Global dynamics of an SEI model with acute and chronic stages

A model with acute and chronic stages in a population with exponentially varying size is proposed. An equivalent system is obtained, which has two equilibriums: a disease-free equilibrium and an endemic equilibrium. The stability of these two equilibriums is controlled by the basic reproduction number R0R0. When R0<1R0<1, the disease-free equilibrium is globally stable. When R0>1R0>1, the disease-free equilibrium is unstable and the unique endemic equilibrium is locally stable. When R0>1R0>1 and γ=0,α=0γ=0,α=0, the endemic equilibrium is globally stable in Γ0Γ0.