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This talk is concerned with stochastic SIR and SEIR epidemi c models on random networks in which individuals may rewire away from infected neighbors at some r ate &omega\; (and reconnect to non-infectious indi viduals with probability &alpha\; or else simply drop the edge if &alpha\;=0)\, so-called preventi ve rewiring. The models are denoted SIR-&omega\; a nd SEIR-&omega\;\, and we focus attention on the early stages of an outbreak\, where we derive exp ression for the basic reproduction number R0 and t he expected degree of the infectious nodes E(DI) using two different approximation approaches. The first approach approximates the early spread of a n epidemic by a branching process\, whereas the s econd one uses pair approximation. The expression s are compared with the corresponding empirical m eans obtained from stochastic simulations of SIR-& omega\; and SEIR-&omega\; epidemics on Poisson an d scale-free networks. To appear in Bull Math Bio l. LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR