Apolloni completed his undergraduate studies in Physics at the University of Perugia, Italy, in 2002, with a thesis on 'Non-commutative lattice gauge theory in 2 dimensions'. At the end of the same year he entered in the PhD program in High Energy Theoretical physics at the University of Turin, where he graduated in 2006 defending a thesis on 'A new Large-N phase transition in YM2'. After a year spent in a research team aiming to evaluate the Avogadro’s number, in 2007 he moved for his first post-doc to the Network Dynamics and Simulation Science Laboratory (NDSSL), Virginia Tech, Virginia. In 2010 he moved back to Europe, starting a post-doc position at IXXI Rhône Alpes Complex Systems Institute ENS-Lyon, France. Since November 2011 Apolloni has joined the ISI Foundation in Turin.
Apolloni’s research activity has spanned several branches of physics: from High Energy Theoretical Physics (undergraduate and graduate studies) through Experimental Condensed Matter Physics (2006-2007) to Complex Systems. The main research activities in the last years have focused on modeling the diffusion of influenza like illness at different scales, providing mathematical methods for optimal vaccine distributions and understanding the effect of network topology and evolution on diffusion processes. The approach combined mathematical aspects for estimating possible effects, numerical simulations for validating theoretical results, and social analysis for understanding demographical determinants at the base of certain network characteristics and implement a mathematical model in an effective public health perspective. Apolloni has also been working on the analysis of longitudinal datasets for studying the diffusion of obesity among American teenagers (AddHealth), and the geographical localization of co-authorship (ISI Web of Knowledge).