  The present paper introduces a new model used to study and analyse the severe
acute respiratory syndrome coronavirus 2 (SARS-CoV2) epidemic-reported-data
from Spain. This is a Hidden Markov Model whose hidden layer is a regeneration
process with Poisson immigration, Po-INAR(1), together with a mechanism that
allows the estimation of the under-reporting in non-stationary count time
series. A novelty of the model is that the expectation of the innovations in
the unobserved process is a time-dependent function defined in such a way that
information about the spread of an epidemic, as modelled through a
Susceptible-Infectious-Removed dynamical system, is incorporated into the
model. In addition, the parameter controlling the intensity of the
under-reporting is also made to vary with time to adjust to possible
seasonality or trend in the data. Maximum likelihood methods are used to
estimate the parameters of the model.
