Dynamic of West Nile Virus transmission considering several coexisting avian populations

West Nile Virus is an arthropod-borne flavivirus that appeared for the first time in New York City in the summer of 1999 and then spread prolifically within birds, with over 200 species having been infected. Mammals, such as humans and horses, do not develop sufficiently high bloodstream titers to play a significant role in transmission, which is a reason for considering the mosquito-bird cycle. In this paper we propose a model to study bird involvement in transmitting West Nile Virus using a system of ordinary differential equations considering the mosquito and several avian populations. A threshold value R0, depending on the model's parameters, is obtained that determines the disease level and allows us to propose possible control strategies. We determine the effects regarding the disease transmission considering the coexistence of two bird species, and then generalize this taking into account several bird species. We conclude that knowledge of the relative abundance of several bird species allows us to estimate with accuracy the risk for overall West Nile Virus transmission. Also, the establishment of the disease at an endemic level can be explained by the interaction between responsible populations of birds and mosquitoes.