In this paper, we propose a periodic reaction-diffusion model of Zika virus with seasonal and spatial heterogeneous structure in host and vector population. We introduce the basic reproduction ratio [Formula: see text] for this model and show that the disease-free periodic solution is globally asymptotically stable if [Formula: see text], while the system admits a globally asymptotically stable positive periodic solution if [Formula: see text]. Numerically, we study the Zika transmission in Rio de Janeiro Municipality, Brazil, and investigate the effects of some model parameters on [Formula: see text]. We find that the neglect of seasonality underestimates the value of [Formula: see text] and the maximum carrying capacity affects the spread of Zika virus.
Keywords: Basic reproduction ratio; Global stability; Reaction–diffusion model; Seasonality; Zika virus.