Stability analysis of a stage structured SIS model with general incidence rate
A stage structured SIS model with a general incidence rate is investigated. The population is divided into three subclasses of juvenile, mature and infectious individuals. The incidence rate \(aU(S)I\), where \(U\) is a function of \(S\), includes the bilinear mass-action form \(\beta SI\), the nonlinear form \(\beta I^p S^q (p=1)\) and the saturation form \(\beta SI/(1+\alpha S)\). By identifying a basic reproductive number \(R_0\), a global dynamics analysis is carried out. If \(R_0<1,\) the disease-free equilibrium is globally asymptotically stable and therefore the disease dies out over time. Whereas, if \(R_0>1,\) the endemic equilibrium is globally asymptotically stable and thus the disease will become a pandemic. Finally a numerical simulation is performed.
scientific article; zbMATH DE number 5716752