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We investigate a class of multi-group epidemic models with distributed delays. We establish that the global dynamics are completely determined by the basic reproduction number R 0 . More specifically, we prove that, if R 0 1, then the disease-free equilibrium is globally asymptotically stable; if R 0 > 1, then there exists a unique endemic equilibrium and it is globally asymptotically stable. Our proof of global stability of the endemic equilibrium utilizes a graph-theoretical approach to the method of Lyapunov functionals.

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