Abstract: An epidemic model with bilinear incidence and stage structure is established by assuming that the infection can transmit only among adult individuals and that the growth of adult individuals is density-dependent. The basic reproduction numbers of the population growth and the infection transmission are both obtained, the global stability of equilibriums is established by constructing Lyapunov functions, and the theoretical results are verified through numerical simulation. In conclusion, the dynamic behaviors of this model is completely determined by its two basic reproduction numbers, and the basic reproduction numbers of infection transmission can be depressed through decreasing the incidence or increasing the remove rate.

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