  In this paper, we develop a probabilistic mathematical model for the spread
of coronavirus disease (COVID-19). It takes into account the known special
characteristics of this disease such as the existence of infectious undetected
cases and the different social and infectiousness conditions of infected
people. In particular, it considers the social structure and governmental
measures in a country, the fraction of detected cases over the real total
infected cases, and the influx of undetected infected people from outside the
borders. Although the model is simple and allows a reasonable identification of
its parameters, using the data provided by local authorities on this pandemic,
it is also complex enough to capture the most important effects. We study the
particular case of Lebanon and use its reported data to estimate the model
parameters, which can be of interest for estimating the spread of COVID-19 in
other countries. We show a good agreement between the reported data and the
estimations given by our model. We also simulate several scenarios that help
policy makers in deciding how to loosen different measures without risking a
severe wave of COVID-19. We are also able to identify the main factors that
lead to specific scenarios which helps in a better understanding of the spread
of the virus.
