Aquest article té un Erratum accessible a: https://doi.org/10.1007/s11538-017-0295-0

Agraïments: T.B. is grateful to Riksbankens Jubileumsfond (Grant P12-0705:1) for financial support.

This paper is concerned with stochastic SIR and SEIR epidemic models on random networks in which individuals may rewire away from infected individuals at some rate so-called preventive rewiring. The models are denoted SIR- and SEIR- and we focus attention on the early stages of an outbreak, where we derive expression for the basic reproduction number R_0 and the expected degree of the infectious nodes E(D_I) using two different approximation approaches. The first approach approximates the early spread of an epidemic by a branching process, whereas the second one uses pair approximation. The expressions are compared with the corresponding empirical means obtained from stochastic simulations of SIR- and SEIR- epidemics on Poisson and scale-free networks. For SIR- and the SEIR- case without rewiring of exposed nodes, both approaches predict the same epidemic threshold and the same E(D_I), the latter being very close to the observed mean degree D_I in simulated epidemics over Poisson networks. Above the epidemic threshold, pairwise models overestimate the value of R_0 obtained from the simulations, which turns out to be very close to the one predicted by the branching process approximation. For SEIR- where exposed individuals also rewire (perhaps unaware of being infected), the two approaches give different epidemic thresholds, with the branching process approximation being more in agreement with simulations.