Zika virus (ZIKV) exhibits unique transmission dynamics in that itis concurrently spread by a mosquito vector and through sexual contact. Due to the highly asymmetric durations of infectiousness between males and females-it is estimated that males are infectious for periods up to 10 times longer than females-we show that this sexual component of ZIKV transmission behaves akin 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, because the community most at risk is also one of the least likely to get tested.A bstract modeling of epidemics on networks remains an active field, because some of the most basic features of epidemics are still misunderstood. The classic model is quite simple (1): disease spreads stochastically with a fixed transmission probability, T , through contacts around a given patient zero. The outbreak dies quickly if T is too small but spreads to a macroscopic fraction S of the entire population if T is larger than a threshold Tc. At Tc, most of the typical insights from phase transition theory are valuable. For instance, the sizes of microscopic outbreaks follow a power law distribution, such that the expected size of microscopic outbreaks, s , indicates the position of a phase transition. Indeed, as T increases, s monotonically increases, diverges exactly at Tc, and then monotonically goes down; meanwhile, the expected macroscopic epidemic size, S , starts increasing monotonically at Tc.However, simple modifications to this model can dramatically alter its phenomenology. The epidemic threshold can vanish in networks with a scale-free degree distribution (2) or in growing networks (3). The phase transition can be discontinuous in the case of complex contagions with threshold exposition or reinforcement (4), interacting epidemics (5, 6), or adaptive networks (7-9). Recently, a unique phenomenon of double-phase transitions has also been observed numerically when networks have a very heterogeneous and clustered structure (10, 11).The current Zika virus (ZIKV) epidemic exhibits two unique properties. First, while the main transmission pathway for ZIKV is through a mosquito vector [predominantly Aedes aegypti or Aedes albopictus (13, 14)], a feature which has its own type of well-studied model and behavior (14-16), it can also spread through sexual contacts (17, 18). Second, the probability of sexual transmission is highly asymmetric between males and females. Although this is also true for ot...