SOCIAL CONTACT PROCESSES AND THE PARTNER MODEL

• 成果类型: Article
• 署名作者: Foxall, Eric; Edwards, Roderick; van den Driessche, P.
• 署名单位: University of Victoria
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1117
• 发表日期: 2016
• 页码: 1297-1328
• 关键词: environment

摘要

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 determines 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(logN), 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 comparison to a set of mean-field equations when the infection is widespread, and to a branching process when the infection is sparse.