Global stability of an SIS epidemic model with a finite infectious period. (Q1693269)

The authors consider an SIS epidemic model with no disease induced death rate. They denote by \(F(a)\) the probability that an infective individual is infective up to a time \(a\) which has elapsed since infection. The function \(F\) is nonincreasing and assumed to be zero past some finite maximum infectious period. \(R_0\) is defined to be the basic reproduction number and the authors prove that for \(R_0<1\) the disease free equilibrium is globally stable. The main result is a proof that for \(1<R_0\) the endemic equilibrium is globally asymptotically stable, thus solving a previously published open problem.