Computing the epidemic threshold on time-evolving networks

E Valdano, L Ferreri, C Poletto, V Colizza,
Analytical computation of the epidemic threshold
on temporal networks,
Physical Review X  5, 021005 (2015)

Python code for computing the threshold. 

Highlighted on physics.aps.org

One critical problem underlying the spread of a disease, an idea, a trend or a rumor on a networked system is the characterization of the conditions leading to widespread dissemination of the agent, in order to be able to control it (e.g. for diseases) or to enhance it (e.g. for viral marketing).
The computation of the critical spreading condition (called epidemic threshold) is not trivial, since it depends on the contagion ability of the spreading agent but also, most importantly, on the structure of the underlying contact network and how it may change in time. Efforts have so far been limited to specific cases where one assumes that the temporal variation can be explicitly modeled. But what knowledge can be reached if we do not know the mechanistic temp.oral evolution of the network? We propose a novel theoretical framework for the rigorous analytical derivation of the epidemic threshold for an arbitrary temporal network. Our mathematical modeling provides concrete insights for experiments and also a new theoretical perspective for the study of the interplay between network evolution and spreading dynamics.