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 R₀^V 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. [ABSTRACT FROM AUTHOR]