Global analysis of an SIR epidemic model with infection age and saturated incidence

• An SIR epidemic model with infection age and saturated incidence is studied.
• The basic reproduction number is obtained.
• A threshold dynamics is established.
• The main tool is the Lyapunov functional technique.

Epidemic models with infection age have been extensively studied in the recent decades. Unfortunately, the incidence rate used is the bilinear one. As incidence rate plays an important role in disease transmission, in this paper, we study an SIR epidemic model with infection age and saturated incidence. We establish a threshold dynamics by applying the fluctuation lemma and Lyapunov functional. Roughly, if the basic reproduction number is less than 11, then the disease-free equilibrium is globally asymptotically stable; while if the basic reproduction number is larger than 11, then the endemic equilibrium is globally asymptotically stable in the set with initial infectivity.