Global stability of an SIS epidemic model with a finite infectious period. (English) Zbl 1413.37063

Nakata, Yukihiko; Röst, Gergely

Differ. Integral Equ. 31, No. 3-4, 161-172 (2018).

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.

Reviewer: Carlo Laing (Auckland)

MSC:

37N25	Dynamical systems in biology
92D30	Epidemiology

Keywords:

epidemic model; delay-differential equation