  We are currently facing a highly critical case of a world-wide pandemic. The
novel coronavirus (SARS-CoV-2, a.k.a. COVID-19) has proved to be extremely
contagious and the original outbreak from Asia has now spread to all
continents. This situation will fruitfully profit from the study in regards of
the spread of the virus, assessing effective countermeasures to weight the
impact of the adopted strategies. The standard Susceptible-Infectious-Recovered
(SIR) model is a very successful and widely used mathematical model for
predicting the spread of an epidemic. We adopt the SIR model on a random
network and extend the model to include control strategies {\em lockdown} and
{\em testing} -- two often employed mitigation strategies. The ability of these
strategies in controlling the pandemic spread is investigated by varying the
effectiveness with which they are implemented. The possibility of a second
outbreak is evaluated in detail after the mitigation strategies are withdrawn.
We notice that, in any case, a sudden interruption of such mitigation
strategies will likely induce a resurgence of a second outbreak, whose peak
will be correlated to the number of susceptible individuals. In fact, we find
that a population will remain vulnerable to the infection until the herd
immunity is achieved. We also test our model with real statistics and
information on the epidemic spread in South Korea, Germany, and New York and
find a remarkable agreement with the simulation data.
