Stability analysis of a delayed SIS epidemiological model (Q2289479)

Summary: In this paper, we investigate global stability of the endemic steady state of the SIS epidemic model studied recently in terms of fluctuations. The epidemiological model has an exponential demographic structure, disease-related deaths and a delay corresponding to the infectious period. The disease spread is governed by a scalar delay differential equation. Our study is mainly based on the monotone dynamical systems theory. We begin by simplifying the classical framework of stability analysis for non-quasi-monotone scalar autonomous delay differential equations by using recent results on essentially strongly order-preserving semiflows. Under certain conditions, it is proved that the endemic equilibrium is globally asymptotically stable on a closed subset of the phase space C. To our knowledge, this is the first study proving the endemic steady state's global stability for this model. Numerical simulations which illustrate the results are carried out.