A west nile virus transmission model with periodic incubation periods∗

West Nile virus (WNv) is a mosquito-borne disease caused by Flavivirus. To investigate the combined effects of vertical transmission, temperature-dependent incubation periods and seasonality on the transmission of WNv, we develop a delay differential system with stage-structure and time-varying delays. We then derive the mosquito reproduction number RV0 and basic reproduction number R0 and show that these two numbers serve as threshold parameters that determine whether WNv will spread. As an application, we conduct a case study for WNv transmission in Los Angeles County, California. We also carry out numerical simulations to identify the situations that require time-periodic delays. Moreover, we find that rising temperatures may potentially increase the risk of disease outbreaks. c 2019 Society for Industrial and Applied Mathematics.