Many aspects of human (and animal) activity, such as the frequency of contacts of an individual, the number of interaction partners, and the time between the contacts of two individuals, are characterized by heavy-tailed distributions. Heavy-tailed nature of interevent times has a large impact on dynamical processes occurring on networks and populations, such as contagion. In this presentation, we introduce a two-state modeling approach in which each node switches between a high-activity and low-activity states over time in a Markovian manner. This assumption facilitates theoretical analyses and also provides models that mimic heavy-tailed distributions of interevent times because a mixture of two (or a few) exponential distributions phenomenologically look similar to heavy-tailed distributions across a practically relevant scale. In the first part of the presentation, we present a model of interevent times in which each pair of individuals interacts at an enhanced rate if and only if both of them are in the high-activity state (i.e., they chat with each other only when both of them want to). In the second part, we analyze the susceptible-infected-susceptible/recovered (SIS/R) models when each node similarly switches between two states over time. We analytically and numerically argue that it is not the tail but the small values of interevent times that control spreading dynamics.