Abstract
Initially emerged in the Chinese city Wuhan and subsequently spread almost worldwide causing a pandemic, the SARS-CoV-2 virus follows reasonably well the Susceptible–Infectious–Recovered (SIR) epidemic model on contact networks in the Chinese case. In this paper, we investigate the prediction accuracy of the SIR model on networks also for Italy. Specifically, the Italian regions are a metapopulation represented by network nodes and the network links are the interactions between those regions. Then, we modify the network-based SIR model in order to take into account the different lockdown measures adopted by the Italian Government in the various phases of the spreading of the COVID-19. Our results indicate that the network-based model better predicts the daily cumulative infected individuals when time-varying lockdown protocols are incorporated in the classical SIR model.
Highlights
The outbreak of the greatest epidemic of the twenty first century caused by the SARSCoV-2 virus has stimulated researchers to understand and control the spread of the disease inside a population with the help of mathematical models developed in recent years (Hethcote 2000; Pastor-Satorras et al 2015)
We extend Network Inference-based Prediction Algorithm (NIPA) to Network Inference based Prediction Approach with LockDown (NIPA-LD) (NIPA with LockDown), that takes into account the different lockdown measures adopted in the various phases of the COVID-19 spreading in Italy by adapting the ideas of Song et al (2020)
The Veneto case (Fig. 5), another region of the North Italy highly affected by the COVID-19, on the contrary, is accurately predicted by NIPA-LD, while classical NIPA without lockdown clearly overestimates the number of infections
Summary
The outbreak of the greatest epidemic of the twenty first century caused by the SARSCoV-2 virus has stimulated researchers to understand and control the spread of the disease inside a population with the help of mathematical models developed in recent years (Hethcote 2000; Pastor-Satorras et al 2015). We briefly review the epidemic SIR model on contact networks (Youssef and Scoglio 2011; Prasse and Van Mieghem 2020b) and the prediction of the COVID-19 infection, caused by the SARS-CoV-2 virus, based on the SIR model (Prasse et al 2020). The viral state of any node i at time k is denoted by the 3 × 1 vector vi[k] = (Si[k], Ii[k], Ri[k])T , where Si[k], Ii[k], Ri[k] are the fractions of susceptible, infectious, and recovered individuals, respectively, satisfying the conservation law Si[k] + Ii[k] + Ri[k] = 1. The discrete-time SIR model (Youssef and Scoglio 2011; Prasse and Van Mieghem 2020b) defines the evolution of the viral state vi[k ] of each node i as: N
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