Article,
Analytical Computation of the Epidemic Threshold on Temporal Networks
Physical Review X, (Apr 8, 2015)
DOI: 10.1103/PhysRevX.5.021005
Abstract
The time variation of contacts in a networked system may fundamentally alter
the properties of spreading processes occurring on it and affect the condition
at which epidemics become possible, as encoded in the epidemic threshold
parameter. Despite the great interest of the problem for the physics, applied
mathematics, and epidemiology communities, its complete theoretical
understanding still represents a challenge and is currently limited to the
cases where the time-scale separation between the spreading process and the
network time-variation holds, or to specific temporal network models. Here we
introduce a Markov chain description of the Susceptible-Infectious-Susceptible
process on a generic temporal network and we adopt a multi-layer perspective to
analytically derive its epidemic threshold. We find that the critical parameter
can be computed as the spectral radius of a matrix, analogously to the static
networks case, once it encodes the temporal structure and topology of the
network. Its application to a set of time-varying network models and empirical
networks and the comparison with stochastic numerical simulations show that the
proposed analytical approach is accurate and general. This result is of
fundamental and practical interest as the introduced framework provides the
basis for new analytical understandings of the interplay between temporal
networks and spreading dynamics.
