Zika virus is in the family of Flaviviridae, and is often transmitted to human by Aedes aegypti, a common vector for transmitting several tropical fevers, including dengue and chikungunya. The environmental heterogeneity and intervention strategies of Zika spread also involve seasonality, co-circulation of other vector-borne diseases, and demographic structures of the mosquito population.

We have been developing a variety of dynamical models to understand the transmission dynamics with focus on different aspects of environmental heterogeneities. We first consider the co-infection and co-circulation of dengue and Zika and their implication of dengue vaccination program for Zika control in the presence of experimentally reported antibody-dependent enhancement. We then consider the impact of heterogeneity of vector demographics on the initial outbreak rate and outbreak potential using age-structured partial differential equation systems and calculating the relevant threshold using non-linear semigroup theory and spectral theory. We also examine both numerically and analytically the mechanisms for potential nonlinear oscillations using the global bifurcation theory in delay differential equations.