  We present a stochastic epidemic model to study the effect of various
preventive measures, such as uniform reduction of contacts and transmission,
vaccination, isolation, screening and contact tracing, on a disease outbreak in
a homogeneously mixing community. The model is based on an infectivity process,
which we define through stochastic contact and infectiousness processes, so
that each individual has an independent infectivity profile. In particular, we
monitor variations of the reproduction number and of the distribution of
generation times. We show that some interventions, i.e. uniform reduction and
vaccination, affect the former while leaving the latter unchanged, whereas
other interventions, i.e. isolation, screening and contact tracing, affect both
quantities. We provide a theoretical analysis of the variation of these
quantities, and we show that, in practice, the variation of the generation time
distribution can be significant and that it can cause biases in the estimation
of reproduction numbers. The framework, because of its general nature, captures
the properties of many infectious diseases, but particular emphasis is on
COVID-19, for which numerical results are provided.
