Global stability of multi-group vaccination epidemic models with delays

Abstract In this paper, we investigate a class of multi-group vaccination epidemic models with delays. We show that the global dynamics are determined by the threshold criterion σ ( A ) . We present that when σ ( A ) 0 , there is a unique disease-free equilibrium which is globally asymptotically stable; when σ ( A ) > 0 , there exists a unique endemic equilibrium and it is globally asymptotically stable proved by a graph-theoretic approach to the method of global Lyapunov functionals.

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