In 2015 and 2016, Zika virus (ZIKV) swept through dengue virus (DENV) endemic areas of Latin America. These viruses are of the same family, share a vector and may interact competitively or synergistically through human immune responses. We examine dengue incidence from Brazil and Colombia before, during, and after the Zika epidemic. We find evidence that dengue incidence was atypically low in 2017 in both countries. We investigate whether subnational Zika incidence is associated with changes in dengue incidence and find mixed results. Using simulations with multiple assumptions of interactions between DENV and ZIKV, we find cross-protection suppresses incidence of dengue following Zika outbreaks and low periods of dengue incidence are followed by resurgence. Our simulations suggest correlations in DENV and ZIKV reproduction numbers could complicate associations between ZIKV incidence and post-ZIKV DENV incidence and that periods of low dengue incidence are followed by large increases in dengue incidence.