Bifurcations in network epidemics

Sergei Taraskin (University of Cambridge)

Continuous and discontinuous phase transitions are typical features for spreading processes such as epidemics in complex networks. A general discrete- and continuous-time model incorporating non-linear (synergy) effects in transmission of ''infection'' between nodes is introduced and used for analysis of threshold behaviour of epidemics. The key ingredient of this synergy model is that the transmission of infection between nodes is described by means of continuous, in contrast to discrete for the threshold models, functions of discrete variables such as the number of nearest neighbours in a certain state. This feature of the model allows the bifurcation analysis to be undertaken for the whole parameter space. Very rich bifurcation diagrams containing new types of bifurcations of high codimension emerge from such analysis. As an example, behaviour of the synergistic SIS (susceptible-infected-susceptible) process on k-regular, binary and Erdos-Renyi random graphs will be discussed in this talk.