This paper presents a convection-reaction-diffusion system; our objective is to apply this model in quantifying and analyzing the spatial arrangement of bacteria resistant to antibiotics within a river. By means of our research, we successfully determine a sufficient condition for the presence of a non-constant positive solution for the associated elliptic system through Leray-Schauder's degree theory. To further support our findings, we have included numerical simulations that align with our theoretical analysis.
Mostefaoui et al. (Thu,) studied this question.