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Analysis on critical waves for a diffusive epidemic model with saturating incidence rate and infinitely distributed delay

The purpose of this paper is to obtain an existence theorem of critical waves for a diffusive Susceptible‐Infected‐Removed (SIR) epidemic model with saturating incidence rate and infinitely distributed delay. Our results completely answer an aforementioned unsolved questions by using the Schauder's fixed point theorem and constructing a perfect pair of upper‐lower solutions.