THE onset of an epidemic depends on many factors, including the ease of contact that spreads the disease and the details of the underlying network that links infected individuals. To design appropriate containment and control measures, it is important to understand the conditions that make an infectious disease reach an “epidemic threshold”. Existing theories compute this threshold only under simplifying assumptions, for example, that the network of contacts through which disease spreads is static. But in real-world situations, diseases spread between individuals in a dynamic pattern of encounters, gatherings or travels.
Vittoria Colizza of Inserm and the Université Pierre et Marie Curie, France, and co-workers developed a model to compute the epidemic threshold for networks with any kind of temporal dynamics. They used tools from graph theory and improved upon a well-known epidemic model so that it could describe an epidemic spreading in a network which changes in time. They could accurately predict the epidemic threshold for several networks, including three for which empirical data were available: face-to-face encounters between researchers at conference, contacts between sex workers and their clients over the course of a year, and contact between teenagers during one day at a high school. The formalism could also describe similar “contagion” phenomena, from the dissemination of trends through social networks to the propagation of cyber viruses through the Internet. This work is published in Physical Review X.