  Motivated by the recent outbreak of coronavirus (COVID-19), we propose a
stochastic model of epidemic temporal growth and mitigation based on a
time-modulated Hawkes process. The model is sufficiently rich to incorporate
specific characteristics of the novel coronavirus, to capture the impact of
undetected, asymptomatic and super-diffusive individuals, and especially to
take into account time-varying counter-measures and detection efforts. Yet, it
is simple enough to allow scalable and efficient computation of the temporal
evolution of the epidemic, and exploration of what-if scenarios. Compared to
traditional compartmental models, our approach allows a more faithful
description of virus specific features, such as distributions for the time
spent in stages, which is crucial when the time-scale of control (e.g.,
mobility restrictions) is comparable to the lifetime of a single infection. We
apply the model to the first and second wave of COVID-19 in Italy, shedding
light into several effects related to mobility restrictions introduced by the
government, and to the effectiveness of contact tracing and mass testing
performed by the national health service.
