Monotone dynamics and global behaviors of a West Nile virus model with mosquito demographics

In this paper a mathematical model is formulated to study transmission dynamics of West Nile virus (WNv), which incorporates mosquito demographics including pair formation, metamorphic stages and intraspecific competition. The global behaviors of the model are obtained from a geometric approach and theory of monotone dynamics, even though bistability is present due to backward bifurcation. It turns out that the model can be investigated through two auxiliary subsystem, which are cooperative and K -competitive, respectively. Together with implement of compound matrices and Poincaré–Bendixson theorem, a thorough classification of dynamics of the full model is characterized by mosquito reproduction number R M , WNv reproduction number R 0 and a bistability subthreshold R 0 c . The theoretical results show that if R M is not greater than 1, mosquitoes will not survive, and the WNv will die out; if R M is greater than 1, then mosquitoes will persist, and disease may prevail or vanish depending on basin of attraction of the local attractors which are singletons. Our method in this paper can be applied to other mosquito-borne diseases such as malaria, dengue fever which have a similar monotonicity.