A West Nile Virus Model with Vertical Transmission and Periodic Time Delays

摘要

Seasonal change has played a critical role in the evolution dynamics of West Nile virus transmission. In this paper, we formulate and analyze a novel delay differential equation model, which incorporates seasonality, the vertical transmission of the virus, the temperature-dependent maturation delay and the temperature-dependent extrinsic incubation period in mosquitoes. We first introduce the basic reproduction ratio R0. It is also shown that the disease-free periodic solution is attractive if R0<1. Numerically, we study the West Nile virus transmission in Orange County, California, USA.