  A mathematical model was developed describing the dynamic of the COVID-19
virus over a population considering that the infected can either be symptomatic
or not. The model was calibrated using data on the confirmed cases and death
from several countries like France, Philippines, Italy, Spain, United Kingdom,
China, and the USA. First, we derived the basic reproduction number,
$\mathcal{R}_0$, and estimated the effective reproduction $\mathcal{R}_{\rm
eff}$ for each country. Second, we were interested in the merits of
interventions, either by distancing or by treatment. Results revealed that
total and partial containment is effective in reducing the transmission.
However, its duration may be long to eradicate the disease (104 days for
France). By setting the end of intervention as the day when hospital capacity
is reached, numerical simulations showed that the duration can be reduced (up
to only 39 days for France if the capacity is 1000 patients). Further, results
pointed out that the effective reproduction number remains large after
containment. Therefore, testing and isolation are necessary to stop the
disease.
