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 re-production 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 bi-furcation occurs,which shows that infectious diseases gradually evolve into endemic diseases during long-term transmission.Finally,the theoretical results are illustrated by numerical simulations.
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