heterogeneous population. That level is comparable to prevalences found in serological surveys. We expect that our study will be followed by more extensive data-driven research on epidemiological dynamics in heterogeneous populations.