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 _R0$R_0$. When _R0<1$R_0<1$, the disease-free equilibrium is globally stable. When _R0>1$R_0>1$, the disease-free equilibrium is unstable and the unique endemic equilibrium is locally stable. When _R0>1$R_0>1$ and γ=0,α=0$\gamma =0,\alpha =0$, the endemic equilibrium is globally stable in Γ⁰${\Gamma }^0$.