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Contacts between individuals serve as pathways where infections maypropagate. These contact patterns can be represented by network structures.Static structures have been the common modeling paradigm but recent resultssuggest that temporal structures play different roles to regulate the spread ofinfections or infection-like dynamics. On temporal networks a vertex is activeonly at certain moments and inactive otherwise such that a contact is notcontinuously available. In several empirical networks, the time between twoconsecutive vertex-activation events typically follows heterogeneous activity(e.g. bursts). In this chapter, we present a simple and intuitive stochasticmodel of a temporal network and investigate how epidemics co-evolves with thetemporal structures, focusing on the growth dynamics of the epidemics. Themodel assumes no underlying topological structure and is only constrained bythe time between two consecutive events of vertex activation. The mainobservation is that the speed of the infection spread is different in case ofheterogeneous and homogeneous temporal patterns but the differences depend onthe stage of the epidemics. In comparison to the homogeneous scenario, thepower law case results in a faster growth in the beginning but turns out to beslower after a certain time, taking several time steps to reach the wholenetwork.

Epidemics on a stochastic model of temporal network