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In this paper, we consider a discrete-time SIR epidemic model. Codimension-two bifurcations associated with 1:2, 1:3 and 1:4 strong resonances are analyzed by using a series of affine transformations and bifurcation theory. Numerical simulations are carried out to verify and illustrate these theoretical results. More precisely, two kinds of high-resolution stability phase diagrams are exhibited to describe how the system's complexity unfolds with control parameters varying.