  We propose two stochastic models for the Coronavirus pandemic. The
statistical properties of the models, in particular the correlation functions
and the probability density function, have duly been computed. Our models,
which generalises a model previously proposed and published in a specialised
journal, take into account the adoption of the lockdown measures as well as the
crucial role of the hospitals and Health Care Institutes. To accomplish this
work we have analysed two scenarios: the SIS-model (Susceptible => Infectious
=> Susceptible) in presence of the lockdown measures and the SIS-model
integrated with the action of the hospitals (always in presence of the lockdown
measures). We show that in the case of the pure SIS-model, once the lockdown
measures are removed, the Coronavirus will start growing again. However, in the
second scenario, beyond a certain threshold of the hospital capacities, the
Coronavirus is not only kept under control, but its capacity to spread tends to
diminish in time. Therefore, the combined effect of the lockdown measures with
the action of the hospitals and health Institutes is able to contain and dampen
the spread of the SARS-CoV-2 epidemic. This result can be used during a period
of time when the massive distribution of delivery of a limited number of
vaccines in a given population is not yet feasible. By way of example, we
analysed the data for USA and France where the intensities of the noise have
been estimated by Statistical Mechanics. In particular, for USA we have
analysed two possible hypotheses: USA is still subject to the first wave of
infection by and USA is in the second (or third) wave of SARS-CoV-2
infection.The agreement between theoretical predictions and real data confirms
the validity of our approach.
