By characterizing the time evolution of COVID-19 in term of its' velocity'(log of the new cases per day) and its rate of variation, or'acceleration', we show that in many countries there has been a deceleration even before lockdowns were issued. This feature, possibly due to the increase of social awareness, can be rationalized by a susceptible-hidden-infected-recovered model introduced by Barnes, in which a hidden (isolated from the virus) compartment H is gradually populated by susceptible people, thus reducing the effectiveness of the virus spreading. By introducing a partial hiding mechanism, for instance due to the impossibility for a fraction of the population to enter the hidden state, we obtain a model that, although still sufficiently simple, faithfully reproduces the different deceleration trends observed in several major countries.