Global Stability of a SIR Epidemic Model with Nonlinear Incidence Rate and Time Delay,” Nonlinear Analysis

Abstract. In this paper, an SIR epidemic model for the spread of an in-fectious disease transmitted by direct contact among humans and vectors (mosquitoes) which have an incubation time to become infectious is formu-lated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point (if it exists) is globally stable with respect to a “weak delay”. Some known results are generalized. 1. Introduction.