  Empirical studies suggest that contact patterns follow heterogeneous
inter-event times, meaning that intervals of high activity are followed by
periods of inactivity. Combined with birth and death of individuals, these
temporal constraints affect the spread of infections in a non-trivial way and
are dependent on the particular contact dynamics. We propose a stochastic model
to generate temporal networks where vertices make instantaneous contacts
following heterogeneous inter-event times, and leave and enter the system at
fixed rates. We study how these temporal properties affect the prevalence of an
infection and estimate R0, the number of secondary infections, by modeling
simulated infections (SIR, SI and SIS) co-evolving with the network structure.
We find that heterogeneous contact patterns cause earlier and larger epidemics
on the SIR model in comparison to homogeneous scenarios. In case of SI and SIS,
the epidemics is faster in the early stages (up to 90% of prevalence) followed
by a slowdown in the asymptotic limit in case of heterogeneous patterns. In the
presence of birth and death, heterogeneous patterns always cause higher
prevalence in comparison to homogeneous scenarios with same average inter-event
times. Our results suggest that R0 may be underestimated if temporal
heterogeneities are not taken into account in the modeling of epidemics.
