  The epidemic threshold of a spreading process indicates the condition for the
occurrence of the wide spreading regime, thus representing a predictor of the
network vulnerability to the epidemic. Such threshold depends on the natural
history of the disease and on the pattern of contacts of the network with its
time variation. Based on the theoretical framework introduced in (Valdano et
al. PRX 2015) for a susceptible-infectious-susceptible model, we formulate here
an infection propagator approach to compute the epidemic threshold accounting
for more realistic effects regarding a varying force of infection per contact,
the presence of immunity, and a limited time resolution of the temporal
network. We apply the approach to two temporal network models and an empirical
dataset of school contacts. We find that permanent or temporary immunity do not
affect the estimation of the epidemic threshold through the infection
propagator approach. Comparisons with numerical results show the good agreement
of the analytical predictions. Aggregating the temporal network rapidly
deteriorates the predictions, except for slow diseases once the heterogeneity
of the links is preserved. Weight-topology correlations are found to be the
critical factor to be preserved to improve accuracy in the prediction.
