A physical model of the Jovian trapped protons with kinetic energies higher than 1 MeV inward of the orbit of the icy moon Europa is presented. The model, named Salammbô, takes into account the radial diffusion process, the absorption effect of the Jovian moons, and the Coulomb collisions and charge exchanges with the cold plasma and neutral populations of the inner Jovian magnetosphere. Preliminary modeling of the wave-particle interaction with Electromagnetic Ion Cyclotron (EMIC) waves near the moon Io is also performed. Salammbô is validated against in-situ proton measurements of Pioneer 10, Pioneer 11, Voyager 1, Galileo Probe, and Galileo Orbiter. A prominent feature of the MeV proton intensity distribution in the modeled area is the two orders of magnitude flux depletion observed in MeV measurements near the orbit of Io. Our simulations reveal that this is not due to direct interactions with the moon or its neutral environment but results from scattering of the protons by EMIC waves.