System (1.2) with cycling treatment, i.e., when fa = 1, fb = fab = 0, we choose parameters Λ = 10, d = 2, b = 1, q = 0.1, s = 0.3, c = 1.5, h = 0.2, initial values x(0) = 0.65, yw (0) = 0.35, ya(0) = 2.4, yb(0) = 0.5, yab(0) = 0.2, and let rw, ra, rb, rab and h vary such that R0 > 1. (i) When ra < min{rw + h, rb + h, rab}, the semitrivial equilibrium Ea is stable; (ii) when rab < min{rw + h, ra, rb + h}, the semitrivial equilibrium Eab is stable; (iii) when rw + h < min{ra, rb + h, rab}, the semitrivial equilibrium Ew,a is stable; (iv) when rb + h < min{rw + h, ra, rab}, the semitrivial equilibrium Eb,ab is stable.