We study the endemic behaviour of a homogeneously mixing SIS epidemic in a population of size N with a general infectious period, Q, by introducing a novel subcritical branching process with immigration approximation. This provides a simple but useful approximation of the quasistationary distribution of the SIS epidemic for finite N and the asymptotic Gaussian limit for the endemic equilibrium as N → ∞. A surprising observation is that the quasistationary distribution of the SIS epidemic model depends on Q only through E[Q].
"Endemic behaviour of SIS epidemics with general infectious period distributions." Adv. in Appl. Probab. 46 (1) 241 - 255, March 2014. https://doi.org/10.1239/aap/1396360112