  The identification of the transmission parameters of a virus is fundamental
to identify the optimal public health strategy. These parameters can present
significant changes over time caused by genetic mutations or viral
recombination, making their continuous monitoring fundamental. Here we present
a method, suitable for this task, which uses as unique information the daily
number of reported cases. The method is based on a time since infection model
where transmission parameters are obtained by means of an efficient
maximization procedure of the likelihood. Applying the method to SARS-CoV-2
data in Italy we find an average generation time $z = 3.2 \pm 0.8$ days, during
the temporal window when the majority of infections can be attributed to the
Omicron variants. At the same time we find a significantly larger value $z =
6.2 \pm 1.1$ days, in the temporal window when spreading was dominated by the
Delta variant. We are also able to show that the presence of the Omicron
variant, characterized by a shorter $z$, was already detectable in the first
weeks of December 2021, in full agreement with results provided by sequences of
SARS-CoV-2 genomes reported in national databases. Our results therefore
indicate that the novel approach can indicate the existence of virus variants
resulting particularly useful in situations when information about genomic
sequencing is not yet available.
