The global asymptotical stability of pseudorabies model with age-structure.

In this paper, the dynamics of an infectious disease is studied by considering age-structured models; a stage structure and an age-structured epidemic model. The respective basic reproduction numbers for the proposed models are calculated, and the local analyses of the equilibria of the models are investigated by using the method of linearization. The global dynamics of the two models are analyzed by using the wave lemma and the Lyapunov function theory. This study establishes a solid theoretical framework and a rigorous mathematical formulation for the prevention and control of pseudorabies.