Abstract: Based on the facts that some diseases spread only among adults, and that the growth of adult individuals is density-dependent an adult epidemic model with stage structure is proposed in this paper, where it is assumed that individuals in the population consist of juveniles and adults, that the birth function of juveniles is of the Beverton-Holt type. The global stability of the model is completely investigated by constructing the appropriate Lyapunov functions and qualitative analysis, and the basic reproduction numbers of the population growth and the disease transmission, determining the dynamics of the model, is found. The obtained results suggest that, when the basic reproduction number of the population growth is not greater than unity, the population eventually dies out; when the basic reproduction number of the population growth is greater than unity, and the number of the disease transmission is less than or equal to unity, the population persists and the disease dies out; when the basic reproduction number of the disease transmission is greater than unity, the disease persists and becomes endemic as the population survives.

Key words: stage structure, epidemic model, equilibrium, global stability, basic reproduction number