While I’d love to see us evolve toward supporting vertical packaging†, I’m not sure how OpenMRS could respond to the Zika epidemic. With Ebola, people with fevers are quarantined for a relatively short period as they are diagnosed and the requirement for complete isolation (nothing goes out of the red zone without soaking in bleach) posed a specific problem that OpenMRS could help solve: help multi-gloved users in hot, full-body gear provide care with an electronic system designed to address their special needs.
With Zika, the symptoms are far less obvious (many are asymptomatic) and most of the efforts to address the problem are preventive – i.e., avoid the region if possible, avoid getting pregnant, and find ways to reduce mosquito populations. I could imagine ways to help (information dissemination, decision support rules, system(s) to assist with prophylaxis, etc.), but none are as obvious a fit for OpenMRS as was the case for Ebola.
My suggestion would be to reach out to those most affected – i.e., people in the most-affected areas – and see what problems they are having. As a general rule in informatics, it is always better to start with the problem and then design the solution than to start with a solution and look for a problem. The Zika epidemic is certainly a problem, but you’d need a far more specific problem definition before you could start designing an appropriate solution. Unfortunately, I’m not able to guess what these specific problems might be.
Right now, this feels like we’re starting with the hammer and looking for a nail. If we first find whether there are screws that are loose, wires to be soldered, nails to be hammered, or wood to be cut, then we can decide if a hammer is the best tool for the job. 
It’s great to see the concern & love in the community. Sometimes I turn on the news (especially political news in the U.S. these days) and wonder what else can go wrong with the world. Then I see conversations like this within our community and I feel more hopeful. 
Cheers,
-Burke 
† “Vertical packaging” is the term I’ve used to describe the packaging & versioning of related content & behaviors needed to address a particular problem (HIV, TB, Ebola, Mental Health, Cancers, etc.). The idea is that, assuming we were smart enough to allow these packages to overlap (share content or behaviors at times), implementations could take their “horizontal” (flexible) platform and install one or more “vertical” (disease- or problem-specific) solutions onto the platform to meet their needs.
What do I mean by “vertical”? Typically, generic platforms like OpenMRS are considered “horizontal” solutions that try to flexibly address a wide variety of needs and “vertical” solutions are those that address a specific disease or problem.
What do I mean by “content & behaviors”? Content refers to metadata, concepts, forms, reports, etc. Behaviors refers to modules, apps, etc.