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

Abstract

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}_\infty $ are obtained so that the disease dies out when $ \mathcal{R}_0 < 1 $; and the infective persists indefinitely when $ \mathcal{R}_\infty > 1 $.

Keywords

• non-autonomous sirs model
• threshold parameters
• extinction
• permanence
• number of hospital beds