Abstract
A delayed discrete multi-group nonlinear epidemic model with vaccination and latency is derived by the application of a nonstandard finite difference scheme. It is proved that the extinction and persistence of the disease are determined by a threshold parameter in term of the basic reproduction number $ R $. More precisely, when $ R\leq 1 $ the disease goes to extinction with the globally asymptotically stable disease-free equilibrium, while the disease is persistent with the globally asymptotically stable endemic equilibrium when $ R>1 $.
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