  The presence of a large number of infected individuals with few or no
symptoms is an important epidemiological difficulty and the main mathematical
feature of COVID-19. The A-SIR model, i.e. a SIR (Susceptible-Infected-Removed)
model with a compartment for infected individuals with no symptoms or few
symptoms was proposed by Giuseppe Gaeta, arXiv:2003.08720 [q-bio.PE] (2020). In
this paper we investigate a slightly generalized version of the same model and
propose a scheme for fitting the parameters of the model to real data using the
time series only of the deceased individuals. The scheme is applied to the
concrete cases of Lombardy, Italy and S\~ao Paulo state, Brazil, showing
different aspects of the epidemics. For each case we show that we may have good
fits to the data up to the present, but with very large differences in the
future behavior. The reasons behind such disparate outcomes are the uncertainty
on the value of a key parameter, the probability that an infected individual is
fully symptomatic, and on the intensity of the social distancing measures
adopted. This conclusion enforces the necessity of trying to determine the real
number of infected individuals in a population, symptomatic or asymptomatic.
