Global stability of the SEIR epidemic model with infectivityin both latent period and infected period

An epidemic model with infectivity and recovery in both latent and infected period is introduced. Utilizing the LaSalle invariance principle and Bendixson criterion, the basic reproduction number is found, we prove that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number is less than one. The disease-free equilibrium is unstable and the unique positive equilibrium is globally asymptotically stable when the basic reproduction number is greater than one. Numerical simulations support our conclusions.