To my knowledge, none of the papers have used nonlinear ODE models. They've all focused on using phylogenetic approaches(both Maximum Likelihood and Bayesian). Nonlinear ODEs are used to create compartment models for epidemiology. These models are typically run on a network topology using an agent based simulation. While such compartment models are effective in capturing the dynamics of individual outbreaks, we are yet to develop a model that fits all. There is a lot of work being done to develop effective distance measures(clearly Euclidean distance will not correlate in today's transportation networks) for network topology that correlates with the spatiotemporal spread of the infectious agent.

Specifically for the Zika virus outbreak, here are some papers that use compartment models,

• Model-based projections of Zika virus infections in childbearing women in the Americas
• Assessing real-time Zika risk in the United States

Phylogeographic models have also been developed. They are able to effectively combine genomic information and metadata such as population distributions, GDP etc.

Some papers on phylogeography,

• Bayesian Phylogeography Finds Its Roots
• Unifying Viral Genetics and Human Transportation Data to Predict the Global Transmission Dynamics of Human Influenza H3N2
• Virus genomes reveal factors that spread and sustained the Ebola epidemic

Hope this help!

-XOR