Spatial dynamics of population-toxicant interactions in heterogeneous aquatic ecosystems: A reaction–diffusion–advection approach

Spatial diffusion and advection are important factors affecting population dynamics in aquatic environments. This paper presents a reaction–diffusion–advection model that incorporates spatial heterogeneity to study the interactions between populations and toxicants in contaminated ecosystems. We analyze the existence and uniqueness of the semi-trivial steady state of the model using the eigenvalue theory of elliptic systems and establish the well-posedness through an inductive method. By studying the corresponding elliptic eigenvalue problem, we derive the variational expression for the basic reproduction number [Formula: see text] and investigate its role as a threshold parameter for population persistence or extinction. Furthermore, we discuss the monotonicity and asymptotic profiles of [Formula: see text] with respect to the diffusion rate and advection rate. In addition, the habitat is classified into lightly polluted area and heavily polluted area, and the spatial dynamics of the model are analyzed through the level set classification of [Formula: see text]. Finally, numerical simulations validate and complement our theoretical analysis results, illustrating the impact of spatial heterogeneity on population persistence. This work provides new insights into the mechanisms of population-toxicant interactions and offers a framework for ecological protection in polluted aquatic ecosystems.