A study of SARS-CoV-2 epidemiology in Italy: from early days to secondary effects after social distancing

Abstract

Background

The outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has led to 101,739 confirmed cases, in Italy, as of March 30th, 2020. While the analogous event in China appears to be under control at the moment, the outbreaks in western countries are still at an early stage of development. Italy, at present, is playing a major role in understanding the transmission dynamics of these new infections and evaluating the effectiveness of control measures in a western social context.

Methods

We combined a quarantined model with early-stage development data in Italy (during the period February 20th–March 30th) to predict longer-term progression (from March 30th, till June 25th, 2020 in a long-term view) with different control measures. Due to significant variations in the control strategies, which have been changing over time, and thanks to the introduction of detection technologies leading to faster confirmation of the SARS-CoV-2 infections, we made use of time-dependent contact and diagnosis rates to estimate when the effective daily reproduction ratio can fall below 1. Within the same framework, we analyze the possible secondary infection event after relaxing the isolation measures.

Outcomes and interpretation

We study two simplified scenarios compatible with the observation data and the effects of two stringent measures on the evolution of the epidemic. On one side, the contact rate must be kept as low as possible, but it is also clear that, in a modern developed country, it cannot fall under certain minimum levels and for a long time. The complementary parameter tuned is the transition rate of the symptomatic infected individuals to the quarantined class, a parameter ${\delta }_I$ I connected with the time t_I = 1/δ_I$\mathrm{ }$ needed to perform diagnostic tests. Within the conditions of the outbreak in Italy, this time must fall under 12–8 h in order to make the reproduction number less than 1 to minimize the case numbers. Moreover, we show how the same parameter plays an even more important role in mitigating the effects of a possible secondary infection event.

Keywords:

• Outbreak
• infection
• SARS-CoV-2
• secondary effects

Acknowledgements

MCT and RF thank Francesca Greselin, Department of Statistics and Quantitative Methods, University of Milano-Bicocca for her interest and help in the elaboration of the model. MCT thanks the members of the Institut de Physique Théorique, Université Paris-Saclay, for their warm hospitality during a recent visiting period. He also thanks the Physics Department of Valencia University for support and friendly hospitality. Useful remarks by Hervé Tricoire, Paris University/CNRS, and critical reading of the manuscript by Cristina Di Girolami, Le Mans University, are gratefully acknowledged.

Disclosure statement

We declare a non-competing interest.