  We have established a novel mathematical model that considers various aspects
of the spreading of the virus, including, the transmission based on being in
the latent period, environment to human transmission, governmental decisions,
and control measures. To accomplish this, a compartmental model with eight
batches (sub-population groups) has been proposed and the simulation of the set
of differential equations has been conducted to show the effects of the various
involved parameters. Also, to achieve more accurate results and closer to
reality, the coefficients of a system of differential equations containing
transmission rates, death rates, recovery rates and etc. have been proposed by
some new step-functions viewpoint. Results: First of all, the efficiency of the
proposed model has been shown for Iran and Italy, which completely denoted the
flexibility of our model for predicting the epidemic progress and its moment
behavior. The model has shown that the reopening plans and governmental
measures directly affect the number of active cases of the disease. Also, it
has specified that even releasing a small portion of the population (about 2-3
percent) can lead to a severe increase in active patients and consequently
multiple waves in the disease progress. The effects of the healthcare
capacities of the country have been obtained (quantitatively), which clearly
specify the importance of this context. Control strategies including strict
implementation of mitigation (reducing the transmission rates) and
re-quarantine of some portion of population have been investigated and their
efficiency has been shown.
