The prevalence of COVID-19 has been the most serious health challenge of the
21th century to date, concerning national health systems on a daily basis,
since December 2019 when it appeared in Wuhan City. Prediction of pandemic
spread plays an important role in effectively reducing this highly contagious
disease. Nevertheless, most of the proposed mathematical methodologies, which
aim to describe the dynamics of the pandemic, rely on deterministic models that
are not able to reflect the true nature of the spread of COVID. In this paper,
we propose a SEIHCRDV model - an extension of the classic SIR compartmental
model - which also takes into consideration the populations of exposed,
hospitalized, admitted in intensive care units (ICU), deceased and vaccinated
cases, in combination with an unscented Kalman filter (UKF), providing a
dynamic estimation of the time dependent parameters of the system. Apparently,
this new consideration could be useful for examining also other pandemics. We
examine the reliability of our model over a long period of 265 days, where we
observe two major waves of infection, starting in January 2021 which signified
the start of vaccinations in Europe, providing quite encouraging predictive
performance. Finally, special emphasis is given to proving the non-negativity
of SEIHCRDV model, to achieve a representative basic reproductive number R0 and
to investigating the existence and stability of disease equilibriums in
accordance with the formula produced to estimate R0.Comment: 31 pages, 13 figure