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Highlights Identification of the signatures of the fractal structure on real data. New SIR-like model that includes the fractal structure in the spread of the virus. Analysis performed on data observed in several regions around the world. Time evolution analysis using the newly developed model.

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In this work we present a bag-type model within a non-extensive statistics applied to the description of the properties of a hadronic system with an underlying fractal structure. The non-extensive ideal gas inside the bag is determined by the grand canonical partition function from which pressure, energy and particle density as well as temperature and chemical potential are obtained for the hadronic system. These quantities are studied in the approximation of fixed mass for all bag constituents but also for discrete and continuum masses. In all cases, the freeze-out line, corresponding to the energy per particle equal to 1 GeV and the lines corresponding to a fractal structure inside the proton volume are obtained. Finally, the pressure on the bag surface of the proton is calculated and the resulting value (0.135 GeV) 4 obtained.