Many attempts to build epidemic models of the current Covid-19 epidemic have been made in the recent past. However, only models postulating permanent immunity have been proposed. In this paper, we propose a SI(R) model in order to forecast the evolution of the epidemic under the hypothesis of not permanent immunity. This model offers an analytical solution to the problem of finding possible steady states, providing the following equilibrium values: Susceptible about 17%, Recovered (including deceased and healed) ranging from 79 to 81%, and Infected ranging from 2 to 4%. However, it is crucial to consider that the results concerning the recovered, which at first glance are particularly impressive, include the huge proportion of asymptomatic subjects. On the basis of these considerations, we analyse the situation in the province of Pesaro-Urbino, one of the main outbreaks of the epidemic in Italy.