A comparative analysis of the Covid-19 diffusion in North African countries, Algeria, Egypt, Morocco, and Tunisia has been carried out, with the aim to study the effects of the containment efforts in different nations and the reliability of the predictions based on the data fits by macroscopic growth laws, with a small number of free parameters. The comparison with data shows that the Coronavirus spreading has often different phases: an initial exponential behavior, followed by a Gompertz one

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... d/or by a logistic phase, due to containment effort. The study of the growth phases permits to verify the restarting of the disease spreading after a stationarity period, due to new outbreaks or to the weakness of the social control measures. The response of the National Health Systems to the emergency is discussed and some short term predictions on the cumulative number of confirmed infected, on the hospitalizations and on the total number of deaths is done. The possible correlation with immigration in other Mediterranean Countries has been analyzed. Stable (or unstable) condition of the spreading can quickly change due to a stronger or weaker application of the lockdown measures and short term predictions turn out to be reliable