We present a model for the COVID-19 epidemic that offers analytical expressions for the newly registered and latent cases. This model is based on an epidemic branching process with latency that is greatly simplified when the bare memory kernel is given by an exponential function as observed in this pandemic. We expose the futility of the concept of “bending the curve” of the epidemic as long as the number of latent cases is not depleted. Our model offers the possibility of laying out different scenarios for the evolution of the epidemic in different countries based on the most recent observations and in terms of only two constants obtained from clinical trials.