Solvable delay model for epidemic spreading: the case of Covid-19 in Italy

We present a simple but realistic model for describing the diffusion of an infectious disease on a population of individuals. The dynamics is governed by a single functional delay differential equation, which, in the case of a large population, can be solved exactly, even in the presence of a time-dependent infection rate. This delay model has a higher degree of accuracy than the so-called SIR model, commonly used in epidemiology, which, instead, is formulated in terms of a set of three ordinary differential equations. We apply our model to describe the outbreak of the new virus COVID-19 in Italy, taking into account the containment measures implemented by the government in order to mitigate the spreading of the virus and the social costs for the population.