Global stability of an SIS epidemic model with a finite infectious period

Abstract

Assuming a general distribution for the sojourn time in the infectious class, we consider an SIS type epidemic model formulated as a scalar integral equation. We prove that the endemic equilibrium of the model is globally asymptotically stable whenever it exists, solving the conjecture of Hethcote and van den Driessche (1995) for the case of nonfatal diseases.