A reaction-diffusion-advection model of harmful algae growth with toxin degradation

This paper is devoted to the study of a reaction-diffusion-advection system modeling the dynamics of a single nutrient, harmful algae and algal toxin in a flowing water habitat with a hydraulic storage zone. We introduce the basic reproduction ratio R0 for algae and show that R0 serves as a threshold value for persistence and extinction of the algae. More precisely, we prove that the washout steady state is globally attractive if R0<1, while there exists a positive steady state and the algae is uniformly persistent if R0>1. With an additional assumption, we obtain the uniqueness and global attractivity of the positive steady state in the case where R0>1.