The advent of the COVID-19 pandemic (C19) has put a strain on the tightness of the epidemiological forecasting algorithms. These predictive models are traditionally based on SIR (Susceptible, Infected, Removed) and its updates. However, they did not provide reliable answers, especially in the first delicate phase, in which governments must take rapid decisions that are deemed to affect deeply the development and the outcome of the outbreak. This inadequacy derives not only from the model itself; it is also and undoubtedly generated by the lack of correct and timely data. Moreover, on the onset of a new pandemic, the disease is not known or it is only partially known. The first problem is the attitude of predicting it a priori, assuming the trend starting from a known mathematical curve. This approach is flawed, because it is impossible to provide a truthful forecast at the beginning of the epidemics (or of a new wave of infections), when, however, it is necessary to act promptly. Though as expected, as the epidemic progresses and the situation becomes homogeneous, mathematical models of pure interpolation and also SIR give more and more correct results. But during an epidemic, producing precise diffusion forecasts, including information on the structure of the wave front and its speed, is of paramount importance to organize an effective containment response.