Spreading speed for a West Nile virus model with free boundary

Abstract

The purpose of this paper is to determine the precise asymptotic spreading speed of the virus for a West Nile virus model with free boundary, introduced recently in Lin and Zhu (J Math Biol 75:1381–1409, 2017), based on a model of Lewis et al. (Bull Math Biol 68:3–23, 2006).We show that this speed is uniquely defined by a semiwave solution associated with theWest Nile virus model. To find such a semiwave solution, we firstly consider a general cooperative system over the half-line [0,∞), and prove the existence of amonotone solution by an upper and lower solution approach; we then establish the existence and uniqueness of the desired semiwave solution by applying this method together with some other techniques including the sliding method. Our result indicates that the asymptotic spreading speed of theWest Nile virus model with free boundary is strictly less than that of the corresponding model in Lewis et al. (2006).