Dynamics of a Zika virus transmission model with seasonality and periodic delays

Zika virus is an arbovirus transmitted by mosquitoes, which can cause low fever, mild skin rash and eye swelling. In severe cases, it may cause neurological and autoimmune complications, such as microcephaly. Climate factors and weather, especially temperature, have a strong effect on the transmission dynamics of vector-borne diseases, such as Dengue, West Nile virus, Schistosomiasis, and Zika. To study the comprehensive effects of spatial structure, seasonality and the temperature sensitivity of incubation period on the transmission of Zika virus, we propose a PDE model with periodic delay. We present the basic reproduction number R0 and explore the global dynamics of the model. Our simulations show that (i) it is possible to overestimate R0 in the periodic system if the spatial averaged system is used; (ii) R0 can be underestimated in the absence of seasonality; and (iii) shortening the incubation period may reduce the risk of disease transmission, which is critical for modeling the transmission of Zika virus dynamics to understand geographic and seasonal limits of Zika risk. •To study the transmission of Zika virus, we propose a PDE model with periodic delay.•We present the basic reproduction number R0.•We explore the global dynamics of the model.