
progression, stabilisation or regression of an epidemic. With its non-integer power, this model helps to unify the phenomena of diffusion in physics and viral propagation in epidemiology. Its representativeness (of real data) is due to its ability to take into account an unlimited number of internal dynamics of different speeds. The model can therefore represent all the internal dynamics of an epidemic, from the slowest, originating in very desertified rural areas, to the fastest, originating in large, densely populated cities. Its predictive power is due to its ability to take account of the whole of the past, weighting it as appropriate. The model in fact has a long memory predictive form which expresses that any predicted value is a function of all past values, values which turn out to be favourably weighted according to a forgetting factor (which is not without evoking a subtle form of memory). The model thus has the advantage of making the best possible use of the past, especially as only the past can be used to predict the future - in fact, a predictive specificity that makes this model a good predictor for decision-makers. The representativeness of the model was validated using official data from the French Ministry of Health on the spread of COVID-19, in particular the time series of contaminations and hospitalisations. Its predictivity has also been validated by verified predictions in phases of containment and vaccination, and even for the vaccination itself.