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This article deals with model- and data-based consensus control of heterogenous leader-following multi-agent systems (MASs) under an event-triggering transmission scheme. A dynamic periodic transmission protocol is developed to significantly alleviate the transmission frequency and computational burden, where the followers can interact locally with each other approaching the dynamics of the leader. Capitalizing on a discrete-time looped-functional, a model-based consensus condition for the closed-loop MASs is derived in form of linear matrix inequalities (LMIs), as well as a design method for obtaining the distributed controllers and event-triggering parameters. Upon collecting noise-corrupted state-input measurements during open-loop operation, a data-driven leader-following MAS representation is presented, and employed to solve the data-driven consensus control problem without requiring any knowledge of the agents' models. This result is then extended to the case of guaranteeing an $\mathcal{H}_{\infty}$ performance. A simulation example is finally given to corroborate the efficacy of the proposed distributed event-triggering scheme in cutting off data transmissions and the data-driven design method.