  Zika virus (ZIKV) exhibits unique transmission dynamics in that it is
concurrently spread by a mosquito vector and through sexual contact. We show
that this sexual component of ZIKV transmission induces novel processes on
networks through the highly asymmetric durations of infectiousness between
males and females -- it is estimated that males are infectious for periods up
to ten times longer than females -- leading to an asymmetric percolation
process on the network of sexual contacts. We exactly solve the properties of
this asymmetric percolation on random sexual contact networks and show that
this process exhibits two epidemic transitions corresponding to a
core-periphery structure. This structure is not present in the underlying
contact networks, which are not distinguishable from random networks, and
emerges because of the asymmetric percolation. We provide an exact analytical
description of this double transition and discuss the implications of our
results in the context of ZIKV epidemics. Most importantly, our study suggests
a bias in our current ZIKV surveillance as the community most at risk is also
one of the least likely to get tested.
