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Social contact processes and the partner model. (English) Zbl 1345.60115

Summary: We consider a stochastic model of infection spread on the complete graph on \(N\) vertices incorporating dynamic partnerships, which we assume to be monogamous. This can be seen as a variation on the contact process in which some form of edge dynamics determine the set of contacts at each moment in time. We identify a basic reproduction number \(R_{0}\) with the property that if \(R_{0}<1\) the infection dies out by time \(O(\log N)\), while if \(R_{0}>1\) the infection survives for an amount of time \(e^{\gamma N}\) for some \(\gamma>0\) and hovers around a uniquely determined metastable proportion of infectious individuals. The proof in both cases relies on the comparison to a set of mean-field equations when the infection is widespread, and to a branching process when the infection is sparse.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60J25 Continuous-time Markov processes on general state spaces
92D30 Epidemiology
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References:

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