Since the beginning of the COVID-19 pandemic, a large number of epidemiological models have been developed. The principal objective of the present study is to provide a new six-compartment model for the COVID-19 pandemic, which takes into account both the possibility of re-infection and the differentiation between asymptomatic and symptomatic infected subjects. The model, denoted as θ-SI(R)D, is a six-compartment model, described by as many ordinary differential equations. The six compartments are denoted as Susceptible (S), Symptomatic Infected (Is), Asymptomatic Infected (Ia), Recovered from Asymptomatic fraction (Ra), Recovered from Symptomatic fraction (Rs), and Deceased (D). Such a model has no analytical solutions, so we performed both a simulation and a model validation (R2=0.829). Based on the results of our simulations (and, on the other hand, on the results of most of the models in the scientific literature), it is possible to draw the reasonable conclusion that the epidemic tends, even without vaccination, to a steady state.