  Complex networks represent the natural backbone to study epidemic processes
in populations of interacting individuals. Such a modeling framework, however,
is naturally limited to pairwise interactions, making it less suitable to
properly describe social contagion, where individuals acquire new norms or
ideas after simultaneous exposure to multiple sources of infections. Simplicial
contagion has been proposed as an alternative framework where simplices are
used to encode group interactions of any order. The presence of higher-order
interactions leads to explosive epidemic transitions and bistability which
cannot be obtained when only dyadic ties are considered. In particular,
critical mass effects can emerge even for infectivity values below the standard
pairwise epidemic threshold, where the size of the initial seed of infectious
nodes determines whether the system would eventually fall in the endemic or the
healthy state. Here we extend simplicial contagion to time-varying networks,
where pairwise and higher-order simplices can be created or destroyed over
time. By following a microscopic Markov chain approach, we find that the same
seed of infectious nodes might or might not lead to an endemic stationary
state, depending on the temporal properties of the underlying network
structure, and show that persistent temporal interactions anticipate the onset
of the endemic state in finite-size systems. We characterize this behavior on
higher-order networks with a prescribed temporal correlation between
consecutive interactions and on heterogeneous simplicial complexes, showing
that temporality again limits the effect of higher-order spreading, but in a
less pronounced way than for homogeneous structures. Our work suggests the
importance of incorporating temporality, a realistic feature of many real-world
systems, into the investigation of dynamical processes beyond pairwise
interactions.
