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 $R_0$ and explore the global dynamics of the model. Our simulations show that (i) it is possible to overestimate $R_0$ in the periodic system if the spatial averaged system is used; (ii) $R_0$ 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.

寨卡病毒是一种由蚊子传播的虫媒病毒，可引起低烧、轻度皮疹和眼睛肿胀。在严重的情况下，它可能会导致神经和自身免疫并发症，例如小头畸形。气候因素和天气，尤其是温度，对登革热、西尼罗河病毒、血吸虫病和寨卡病毒等媒介传播疾病的传播动态有很大影响。为了研究空间结构、季节性和潜伏期温度敏感性对寨卡病毒传播的综合影响，我们提出了具有周期性延迟的PDE模型。我们提供基本再生数$R_0$并探索模型的全局动态。我们的模拟表明 (i) 可能高估$R_0$如果使用空间平均系统，则在周期系统中；(二)$R_0$在没有季节性的情况下可能被低估；(iii) 缩短潜伏期可能会降低疾病传播的风险，这对于模拟寨卡病毒传播动态以了解寨卡风险的地理和季节性限制至关重要。