  The ongoing Coronavirus disease 2019 (COVID-19) is a major crisis that has
significantly affected the healthcare sector and global economies, which made
it the main subject of various fields in scientific and technical research. To
properly understand and control this new epidemic, mathematical modelling is
presented as a very effective tool that can illustrate the mechanisms of its
propagation. In this regard, the use of compartmental models is the most
prominent approach adopted in the literature to describe the dynamics of
COVID-19. Along the same line, we aim during this study to generalize and
ameliorate many existing works that consecrated to analyse the behaviour of
this epidemic. Precisely, we propose an SQEAIHR epidemic system for
Coronavirus. Our constructed model is enriched by taking into account the media
intervention and vital dynamics. By the use of the next-generation matrix
method, the theoretical basic reproductive number $R_0$ is obtained for
COVID-19. Based on some nonstandard and generalized analytical techniques, the
local and global stability of the disease-free equilibrium are proven when $R_0
< 1$. Moreover, in the case of $R_0 > 1$, the uniform persistence of COVID-19
model is also shown. In order to better adapt our epidemic model to reality,
the randomness factor is taken into account by considering a proportional white
noises, which leads to a well-posed stochastic model. Under appropriate
conditions, interesting asymptotic properties are proved, namely: extinction
and persistence in the mean. The theoretical results show that the dynamics of
the perturbed COVID-19 model are determined by parameters that are closely
related to the magnitude of the stochastic noise. Finally, we present some
numerical illustrations to confirm our theoretical results and to show the
impact of media intervention and quarantine strategies.
