  In this paper, a reaction-diffusion system is proposed to model the spatial
spreading of West Nile virus in vector mosquitoes and host birds in North
America. Infection dynamics are based on a simplified model for cross infection
between mosquitoes and birds, and the free boundary is introduced to model and
explore the expanding front of the infective region. The spatial-temporal risk
index $R_0^F(t)$, which involves time and characters of the region, is defined
for the simplified model with the free boundary to compare with other related
threshold values, including the usual basic reproduction number $R_0$.
Sufficient conditions for the virus to vanish or spread are given. Our results
suggest that the virus will be in a scenario of vanishing if $R_0\leq 1$, and
the virus will spread to the whole region if $R_{0}^F(t_0)\geq 1$ for some
$t_0\geq 0$, while if $R^F_0(0)<1<R_0$, the spreading or vanishing of the virus
depends on the initial numbers of infected mosquitoes and birds, the area of
the infected region and diffusion rates. Moreover, some remarks on the basic
reproduction numbers and the spreading speed are presented and compared.
