Global stability and bifurcation analysis of a class of SEIRQ models

The global stability and bifurcation of a SEIRQ model of infectious disease are studied. Based on the basic reproduction number, the endemic equilibrium’s existence conditions are derived. The local stability conditions of the endemic and disease-free equilibrium are given. Moreover, the Li-Muldowney geometric technique is applied to study the global stability of endemic disease equilibrium. By the center manifold theorem and normal form theory, it is proved that the transcritical bifurcation occurs, which shows that infectious diseases gradually evolve into endemic diseases during long-term transmission. Finally, the theoretical results are illustrated by numerical simulations.