We study the dynamical properties of human communication through different channels, ie, short messages, phone calls, and emails, adopting techniques from neuronal spike train analysis in order to characterize the temporal fluctuations of successive interevent times. We first measure the so-called local variation (LV) of incoming and outgoing event sequences of users and find that these in-and out-LV values are positively correlated for short messages and uncorrelated for phone calls and emails. Second, we analyze the response-time distribution after receiving a message to focus on the input-output relationship in each of these channels. We find that the time scales and amplitudes of response differ between the three channels. To understand the effects of the response-time distribution on the correlations between the LV values, we develop a point process model whose activity rate is modulated by incoming and outgoing events. Numerical simulations of the model indicate that a quick response to incoming events and a refractory effect after outgoing events are key factors to reproduce the positive LV correlations.