Some implications of Scale Relativity theory in avascular stages of growth of solid tumors in the presence of an immune system response

► Model of cancer cell invasion accounting for cytotoxic response of immune system, analyzed in the framework of non-differentiability. ► We show even in avascular stages tumor might propagate and invade healthy tissues. ► An analytical traveling wave solution was established. ► For a particular choice of parameters, the phenomenon of cancer dormancy was explained. ► The propagation of a perturbation in the tumor cell concentration is achieved by means of cnoidal modes.