The Global Stability Analysis for an SIS Model with Age and Infection Age Structures

Abstract

A general SIS model with chronological age and infection age structures is formulated. We analyze the global dynamics of the model with a constructive iteration procedure. The basic reproductive number R 0 is calculated using the next generation operator approach. R 0 plays a sharp threshold role in determining the global dynamics, i.e., the endemic steady-state is globally asymptotically stable if R 0 {\textgreater} 1, while the disease-free steady-state is globally asymptotically stable if R 0 ≤ 1. The basic reproductive number is over estimated where the infection age is ignored.