I'm going to dispense with the basic schtick about this. Zika's a virus that's been around for some time, and for a long time was confined by geography to a small-ish area in the Pacific region. Now, it's out, and this was inevitable in a world that gets smaller with every intercontinental flight.
Zika is mostly a modest disease, although as we see with everything, some people do suffer catastrophic results. Homeopathically, of course, I'd take the case, although one would consider China, Belladonna, Ferrum phos, or Gelsemium as possible presentations. In regular medicine, treatment at this time is mainly supportive. The paralytic syndrome Guillain-Barre is reportedly more common in Zika infection. Conium or Curare come to mind as possible remedies.
The eye-catching message is when we see that pregnant women's babies may be affected. A firm biological connection between Zika and babies being born with small heads and underdeveloped brains has not been conclusively established. Recently a student asked me about the possibility that vaccines are responsible. I have an article on my main website that explains in detail, but in short, it's possible. But it isn't very likely. I told the student that microcephaly can have other causes, such as mercury toxins. Many parts of the world are badly polluted with industrial waste, especially many of the Southern Hemisphere countries here in the the Americas.
It's rational to have concerns about something like Zika. Commonsense measures can be found at the CDC website. Yet we shouldn't lose sight of other possible causes, some that are bigger and more complex than a mosquito-borne germ. Yes, Zika's occurring in the U.S., but as an import. It's not native yet. It's also rational to look ahead. Trash, warming temperatures, heavy rains, and poverty all have their roles to play, and by working to ameliorate these things we can leverage our efforts into greater gains for our safety. They are bigger, more imposing challenges than simply trying to come up with a new antiviral or vaccine. (Zika's been resistant to formulation into a vaccine, so far.) Restrictive immigration polices don't solve the problem--people don't disclose when they fear deportation.
If you are pregnant, it's not unreasonable to change your travel plans if they are to areas identified as Zika-active. Alternatively, protection can be afforded from mosquito netting at night, covering clothing, and possibly bug repellents. These latter recommendations apply even to the non-pregnant, although most people won't get very ill from Zika. A variety of herbal antivirals may help: Astragalus may help if one becomes ill. Echinacea may help, although I would not use this in cases of Guillain-Barre syndrome (might aggravate the autoimmune nature of this disease). If you have access to homeopathic medicines, I listed some starting points above, although individual case-taking is the rule.
As for insect repellents, yes, they are toxic. At this moment, all of the ones said to be good for repelling mosquitoes are man-made neurotoxins. These things aren't ruthlessly unsafe...but they aren't without their hazards for some people. So far, my research hasn't turned up any alternatives. If I find any I will post them here. If my travels come across any cases treated successfully with homeopathic medicine, I will also pass this along (for educational purposes).