We investigate a non-autonomous discrete-time SIRS epidemic model with nonlinear incidence rate and distributed delays combined with a nonlinear recovery rate taken into account the impact of health care resources. Two threshold parameters ${\mathcal{R}}_0,{\mathcal{R}}_{\mathrm{\infty }}$ are obtained so that the disease dies out when ${\mathcal{R}}_0<1$; and the infective persists indefinitely when ${\mathcal{R}}_{\mathrm{\infty }}>1$.