Global dynamics of a nonlocal reaction–diffusion system modeling the West Nile virus transmission

This paper proposed and analyzed a nonlocal and time-delayed system describing the West Nile virus (WNV) transmission between mosquitoes and birds, in which a fixed latency of WNV in the mosquitoes was included. By the concept of the next infection operator, the basic reproduction number of WNV, [Formula presented], is defined for the model system. It turns out that the extinction/persistence of WNV is determined by the sign of [Formula presented]. For the special case where parameters in the system are all positive constants, we show that [Formula presented] can be expressed in an explicit formula.