In this paper, we deal with the problem of including real-world phenomena into a mathematically tractable framework for the spread of epidemics on time-varying networks. Specifically, we consider individual behavioral modifications of the node dynamics due to self-excitement mechanisms and activity reduction due to infection. We develop our model within the framework of activity driven networks, which have recently emerged as a powerful tool to study the co-evolution of a network and of a spreading processes on it. First, we present a recent model extension that allows for the inclusion of self-excitement mechanisms. Then, we extend the model by including activity reduction due to infection, and we study its effect on the network propensity to epidemic outbreaks. We determine that, depending on the relative strength of the two concurrent mechanisms (self-excitement and activity reduction due to infection), the network may favor or hinder the spread of an epidemic disease. We analytically characterize these two situations, depending on the model and network parameters. Numerical simulations are provided to support and extend our analytical findings.