  In this paper, we build a mathematical model for the dynamics of COVID-19 to
assess the impact of placing healthy individuals in quarantine and isolating
infected ones on the number of hospitalization and intensive care unit cases.
The proposed model is fully analyzed in order to prove the positivity of
solutions, to study the local and global stability of the disease-free
equilibria and to drive the basic and control reproduction numbers of the
model. Oman COVID-19 data is used to calibrate the model and estimate the
parameters. In particular, the published data for the year 2020 is used, when
two waves of the disease hit the country. Moreover, this period of time is
chosen when no vaccine had been introduced, but only the non-pharmaceutical
intervention (NPI) strategies were the only effective methods to control the
spread and, consequently, control the hospitalization cases to avoid pressuring
the health system. Based on the estimated parameters, the reproduction number
and contribution of different transmission routes are approximated numerically.
Sensitivity analysis is performed to identify the significant parameters in
spreading the disease. Numerical simulation is carried out to demonstrate the
effects of quarantine and isolation on the number of hospitalized cases.
