Global asymptotic stability of an SIS epidemic model with variable population size and a delay (Q2289519)

Summary: An SIS epidemiological model with an exponential demographic structure and a delay corresponding to the infectious period is studied. We derive sufficient conditions for the global asymptotic stability of the infected steady state. The study is mainly based on very recent results of the monotone dynamical systems theory rarely used in mathematical epidemiology. We propose an improved and practical version of an important result in the theory. The obtained results are a partial -- but important -- resolution of the open problem proposed by \textit{H. W. Hethcote} and \textit{P. van den Driessche} [J. Math. Biol. 34, No. 2, 177--194 (1995; Zbl 0836.92022)]. Numerical simulations are conducted to demonstrate our theoretical results.