TWO DIFFERENTIAL INFECTIVITY EPIDEMIC MODELS WITH NONLINEAR INCIDENCE RATE

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.