Subsequently, by exploiting a wide class of infectiousness and recovery kernels allowing reducibility (either to ordinary or delayed differential equations), we investigate in depth a low-dimensional case allowing a non-trivial full analytical treatment also of the transient dynamics connecting the different phases of the epidemic. By applying this hypothesis to a general SIR epidemic model with age-since-infection and piece-wise constant contact and recovery rates, we supply a unified treatment of this multi-phase epidemic showing how the different phases unfold over time. In this article, we provide a kinematic description of an epidemic whose time course is subdivided by mitigation interventions into a sequence of phases, on the assumption that interventions are effective enough to prevent the susceptible proportion to largely depart from 100% (or from any other relevant level).
These interventions and their relaxation have shaped the epidemic into a multi-phase form, namely an early invasion phase often followed by a lockdown phase, whose unlocking triggered a second epidemic wave, and so on. To mitigate the harmful effects of the COVID-19 pandemic, world countries have resorted – though with different timing and intensities – to a range of interventions.
