One of the most recent novelties in volcanology is the finding of a statistically significant influence of remote strong earthquakes on the largest explosive eruptions of the last century. Here, we model such interaction in terms of the coseismic and postseismic stress diffusion. The stress variation consists of the elastic response of the lithosphere, and the viscoelastic relaxation of the asthenosphere and mantle, computed through a spherical, stratified, self-gravitating, viscoelastic Earth model. Our results show that the tectonic earthquakes induce on the volcanoes significant stress variations, from a few tenths to tens of bars, both in dilatation/compression and in shear. Remarkably, the model explains the main features resulting from the empirical study: the time lag (from several months to a few decades), the spatial distances (hundreds of kilometers), and the different intensities of the coupling. This indicates that the coseismic and postseismic stress diffusion might remotely induce eruptions, particularly for volcanoes close to a critical state. However, the results show only weak evidence of a common preeruptive stress evolution, with an overall compression and shear pattern at a few kilometers depth, pointing out the complexity of the mechanism responsible for the reactivation of a volcano. These findings confirm previous suggestions, depicting the volcanic areas to be open systems governed by a high number of degrees of freedom, where the remote seismic activity might represent one of the most relevant. The modeling of such interactions might shed a new light on evaluating the probability of occurrence of a large explosive eruption.