  The daily fluctuations in the released number of Covid-19 cases played a big
role both at the beginning and in the most critical weeks of the outbreak, when
local authorities in Italy had to decide whether to impose a lockdown and at
which level. Public opinion was focused on this information as well, to
understand how quickly the epidemic was spreading. When an increase/decrease
was communicated, especially a large one, it was not easy to understand if it
was due to a change in the epidemic evolution or if it was a fluctuation due to
other reasons, such as an increase in the number of swabs or a delay in the
swab processing. In this work, we propose a nonlinear asymmetric diffusion
model, which includes information on the daily number of swabs, to describe
daily fluctuations in the number of confirmed cases in addition to the main
trend of the outbreak evolution. The class of diffusion models has been
selected to develop our proposal, as it also allows estimation of the total
number of confirmed cases at the end of the outbreak. The proposed model is
compared to six existing models, among which the logistic and the SIRD models
are used as benchmarks, in the five most affected Italian regions.
