Social contact processes and the partner model

We consider a model of infection spread on the complete graph on N vertices. Edges are dynamic, modelling the formation and breakup of non-permanent monogamous partnerships, and the infection can spread only along active edges. We identify a basic reproduction number R0 such that the infection dies off in O(logN) time when R0<1, and survives for at least ecN time when R0>1 and a positive fraction of vertices are initially infectious. We also identify a unique endemic state that exists when R0>1, and show it is metastable. When R0=1, with considerably more effort we can show the infection survives on the order of N1/2 amount of time.