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Eric Foxall : 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 \(R_0\) such that the infection dies off in \(O(\log N)\) time when \(R_0\)<1, and survives for at least \(e^{cN}\) time when \(R_0\)>1 and a positive fraction of vertices are initially infectious. We also identify a unique endemic state that exists when \(R_0\)>1, and show it is metastable. When \(R_0\)=1, with considerably more effort we can show the infection survives on the order of \(N^{1/2}\) amount of time.

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