Analysis of a vector-borne disease model with vector-bias mechanism in advective heterogeneous environment - Liu Jiaxing; Wang Jinliang (Advances in Nonlinear Analysis)
This study proposed and analyzed a vector-borne reaction–diffusion–advection model with vector-bias mechanism and heterogeneous parameters in one-dimensional habitat. The basic reproduction number R0{{\mathfrak{R}}}_{0} in connection with principal eigenvalue of elliptic eigenvalue problem is characterized as the role of determining the threshold dynamics of the system. The main objective of this study is to investigate the asymptotic profiles and monotonicity of R0{{\mathfrak{R}}}_{0} with respect to diffusion rates and advection rates under certain conditions. Through exploring the level set of R0{{\mathfrak{R}}}_{0}, we also find that there exists a unique surface separating the dynamics. Our results also reveal that the infected hosts and vectors will aggregate at the downstream end if the ratio of advection rates and diffusion rates is sufficiently large.