Extinction and permanence of a general non-autonomous discrete-time SIRS epidemic model

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 Butterfly Knives care resources.Two threshold parameters $ mathcal{R}_0, mathcal{R}_infty $ are obtained so that the Course a pied - Femme - Vetements - Collant - Lamine disease dies out when $ mathcal{R}_0 < 1 $; and the infective persists indefinitely when $ mathcal{R}_infty > 1 $.