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 R 0 . When R 0 < 1 , the disease-free equilibrium is globally stable. When R 0 > 1 , the disease-free equilibrium is unstable and the unique endemic equilibrium is locally stable. When R 0 > 1 and γ = 0 , α = 0 , the endemic equilibrium is globally stable in Γ 0 .