Two differential infectivity epidemic models with nonlinear incidence rate

Abstract

This paper considers two differential infectivity (DI) epidemic models with a nonlinear incidence rate and constant or varying population size. The models exhibits two equilibria, namely: a disease-free equilibrium O and a unique endemic equilibrium. If the basic reproductive number σ is below unity, O is globally stable and the disease always dies out. If σ>1, O is unstable and the sufficient conditions for global stability of endemic equilibrium are derived. Moreover, when σ>1, the local or global asymptotical stability of endemic equilibrium for DI model with constant population size in n-dimensional or two-dimensional space is obtained.