In this paper, we consider the boundary value problems of a one-dimensional steady-state SIS epidemic reaction-diffusion-advection system in the following two cases: (ⅰ) the advection rate is relatively large comparing to the diffusion rates of infected and susceptible populations; (ⅱ) the diffusion rate of the susceptible population approaches zero. By introducing a singular parameter, the system can be viewed as a singularly perturbed problem. By the renormalization group method, we construct the first-order approximate solutions and obtain error estimates.
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