In this work we study a spatial model for the West Nile Virus (WNV) propagation across the USA from the east to the west. WNV is an arthropod-borne flavivirus that appeared at first time in New York city in the summer of 1999 and then spread prolifically within birds. Mammals, as human and horse, do not develop sufficiently high bloodstream titers to play a significant role in transmission, which is the reason to consider the mosquito-bird cycle. The proposed model aims to study this propagation in a system of partial differential reaction-diffusion equations considering the mosquito and the avian populations. The diffusion is allowed to both populations, being greater in avian than in the mosquito. When a threshold value R0, depending on the model's parameters, is greater than one, the disease remains endemic and could propagate to regions previously free of disease. The travelling wave solutions of the model are studied to determine the speed of the disease propagation. This wave speed is obtained as a function of the model's parameters, for instance, vertical transmission rate and avian diffusion coefficient.
